A booke called the Treasure for traueilers, deuided into fiue Bookes or partes, contaynyng very necessary matters, for all sortes of Trauailers, eyther by Sea or by Lande, written by William Bourne.
¶Imprinted at London for Thomas Woodcocke, dwelling in Paules Churchyarde, at the sygne of the blacke Beare. 1578.
¶To the Right worshipfull syr William Winter Knight, Maister of the Queenes Maiesties Ordinaunce by Sea, Suruaior of her highnesse marine causes. &c. William Bourne wisheth increase of woorship vnto the state of honour and true felicitie.
WHat great commoditie and profit Right worthy & worshipfull Knight, hath alwaies redownded vnto the common weale, and gouern ours of the same, which in martial affaires and warlike discipline, haue chiefely delighted and taken great paines and care in the same, and vnto what excellent fame and renowme it hath alwayes brought and exalted vnto high dignitie, those that haue taken vpon them, for their Prince and Countries prosperitie great exploytes, rather putting them selues in daunger of their liues, then their Prince and Country shoulde bee dishonoured. Then I may say without any obiection or doubt, that your woorship is one: For I my selfe can witnesse, and of my owne knowledge, know, that no person in this Land hath such great iudgement and knowledge in martial affaires by Sea, both touching the shipping, for that purpose, and also the prouision for the same, as your woorship hath: and as for your courage, valiantnesse, and wisdome, which is not vnknowne vnto the worlde, whereas I being most symple haue written this base and rude volume, whiche I doo call a Treasure for Trauaylers, [Page] am so bolde to dedicate it vnto your worship, not for that the Booke is worthy to be preferred vnto so worthy a person, but for my bounden duetyes sake, to acknowledge my good wyll towardes your worship, for that I haue most largelye tasted of your beneuolence towards mee, being as a poore Gunner, seruing vnder your worthinesse, hoping that your woorship will take this simple woorke in good part: the which woorke is deuided into fiue Bookes, the fyrst is Geometrie perspectiue, the second Booke is appertainyng vnto Cosmographie, the thirde Booke is Geometrie general, the fourth Booke is Statick, and the fyfth and last Booke is appertayning vnto natural Philosophie, as the contentes of the matter doo appeare in the Tables of the Bookes, hoping that your worship wil take this simple thing, as a true token of my good will towardes you, although the thing it selfe be but rude & simple. And thus, I ceasse to trouble your worship any longer, at this time, beseeching the liuing God to prosper you in al your affayres, in perfect health, with all your children and familie, Amen.
The Preface to the Reader.
COnsideryng with my selfe, gentle Reader, with howe infinite paynes and labour, dyuers heretofore, men of most excellent wittes, and of passing knowledge, haue compiled their Bookes, and with what heede and circumspectnesse they haue examined and perused theyr trauayles, and with what feare and warynesse they haue published the same. and not without good cause why, for thereby they haue opened them selues, theyr name, and fame, to no small daungers and harzardes: namely to the veiwe, iudgement, and report of all menne. For which cause, nowe seeyng I haue taken vpon me at this time a harde enterprise, a burthen too heauy for mee to beare or sustaine, who haue at length shewed my selfe so hardly, as to publish this litle Treatise, I being altogether vnlearned, and hauing no helpe of any other learned persons, being of my selfe altogether destitute both of knowledge and learning.
Wherefore I desyre thee, gentle Reader, to beare with my rudenesse, and consider that it is the good wyll which I beare vnto my natyue Countrey, for to profyte the common wealth, as much as lyeth in me, although that it be not learned lyke, yet I pray thee holde me excused, beyng altogeather ignorant, lacking the capac [...]e both of knowledge and eperience (who hauyng taken vppon me) to publyshe this to the scannyng and trying of so many touchestones, and daungerous crimes, that I beyng so simple, should enterpryse so farre to take vpon me to open any Science.
[Page]But notwithstanding, I doo see, that it is so needful a matter to be knowen vnto a number of persons, that doo desyre for to haue instructions in those causes that are conteyned in this symple volume, the which booke I doo call A Treasure vnto Trauaylers, and is diuided intoo fyue Bookes.
The fyrst booke.And the fyrst booke conteyneth the particuler conclusions of the Skall Quardrant or Astrolobe, and in the like maner the particuler conclusion of the Crosse staffe &c. Also the vse of the Horizontall or flatte Sphere, whereby to drawe or take the platte of any countrey. &c.
The seconde booke.The Seconde booke dooth shewe vnto you, if that you doo knowe the Longitude and the Latitude of any place truly, then howe to knowe the distance in myles from you, or any place assygned, and by what poynt of the Compasse that it is from you.
And because that London is the most famous and the most principall place here in Englande, I haue haue named certayne principal places here in Europe, and also in Africa, and in Asia, and also in America, with some of the principallest Ilandes in the worlde, both their Longitude and Latitude, and their distance from the citye of London, and by what poynt of the Compasse that it is from London, and also how much that the Moone doth chaunge rather or later, then it doth at the citie of London, and what length their longest day is of. &c.
The thirde booke.The third booke is as touching the measuring of Superficials and sollid bodies, and howe to augment them, or diminish them, vnto what proportion or bignes you list, whether that it be the tonnage of any shyppe, or the bignesse of any kaske. &c.
The fourth booke.The fourth boke is as touching the Art Statical, as to know the waight of any shyp swimmyng on the water, and such other like. &c.
The fyfth booke.The fifth or the last boke is as touching the natural causes of sand and rockes in the Sea, and diuers such other like causes, as it doth appeare in the table of the contentes, of the [Page] Bookes. &c. The which things, in my opinion, are very necessarie for al maner of persons, and especially vnto such as be Trauaylers: which causeth me to geue the booke vnto name, A Treasure vnto Trauaylers. For what thing can there bee more better vnto a Trauayler, either by Sea or by Lande, (Golde & Siluer onely excepted then to know the distances from place to place, and to haue capacity to know the height and the lownes of any thing, & how to make a Plat or Carde for any countrey. &c. which is declared in the first booke.
And also how necessary a thing it is for a Trauailer to know vnto what quarter of the worlde any place dooth beare from him, & what the distaūce is thither,Geometric perspectiue. & what length the day is of, whē he is the [...]e: as I haue knowne a great number of persons that haue trauayled vnto sundry places, & whē they haue come home, they haue had no iudgement at all, as touching that place that they haue trauayled vnto, for that they haue not knowne vnto what quarter of the worlde the place is, that they haue beene at: neither in respect what the distance is thither. And these matters are shewed in the second booke.
And also it is not hurtfull,Cosmographia. but necessary for a Trauayler to know how to measure al manner of Superficalles, as land, pauementes, bourd, and Glasse, and solid bodies, as Tymber and Stone, and the burthen or tonnage of shyps, and the bignesse of any thing.
And furthermore it is necessary for a Trauailer in like maner,Geometric general. to haue a way to get the true waight of any thing that swimmerh on the water, & in like maner to know the waight of any thing that synketh into the water, & what it waigheth in the water, to be lifted frō the bottome vnto the superficiall part of the water, as it is declared in the fourth boke. And furthermore, it is very necessary & conuenient for Trauaylers either by Sea or by land,Staticke. to haue knowledge in the natural causes of sundry things that are to be seene in trauayling, as the cause of sands & bankes, as well in riuers as in the sea,Naturall Philosophie. and the cause of Marish ground and meddowes, & the cause of cliffes on the sides of riuers, & on the sea coast, with such other like matters, as is declared in the fifth and last Booke.
[Page]And now it is possible, that some persons wyll marueyle, that I being so simple, and not learned, shoulde take vppon me to be a medler in these causes, for that they be matters that doo appertayne vnto learned men. And it is possible, that it wil be dislyked of a nūber of people, as enuie dwelleth generally in the hartes of most men, for that is the propertie of many people, to dislyke all things that are not doone by them selues, vsing to reade Bookes to no other ende, but to fynde faultes in them.
Discouragement.And yet it is possible, that they will do nothing thē selues, which were a cause of discouragyng vnto any person that dooth write: yet notwithstanding it shal not discourage me, for that I am vtterly vnlearned, and therefore it shall not dislyke me, if any learned man dooth fynde any faulte therein: for I beyng simple and vnlearned, it is no discredite for me, eyther to be taught, or to haue the faultes shewed vnto me. For by that meanes I may refourme the faultes, either by them, or my selfe.
And furthermore, I doo not intende to make any booke to teach them that are cunning & learned: But the only cause of my writing of this booke is, to instruct or teach them that are simple and vnlearned: And therefore notwithstandyng, I shal the better lyke of it,Bookes are written to the intent to teach the vnlearned. if any learned man should write or set out any booke, as touching these causes, to refourme this. And my opinion is this, if that any Booke be set foorth vnto the common people in the world, that then it is to the ende, to teach the symplest sort of people that are not instructed in learned causes. But if that it be any high poynt in learned causes, then it is not for the common sort of people, but to be in learned mens Libraries, and therfore as it is not written by a learned man, so in lyke manner you must not looke for fyne or eloquent schole termes, but euen to take the substance of the matter rudely as it is, and more to regarde the necessarinesse of the matter, whether it may doe any good in the common wealth. &c.
[Page]And yet notwithstanding my opinion is this, that no person is to be disliked of, that doth his good wil and endeuour,No person is to be disliked that doth his good wyll to doe good. to doo good in the common wealth, howesoeuer that it prooueth. But those persons are vtterly to be dyslyked of, that doo hurt willyngly in the common wealth, as extortioners and vsurers, and conuayers of Corne and Vitayles, and other necessaries and commodityes that his countrey dooth lacke or hath neede of.
And al those persons are not to be thought well of,Persons that are to be dislyked. that doo desyre to lyue easily, abusing the good benefytes that God dooth blesse the earth with: as al licentious lyuers, as drunkardes, banketters, whoores, and whooremaysters, and such as doo vse an excesse in apparell, much aboue their degree.
And also those people are to be abhorred of al men, who doo annoy the earth, that vse quarrellyng and fyghtyng, robbyng and stealyng, caryng not howe they come by it, so that they may haue it, with which this our countrey of England floweth at this day, (the more is the pytie) for what wickednesse is there that can be deuysed, but that it is vsed here in England amongst al degrees, which must needes procure the wrath of God to lyght vppon vs. And there is as great abuse amongest the Clergie, which should be as Lanternes to geue vs lyght, to leade vs vnto vertue.Abuses of Englande. But now in these dayes they be as Lanternes to leade vs vnto vice. So that al degrees of people are geuen vnto wickednesse, although that we haue the Gospel of Iesus Christ, preached dayly vnto vs, yet wickednes doth abound, for what synne or wickednesse is there, but that it is suffered and vsed, as wichcraft and sorcery, and magical Inchantment, and coungering, which is the greatest and most abominable dishonouring of God, that may be.
For in theyr magicall Inchantment and coungeryng,Magical Inchauntment is a great dishonoring of God. doo they not obserue houres in the making of Carecters, & set vp pickturs of the Roode, and Agnus Dei, and the Doome, and a number of such other pickturs, paynted, and gilded vppon [Page] Virgin Parchment, as they cal it. And then in like maner their cirkles must be perfumed, & inbalmed with sweete odours, and they must haue a knaue priest, made by the Popes lawe, to hallowe a certayne portion, with a number of such vayne Ceremonies. And when that they haue the diuel, whom they doe serue, & doo geue him in some cases some thing for a sacrifice, and when that they doo geue the diuel a charge to tel them any question that they would knowe, then are vsed a number of superstitious wordes, as in the name of the virginitie of the Virgin Mary, and the head of Iohn Baptist, and a number of vaine Saintes more, besides a number of such detestable Ceremonies, to the great dishonouring of God. &c. And who is the cause and the procurement of these most odious and detestable matters, but a number of vaine, & wicked people, yea some of thē be of no smal wealth nor calling, that do procure these matters: For if that they haue lost any thing, thē they must repaire vnto a Coniurer, to know where that is againe. And furthermore, there are some vaine & foolish Gentlemen, which seeke to liue pleasantly and idlely, that must liue by gaming and playe, and he must haue a familiar in a Ryng,What maner of christian is he that desyreth to be familiar with the diuell. or such other like place. But what manner of Christian doo you thinke him to be, that desyreth to be familiar with the diuell? So that a great number of people that are in the world, desire to lyue idlely and pleasantly, caring not, so that they haue their pleasure here, although their soule goe vnto hel, and there to be tormented in fire & Brimstone euer world without end. Wherefore God turne the hartes of those that are the cause of wickednes, and especially here in our natiue countrey, & Realme of England, for that we haue a most gratious and vertuous Queene raigning ouer vs, and such a one as doth alwaies study for the setting foorth of the word of God and sacred Gospel of Iesus Christ,The vertuousnesse of the Queenes maiestie is our preseruation. and dooth alwayes studie for peace & trāquility. And considering the great wickednes that is vsed in England, the wrath of God would haue lighted vpon vs long before this time, but only for the grace & vertuousnesse of the Queenes miaesty, that God hath spared [Page] vs for her sake. Therefore let vs al pray vnto God for her long life and prosperity, that she may raigne long ouer vs. For surely my opinion is this, except we doo repent and turne frō our wickednesse, the wrath of God wil light vpon vs. For in these daies euery man is but for him self, the elder sort of people are geuē generally al vnto excessiue & huge couetousnes, and the yonger sort of people are geuen generally vnto pride and whooredome, and other vaine toyes,The abuses of al degrees. as idlenesse and gamyng, so that in respect fewe or none haue the feare of God before their eyes. And if any persons doo frame them selues to liue vertuously, according vnto the lawe of God, then they shalbe but derided both of the elder sort, & also of the younger: for the couetous rich persons wyl say, he is a foole, he can not make shift to liue, he hath too precise a conscience: and the youngest, vayne glorious proude fooles, will say, He is a scriptured man, he wil not haue vs to be meery nor go clenly.Couetousnes is called good husbandrie. So that in these dayes, extortiō & couetousnes is called good husbandrie: and the one of them wil commende the other, saying, He is a wise felowe, he wil liue, how fraudulētly soeuer he come by his goods. So what wickednesse soeuer that it be,Pride is clenlinesse, swearing lustinesse, drunkennesse, good fellowshyppe. Whoredome, friendship [...] a tricke of youth. the same shalbe commended by them that vse the like: as pride in these daies is called clenlinesse, and swearing lustines, saying, he is a lustie fellowe, and dronkennesse, good fellowship, and whooredome a tricke of youth or freindship, so that the one sort of people doo heape vp the goods on the earth vnsaciably, and the other sort of people, spende it away most vainely and wantonly, so that the good giftes or benefytes of God, which are the riches of the world, are abused on euery side, & not vsed as they ought to be, that is to say, to do good vpon the earth with that, for it was created for the vse of man to a good ende, to take his portion of it, & the rest to vse vnto some good purposes at his discretion, for that God doth sende it hym, vnto that ende, and not to be heaped vp, neyther to throwe it away wickedly, as a number doo: Therefore men do not rightly consider, wherefore they were borne vppon the face of the earth.
[Page] The first cause that man is borne for, is to serue God.Fyrst he is borne to serue God, for that he hath created him, and al mankinde, and hath created him a reasonable creature, and hath created al thing for his vse: as fyrst the earth, with al his mynerals, as we doo digge out of the earth, Gold, Syluer, and al other mettals, and stones, to make vs necessaryes to serue mans vse. And also the face of the earth, he hath created to bring foorth Trees to make vs Timber, and Grasse to feede Cattel, to make vs foode and meate: Corne to make vs breade, with al his other benefytes, which man receyueth from the face of the earth. The Sea with al other Ryuers, bringeth foorth Fish of innumerable sortes, to make vs foode and meate, yea the very Sea is for mans vse, too passe from Countrey vnto Countrey.
The ayre in lyke manner, wherein are multitudes of feathered foules, for mans vse, yea the very Heauens are for mans vse, as the Sunne, Moone, and Starres, are created for the vse of man. And also he hath redeemed vs from the Originall synne of Adam, by his precious bloodde sheeddyng. Wherefore wee are fyrste borne too serue God.
The seconde cause that man is borne is to serue his countrey.And secondly, wee are borne to serue our Prince, and na [...]yue Countrey, that is to saye, to defende our Territoryes, that no other ferreine Nations doo spoyle vs of our labours, or our Prince of her dignitie.
Thirdly man is borne to labour to lyueAnd thyrdly, we are borne to prouide for our houshold, and our familie and to see that they be trayned vp, to lyue in the feare of God, and to knowe theyr duetie to their magistrates, and to trayne them vp vnto some facultie, whereby they may get them a lyuing. &c.
Wherfore I would wish al those persons, that it hath pleased God to blesse vppon the face of the earth, with anye worldly reuenewes, or substance and liuing, to practise some thing, whereby they may doo some good vppon the face of the earth. And in like manner to trayne vp theyr chyldren in the nurture and feare of God. &c.
[Page]Especially the noble men and gentlemen, and they themselues not to desyre to liue pleasantly and idely,The causes of al degrees. but to practise some vertuous thing, as martiall affayres, or such other lyke causes, as their capacitie wyll serue them. For there were two causes in the beginning of all degrees of the temporaltie or layetie, wherof al Noble men and Gentlemen had their originall and beginnyng, and they are worthy to be had in honour vnto the worlds ende, for their parentage, and the much the rather, if that they doo folow the rule of their noble and worthy progenitors.
The fyrst cause was, for their noble actes and deedes in the defending of their Country against their enemies. &c.The fyrst cause. So by that meanes, for their valiantnesse against their enemies, they were extolled and aduanced vnto high dignitie, euerye person according vnto his desertes, and had lyuings to maintayne their state, and they to defend their Territories whilest the common people dyd manure and tyll the ground.
And the second cause in degrees of nobilytie and gentlemen,The second cause. was to them that made good and wholsome lawes for the good gouernement of their common weales. Therefore I would wish al noble mē and gentlemen to folow the noble race of their progenitours: and then they are the highlyer to bee esteemed. But otherwise, what a shame and discredit, if that they do rightly consider of it, is it for them to be euil members in the cōmon weale: considering howe worthyly their ancientrie dyd attaine & come vnto their callyng.Good members in a cō mon weale. Therfore I would wish euery gentleman, to practise something, that he may do good, either to defend the common weale, or els to profyt it some otherway, and not to be idle and to seeke to liue easily, whereby the common weale may be the better mayntayned, the Prince the better serued, and our Countrye the better furnished, with such persons, as are able to defende the Prince, Crowne, and dignytie, as well in their good counsel, and also in their acts and deeds. And also in my opinion, they are very necessary members in the common weale in diuers [Page] respectes, that are Trauaylers into other Countries, and they are able to profyt theyr owne Countrie in diuers respectes: for that hee is able to geue iudgement by his owne Countrie of other, whether it bee as touching the gouernement of the common weale, in the executing of their lawes of the manner of traffick, and in the vsage and nature of the people, bothe in their Cities and Townes, and in their Countrie, and what manner of commodities they haue, and of the situation of their Townes, and in their fortifycation, and also of what strength and force other Princes and states are of, and of the order and manner of vsyng them selues in martial affayres in the warres, and what their Artillerie is, and how they are weaponed and armed, and furnished in euery respect, which is very necessarie to bee knowne vnto the nobilitie, for that they may prouide them selues, and their Countrie for their better safetie, and also they shall knowe what thing shall annoy their enemies most.
Then it is a playne case, that Trauailers into other Countreies doo much profyte the common weale. For suppose this, that if we, or any Country dyd liue in that order, that we did trauaile into no place or Countrie, neither no nation vnto vs, then in processe of time wee should beecome barbarous and sauage. Therfore the Trauaylers are much to bee commended in diuers respectes. Wherefore I wyll shewe you my opinion, what manner of people are meetest to bee trauaylers. For a number of people haue trauayled, and when they haue come home, they haue had no iudgement of their trauayle, but haue beene vtterly ignoraunt of suche thinges as were most meetest of a Trauailer to be noted, and partlye some of them were not capable in those causes,What maner of persons are the meetest to be Trauailers. and some of them many times, their heades are occupied with other vaine and foolish causes. &c. as this fyrst: those people that are able to benefyt their country by their trauaile, when they are come home, ought not to bee to young: for commonlye a young man his head is occupyed with euery vaine and light cause, [Page] as with banketting, and play, and game, & daunsing, and dalying with women, and gazing vpon vaine toyes. &c. So that his head is occupyed with no other thing, but all pleasaunt matters.
Therefore he that is sent to be a Trauailer,What a Trauailer should consider of. to the ende to profyt his Country, ought to be a man that hath a stayed & a modest head, and such a one as is capable, and hath a good witte with him, and learned. And if hee bee seene in the Mathematical Science, it is all the better: For then hee shall the sooner conceaue any matter. And also he ought not to be either to young nor to olde, but betweene the age of .40. and 56. or 57. yeares. &c. And these bee the principallest poyntes, that a trauailer should consider of. First, to consider what maner of Nation he is entred into, whether they bee politicke or wise, or Ciuill people, or whether they be a rude or barbarous nation: and so in his trauailing to frame his vsage accordingly as neare as he can, that the people may like well of him▪ for in so doing he should vnderstande the better of the state and commoditie of the Country, Citie, Towne or place: and when that you do come into any Citie or Towne, view of what maner of grounde it standeth vpon, and what it may be or is subiect vnto, and in like maner how it is fortifyed and prouided, and how it is maintayned, and whether it standeth vpon any hauen or riuer, that hath vent vnto the Sea, or any water, that hath no vent or passage vnto the Sea, but thorow or by some other Citie or Towne, before it commeth vnto the Sea. And also vnder whom it is, and howe it is gouerned, and what theyr Lawes and Ordinaunces bee: And what notable Monuments of buildyngs there be: and any other rare and notable thing that is not common: And also to learne what nation, Country, Citie or Towne that may most annoy them, and also what Countrye, Citie or Towne dooth most pleasure them, and what trade or Marchaundize they are principallest maintayned by, and what commodities are [Page] most plentiest, and what commodities or things necessariest, are most scantest, and what the nature of the soyle or ground is thereabouts, that is to say, what the ground is most aptest to bring foorth, or most vnapt, as touching Corne, Trees, and such other lyke, whatsoeuer it bee. And al [...]o what maner of Money and coyne is vsed, both in Siluer and Golde, and other base Money in Copper, if they haue any. And also what the people hath most pleasure in, and what they do most abhorre or hate, and whether the Countrye bee a playne and champion Countrie, or Hils and Mountaynes, or lowe marsh or marishe grounde, and whether it be full of Riuers or not, and also how the Princes or the other Gouernours doo leuey their Souldiours in the time of their warres, & how they doo arme them, and weapon them, and furnish them in euery respect, and what duties or customes, or tolles, or suche lyke charges are payd, whether it be of them selues, or vpon strangers, or any other kinde of goodes or marchandize, and what thing it is they make most store of, that they wyll not haue passe out of their Countries, with all such other lykenes, that for breuitie I doo omit.
And now such persons as haue noted these causes at their returne home, are able to profyt much the common weale in diuers respects, and are persons of great valure vnto theyr Countrye, for that they are able to profyt the state, and the common weale of their Countrye in diuers respectes. For all those persons are of great valure and price, and are as special Iewels vnto their Country,What persons are of valure in the common weale. and in the common weale, that are politick, cunning, and valyaunt in mar [...]hall affayres: for thereby their Countrye is defended and preserued from the forrayne enemies: For looke what Country is riche and welthye, then other Princes are desyrous therof, for to haue the spoyles, and the benifyts of it: wherfore by polycie and manlynesse they must be defended. Therefore men expert in marshall affayres are very necessary in a common wealth.
And furthermore, all those persons, that are wise and sober, [Page] and discreet in the good gouernemēt of the common weale, such as doo maintayne vertue and suppresse vice, are persons of great valure to their Countrie, and also those persons are able by their wisdome and knowledge to benefyt or profyte their Countrie, whether it be in the teaching of good artes and Sciences, or by any other meanes, so that the common weale be the better mayntayned, are persons of great valure, and are as Iewels vnto their country, and their country is beholding vnto them. But contrariwise, all those persons that are not able to profyt the common weale in any respect, and also desyre to liue pleasauntly and wantonly, and haue great liuynges and riches, and doo no good therewith: all those persons are more beholding vnto their Countrie, then their Countrye is vnto them. But if they haue great store of ryches, and doo couet to heape more, caryng not how they doo come by it, so they may haue it: such persons are the destruction, and are as Caterpillers to the common weale of their Countrye, for that they doo annoy and hurt the prosperity and the state of their Country, for that they catch and heape vp into their custodie more then dooth suffice themselues, by great quantities, whereas thowsandes doo lacke to serue their turnes, that are better members in the Common weale then they are. And all such persons, the Common weale hath a good turne when they are deliuered of such a one: For by that meanes is dispearsed that heape of store vnto a number of persons handes besydes that whiche he would haue heaped vp more, if that hee had continued longer. So that some of the richest sort of people are not the best members in the common weale, but the worste: and yet it behoueth some persons to bee rich, and by their riches the common weale is the better maintained, as thus.
The Prince of any Countrye being godlye and vertuous, the Common Weale dooth the better flourishe, and is continually kept the safer from the forrayne enemyes: [Page] and the Noble men, and Gentlemen, that are vertuous, and giuen to practise the good gouernment, & the preseruement of them selues, and the state of their Country. So then their riches doo good, and also if the Marchaunte bee rich, so that he doo not hurt his owne Country, but winneth his ryches out of other forraine Countries, or any other good and vertuous Subiect, by his riches he may doo good, if hee doo vse that hee hath to the furtheraunce of the common weale: So that it is necessarye that there should bee rich persons in the common weale, for a number of causes, so that those rich persons be vertuously bent, but otherwise they may do hurt. And thus gentle Reader, I doo make an ende, desyring you that you wyll take this simple Booke in good part, and if there be any faults committed by me, either by ignoraunce or negligence, I pray you let mee gentlye vnderstand thereof, for man cannot bee so precise, but that hee may erre. And thus I betake you vnto almightie God, the Creator of all thinges.
¶A briefe note, taken out of M. Dees Mathematical Preface that goeth before Euclides Elementes nowe extant in our Inglish tongue, as touching what the Mathematical Sciences are, that is to say, all those Artes that order number, measure, or wayght, and tyme, without the which, in respect, we can doo nothing. For what can bee doone in any respect, but we must vse number, which is Arithmeticke? or what can be doone, but we must vse measure or wayght, which is Geometrie? or what can there be doone, but that we must vse tyme, which dooth appertayne vnto Astronomie? for by number we knowe howe many or fewe there are: and by measure we knowe whether it be ynches, feete, yardes, scores, myles, leagues, poundes, ounces, galloes, quartes, or tunnes: and by tyme, we knowe whether it be minutes, howres, dayes, weekes, monethes, yeeres. &c. Whereof two are pryncipal, Arithmeticke and Geometrie, wherof al these compounded scientes are sprong of these two Simples.
☞Thinges done by hand Geometricall.
1 Mecometrie. Is the measuring of the length anything whatsoeuer.
2 Embadometrie. Is the measuring the contentes of all flat things, as Land, Boorde, Glasse.
3 Stereometrie. Is the measuring of all solid bodies, as Timber, Stone, Kaske, & such lyke.
☞Thinges measured that haue distaunce from you.
4 Apomecometrie. Is how farre any thing is frō you, whether it be on lande or on water.
5 Hipsomettie. Is how high or deepe any thing seene, is from the leuell, whether it bee on [Page] Lande or water. &c.
6 Platometrie. How broade any thing is. &c.
7 Geodesie. Is the suruaying or measuring of landes, woods, or water, hauing distaunce from you by instrument or otherwise.
8 Geographie. Is the description of Countries, or Kingdomes.
9 Cherographie or Typographie. Is the description of a part of a Country or kingdome. &c.
10 Hydrographie. Is the discription of the Seas, with the Ilandes and rockes, and dangers and lynes, and Courses. &c.
11 Stratarithmetrie. Is the view or measuring of a battel of men, to know the number of them not comming neare them. &c.
12 Perspectiue. Demonstrateth the manner and propertie of all radiations directe, broken, and reflected.
13 Astronomie. Is the mouing of the lightes and Planets. &c.
14 Musike. Teacheth the diuersyty of sounds. &c.
15 Cosmographie. Is the descriptiō of the whole earth, and the Paralell of the heauens answering thereunto &c.
16 Astrologie. Is to geue iudgment by ye signes, lights and planets. &c.
17 Statick. Is an art that doth order and deale with heuines and lightnesse. &c.
18 Anthropographie. Is of thinges appertaynyng to the body of man, to shew them. &c.
19 Trochilike. Doth appertaine vnto the turning of wheels, this art is necessary for Clockmakers, [Page] & Crane makers, and Mylles, & al other sciences, that doo deale with wheeles.
20 Helicosophie. Is an art to drawe hylical or Spheral or winding lines, and is very necessary for Skrewe makers, & diuers other things.
21 Pneumatithmie. This art is necessary for all them that doo make Pumpes or great Bellows, for yt it teacheth al those thinges that goe by wynde and water. &c.
22 Menadrie. Is an art, that teacheth the making of al ingenes, as things to pull to, or thrust fro, or lyfting vp, or pressing downe. &c.
23 Hypogeiodie. Is that arte that dooth appertayne vnto myners in the grounde. &c.
24 Hydrogogie. Is that art to bring water vnto any place assigned. &c.
25 Horometrie, or Horologiographie. Is the making of Dyals of al sortes. &c.
26 Zographie. Is the art of a cunning Painter. &c.
27 Althalmasat. The art of Grauing.
28 Archetectur. Is a cunning Mason or Carpenter. &c.
29 Nauigation. Is sayling on the Sea. &c.
30 Thauruaturaike. Is that which dooth make strange workes, as those that made the brasen head seeme to speake, the brasen Serpēt to hisse, the Doue of wood to flye, the Eagle made by art to flye. &c.
31 Archemastrie. This art teacheth to bryng to actual experience sensible al worthy conclusions, by al the artes Mathematical, &c.
To the Reader of the first booke,
¶The fyrst booke of the treasure for trauellers, contayning the particuler conclusion of the Scall for to know the hieght of any Tower, Steeple, or Hill, or Walle, and the dystance vnto them, and the particuler conclusions of the Crosse staffe, and to know the thinges before rehersed after the playnest order of teachyng, & also there is the conclusion of the horizontal or flat Sphere how to take the plat of any countrey, after the playnest order, with such other lyke, very necessary for all sortes of trauelers eyther by sea or by Land, written by Willyam Bourne.
To the Reader of the first parte.
GEntle Reader, there is conteyned in this first booke, the particular conclusions of the Skal, as touching the knowing o [...] heigthes, bothe by right shadowe, and contrary shadowe: and also howe to knowe any distance by the Skalle. And although that M. Thomas Dygges hath set out a booke called Pantometria, whiche is extant in print, as touching the conclusions of the Skall, whiche is very learnedly done. Yet notwithstanding I doo not thinke it hurtful to shewe it particularly and plainely, whereby they may doo it in most causes, without Arithmetike. For the Skall being put but into .12. partes, it may be counted by the head, without Arithmetike: but if the Skal be put into many partes, then it must of force require the ayde of Arithmetike. And also there is the particular [Page] conclusions of the Crosse staffe, as to take the widenesse betweene any two markes, and the length of any wall, and the distance vnto any place, with other necessarye matters to be donne with the playne Crosse staffe. &c. And also there is the Conclusion of the horizontal or flat Sphere, howe to take the plat of any Countrey, after the playnest order of teaching, that is to saye, by the poynt, and partes of poyntes of the Compasse: For it is al one matter, whether that the Instrument be diuided into degrees, or partes of poyntes: and that same may be done by playne lynes of opposition, without any Instrumēt or circle, which I doo omyt at this tyme to speake of. And although gentle readers, that it seemeth not vnto you, to be learned like done, yet notwithstanding it is possible, that there is some thing that is not common in those books that are extant, that maye doo you pleasure. For the learned sortes of bookes (it may be) are not most necessary to be common, and yet it woulde doo well, that the common sorte of people shoulde haue some instructions.
[Page 2] FOr that it is sufficiently declared in diuers bookes nowe extant in our Englishe tongue, wherefore I doo thinke it superfluous for to shewe what a Pricke is, or what a lyne is, or what a Plat or Superficial is, or what Angles be, and what a sholded bodie is, as it is sufficiently declared in all these bookes: as in Euclides Elementes, and in M. Thomas Dygges booke called Pantometay, and also in M. Leonarde Dygges booke called Tectonicon. &c.A Circle. A Centre. A Circumference. A Diametre A Circle is that whiche is drawen rounde with a payre of Compasses, a Centre is the myddle pricke, Circumference is the compasse, Diameter is the breadth of a Circle. &c.
And furthermore, for that in this first part there is the conclusions of the Scall, and the Crosse staffe, shewyng by them howe for to knowe the distance vnto any place assigned: Therefore it is very necessarie for to knowe the partes of measure, as it is not vnknowen vnto all men, what a foote is, and that .12. ynches maketh a foote, so .3. foote is a yarde, and .5.A Foote. A Yarde. A pase Geometrical. foote is a pase Geometricall: but some persons haue been of that opinion, that .3. foote is a pase, which is a yarde, but it is but a simple steppe,A simple stop of yarde. and fewe men are able to endure to pase a yarde any long tyme togeather: but any person may endure to steppe two foote and a halfe, all a day long togeather. Therefore a pase Geometrical, is two reasonable steppes, and that is fiue foote: and so any man may endure all a day together,A rase is two stepp [...]s. [Page] and twelue pases maketh a score,12. pases is a score, that is, 20. yardes. A myle is a 1000. pases, that is .5000. foote, or 1666. yardes, and 3. A Rod is .16. foote .2. of land measure, and 18. foote is a Rod of woode measure .6. foote is a fadome, and .833 fadome is a myle. and that is twentye yardes, and that maketh .60. foote: and a myle conteyneth .1000. Geometrical pases, and that is .5000. foote, and that maketh 1666. yardes .⅔. and that is .2. foote, and that conteyneth 83. score. ⅓. and that is .20. foote. &c. and a Rod is .16. foote and a halfe, of lande measure, and .18. foote is a Rod of woode measure, according to our Englishe account: and .303. Rodde and .1/33. that is halfe a foote, is a myle of lande measure, and .277. Rodde, and .7/9. that is .14. foote of woode measure, is a myle, and a fadome is .6. foote, and that is .2. yardes: and .10. fadome is a score, and a myle conteyneth .833. fadome, and .⅓. part, that is 2. foote. &c.
And thus muche haue I saide as touching our Englishe account, as concernyng the measuryng of the length, or the distances vnto any place assigned. &c.
¶The first Chapter of the first booke conteynyng the making of the Quadrant with the Skall, whereby you may knowe the height or lowenesse of any thynge. &c.
NOwe begynneth the first part of this booke, called A Treasure for Trauaylers, shewing the conclusions of the Skall, whereby you may knowe the height of any Tower, Steeple, or Wall, or the height of a Hyll, and the distances vnto any marke assigned by the Conclusions of the Skall. And also in this first part there is the Conclusions of the Crosse staffe: shewyng howe to knowe the length of the Corten of a wall, and the distance thereof, or any Towne more playner then is shewed in M. Leonarde Dygges booke called Tectonicon. And also there is the making and the vse of an Instrument, that may be called an Horizontal Sphere, to drawe the plat of any Countrey set out vpon the face of the whole earth: and howe to knowe howe to place the longitude and the latitude of any Towne, with other necessarie thinges. &c. very necessarie and profitable for al trauailers and seruit [...]urs, either by sea, or by lande, as Gonners and Captaines, and leaders of men.
And nowe shall followe the making of a Quadrant,The ma [...]ng of the Quadrant, with the Skal with the Skal diuided but into .xii-partes, although some wyl haue it diuided into .60. partes, and some into 48. partes, and some into moe partes, and some into lesse partes, according vnto the fantasie of sundry Authours. But I doo thinke it b [...] to be diuided into .12. partes: for that diuers people are desirous to knowe the vse of the Skall, that are not seene in Arithmetike, and yet the vse of the Skal is very necessary and profitable for them to knowe, and the Skal diuided but into .12. partes, any reasonable man may haue the vse thereof. But if it be diuided [Page] into .48. or .60. partes, then it dooth require Arithmetike, which is not in many persons: Wherfore I doo thinke the Skall that is diuided into .12. partes, to be most necessary and profitable for al sortes of people. And although that M. Thomas Dygges in his booke called Pantometria, hath written thereof generally, yet I doo thinke it very necessarie, to write of it particularly. &c
And nowe for the marking of the Quadrant, doo this: first take a peece of wel seasoned wood, that is bard, and fine grayned, as Boxe, or such other like, or els you may make it in metal, as in Brasse, or Latten. &c. and then being wel playned or polished, and the larger, the better.
For in a small Instrument you may committe an erroure, soner then in a large: then be sure that one of the corners haue a square or ryght angle, and then there set the one of the feete of your compases, and with the other foote of the compases make a quarter of a circle, for that it is called a Quadrant, it is the .4. parte of a Circle, and no .4. cornered thing. And that beeing done, then deuide the edge thereof into .9. equal parts: and euery one of those partes deuide into .10. equal partes: so that then there wyl be in al .90. equal partes: and euery one of those diuisions or parts, are called a degre. & a degree is no other thing but a whole circle diuided into .360. equall partes, and then at euery .10. or .5. degrees you may make them, as thus .5. and .10. and .15. and .20. or els as this .10.The vse of the degrees. and .20.30. and so forth vnto .90. for that the quadrants is diuided into ·90. equall partes, and the vse of these diuisions or parts called degrees, is to know the heyght of the sunne, or any starre aboue the horizon, whereby they may know the altitude or height of the pole of the world aboue the horizon, as I doe more at large declare in my booke that is extant in prynt called The Regiment for the sea. &c. and also the degrees are very necessary for gunners, to know what ground that any peece of exdenāce doth cast or cōuey the shot at the mont of euery degre, as I do more at large declare in my booke called the Art of shooting in great ordenance. &c. And now furthermore, for the making of the Scal vpon the Quadrant, do thys, at the ryght angle or corner [Page 4] make a square in such sort, that the other corner ryght against it doth stand iust vpon .45. degrees, & loke that it be a ryght or square angule in lyke maner, and so from that to the two sides there wyl be .4. square or ryght angule, and then deuide two of those sydes, that is to say, the two sides that is from the corner where that the Plummet shal hang towards the partes of the degrees, diuide eche of them into .12. equal partes, and then marke .12. at .45. degrees, and then make two sightes vpon one of the sides of the Quadrant: and those diuisions, or partes of that, or next vnto the two sightes, are the partes of right shadowe, and then the other diuisions are the partes of contrary shadowe. And here dooth folowe the demonstration of the Quadrant, with the Seal. &c.
The vse of the Skal is very necessary and profitable in diuers respectes, as to knowe the height of Hylles and Steeples,The vse of the Skal. or Townes, or Walles, and by the laying of the Skal flatte, to knowe the distance vnto any thing, as vnto Shyppes ridyng at the ancore in the sea, or in any hauen, or harborow. &c. But in my [Page] opinion, the Seal of the backside of the Astrolobe, is the better: for with the Quadrant you can not serue the sights with your eye, and see howe the Plummet dooth hang, and all at once: but you may set the Alydeday or Rule with the two sightes, vpon what part you list, and so stand fast, vntyl you haue obserued it. &c.
[Page] But you muste be sure that your Astrolobe hang vpryght as you may proue it by a perpendiculer or plūme lyne from the turret of your Astrolobe .E. downe by the lyne to F. then if your Plumme lyne be iust with the lyne. E. and .F. then it hangeth vpryght: if that it doe not agree, then it hangeth not vpryght.
¶The second Chapter is of vpryght shadowe, that is to say, to know the heyghte of al thyngs taken within the length of the thyng.
NOwe followe the conclusions of the Scall, both of the Quadrant, and also of the Astrolobe, but the Astrolobe is the better. And first, for line of leuel called of Gonners the poynt blanke, turne the other side C. right with the lyne of leuel G. and H. then put your thombe thorow the ridge D. then hold vp your hande that you may looke thorow both the sight A. and B. thē al things that you se thorow is leuel with the sight of your eye, neyther higher nor lower. Now if that you wyl know, the height of any Towne or vpright wal, doe thus turne the Athelida C. to the corner of the Scall, and set it vpon the parte 12.What to obserue in taking of height with the Skall. then goe forwards or backwards, tyll that you doe see the toppe of the wall thorow the two sightes A. and B. then measure how many foote it is from the middle of your foote to the hard wall, so many foote the wall is high. and as much as it is from your eye, downe to your feete, and that you must adde to in all your heightes, & looke that the grounde be leuell, and be sure that you stand vpright, and winke with the one eye. Now furthermore beinge an vpright wall, set the Athelida C. vpon the part one, of vpright shadow:Vpright shadow at on station. then doing as before is rehearsed, than mete the grounde to the wal .12 times the measure shalbe the height of the wal, then the Athelida vpon the part 2. then sixe times the measure to the wall, shall bee the height of the wall the Athelida vpon the part 3. then 4. tymes the measure shall be the height of the wall. then vpon the parte 4. then 3. times the height shall be the measure of the height of the [Page] wal, the Athelida vpō the part 6. thē mete to the wal double, the mesure shalbe the height of the wall. Alwayes prouided, that you ad to the measure the length of your body, from your eye to your feet, now shall you haue a way to get the height of a steeple or wall that hath a ditch: but then you must haue two standings: and still for vpright shadow, set your Athelida vpon the part 12. then looking thorow the sights, holding it vpon your thombe as afore is rehearsed, then with the midle of your foote set a mark, then turne the Athelida to the part 6. of vpright shadow, and there make an other marke, then mete how many feete it is, betwixte the 2. standings, then double that measure shal be the height of the steeple or wall, the first standing vpō the part 12. then turne the Athelida to the part 8. of right shadow, then measure the grounde 3. times: that distaunce shall be the height of the steeple or wal, the first vpon the part 12. and the second vpon the part 9. then 4. times the measure shall bee the height of the steeple, the first standing vpon the parte 12. the next on the part 10. then the measure betweene the two stā dings shall be the 6. part of the height, the first standing on the part 12. the next on the part 11. the mesure betweene the standings shall be the 12. part of the height. yet furthermore for vpright shadow, first set the Athelida vpon the parte 9. of right shadowe, then doing as afore is sayde, set a marke with the midle of your feete: then turne the Athelida to the parte 3. of right shadow, and there set a mark, then measure those two standings, and then double that mesure that shall be the height of the Steeple or wall, or the first standing vpō the part 8. & the next vpō the part 4. thē doyng as before is said, 3. times the mesure shalbe the height of the steeple or wal, and the first standing vpon the part 10. and the next vpon the part 6. of vpright shadow, then doyng as afore is sayde measuring the distances 3. times, that measure shalbe the height of the steeple or wal. Or the first standing vpon the part 7. & the next vpon the part 6. of vpright shadow, then doyng as before is rehearsed mesuring the distaunce 12. times, that measure shalbe the height of the wal. Or the first stāding vpon the part 7. & the next vpon the part 5. thē measure the distaunce 6. times: that measure shall be the height of the wall. Thus much haue I saide for vpright shadow, & vpright [Page 6] shadow is this, all things whose height is taken within the compasse of the length of any thinge mesured, as for ensample this, by the figure folowing.
By a Towre or Steeple being 65.Ensample. foot high of all those questions of vpright shadow afore rehearsed the first was the Athelida vpon the part 12. and to the wall the measure of the grounde was 60. foot, & thē from mine eye to the ground was 5. foot: so that 60. foot and 5. foot, make, 65. foote. So I conclude the whole height of the Towre to be 65. foote. The next is the Athelida vpon the part 1. and the ground to the wall 5. foote, so 12. times 5. is 60. then the next was vpon the part 2. and the measure 10 foote, and sixe times 10 is 60. the next vpon the part 3. and the measure to the wall 15. foote, then 4 times 15. is 60. the next was vpon the part 4. and to the wall 20. foote, and three times 20. is 60. the last vpon the part 6. and to the wall 30. foote, and 2. times 30. is 60.
[Page] Ensamples of two fashions or standinges.Now all the other haue two stations or standinges, therefore you doe not measure to the wall, but the measure betweene the 2. standyngs, the first standing vpon the part 12. the next vpon the parte 6 and the measure betweene the 2. standyngs is 30. foote, then 2. times 30. is 60. then betweene the parte 12. and the parte 8. was 20. foote, and 3. times 20. is 60. then betweene the parte 12. and the parte 9. was 15. foote. and 4. times 15. is 60. then between the parte 12. and the parte 10. was 10. foote. and 6. times 10. is 60. then betweene the part 12. and the parte 11. was 5. foote. and 12. times .5. is 60. And now furthermore where you coulde not goe so farre back as the part 12. the one standing vpon the part 9. and the other vpon the part 3. the measure of grounde was 30. foote. then 2. times 30. is 60. the one standing vpon the parte 8. and the other vpō the part 4. the measure was 20. foote. and 3 times 20. is 60, then the one vpon the part 10. and the next vpon the parte 6. the measure was 20 foote. and 3. times 20. is 60. then the firste standyng vpon the part 7. and the next vpon the part 6. the ground betweene the 2. standings was 5. foote. and 12. times 5. is 60. the one standing vpon the part 7. and the other vpon the parte 5. the measure betweene the 2. standinges was 10. foote. then 6. times 10. is 60 So you may se that euery way the whole height to be 65. foote. adding vnto it as before is sayde the length of your body being 5. foote, thus much haue I sayd of vpright shadow, and now followeth contrary shadow.
The 3. Chapter sheweth howe to knowe the height of any thing with the Scall by contrary shadow (that is to say) without the length of any thing so taken.
NOw foloweth contrary shadow, & contrary shadow is this, that when soeuer any height is taken without the height or length of any thing, as foloweth: first, doing as before is sayd, in al points, putting his thumb thorow the ring of the Astrolobe, set the Athelida vnto the part 12. then with the midle of your foot, make a mark, thē turne the Athelida to the part 6. of cōtrary shadow: thē go bakwards til you may se the top of the steple or towre thorow both [Page] the sights of your Astrolobe, being sure that it is hanging plūbe vpright. Thē at the middle of your foot there make another mark, then measure how many foote there is between your .2. stādings, so many foote is the height of the Steeple or Towre. Thē in lyke manner at the first standing, the Athelida vppon the part .6. then turne the Athelida to the part .4. of cōtrarie shadow. Thē meeting the grounde betweene the .2. standings, it shalbe the height of the Steeple or Towre. Then in lyke manner the Athelida at the one standing vpon the part .4. and the other vpon the part .3. and then measuring the grounde betweene the .2. standinges, shalbe the height of the Steeple or Towre, then at the one standing the Athelida at the part .3. and the other standing the Athelida vpon the part .2. then measuring the grounde betweene the .2. standings, halfe that measure shalbe the height of the Towre, Steeple, or Wall.
Furthermore the one standing the Athelida on the part .2. & the next standing, the Althelida vpō the part one: then measure howe many pases or foote was between the two stādings: the .6. part of that measure shalbe the height of the steple or towre, but you must be sure that the ground be plaine & leuel, or else it may erre. Now for your better ensample, by this fygure here vnder made, by a
Steeple that is from the toppe downe to the grounde .120.Ensample o [...] contrary shadow. foote hyth from the foote to the toppe of the shafte or speare, and nowe by the height is knowne the distaunce, as you shall knowe by all the questions before rehearsed. First the Athelida at the first standing was on the part .12. and at the nexte standing, at the part .6. [Page] and the measure betweene the .2. standings was .120. foote. Now I doo conclude that the heyght of the sayde Steeple is .120. foote from the grounde to the toppe, and the distaunce to the sayde Steeple is .240. foote, that is .48. pases: & the height of the Steeple .24. pase. Then frō the part .6. to the part .4. in like maner once the height of the Steeple, and the distaunce to the Steeple, is .3. tymes the height, that is .360. foote to the Steeple, that is .72. pase: then from the part .4. to the part .3. is once the height of the Steeple: and the distance to the Steeple is .4. tymes the height, that is .480. foote to the Steeple, that is .96. pase. Then from the part .3. to the part .2. is twice the height of the Steeple, and the distaunce to the Steeple is .720. foote, that is in pase .144. pase. Then from the part .2. to the parte .1. the distance of grounde is betweene the .2. standings .720. foote, that is .6. tymes the height of the Steeple: and the whole distance to the Steeple is .12. times the whole height of the wall, that is .1440. foote. The sūme of the whole distaunce from the part one, to the Steeple, and that same in pase is .288. which maketh .24. score: and at the parte .2. the distaunce of scores is .12. then at the part .3. it is to the Steeple .8. score, at the part .4. it is to the Steeple .6. score: at the part .6. it is to the Steeple .4. score, then at the part .12. it is the iust height of the Steeple, being .120. foote, that is .2. score, adding as before is sayd, so much to the height of the Steeple, as from your eye to your feete, which you shall doo in this sort. And specially if the distaunce be farre from the Steeple at euery station, if you wyll worke exactly, when you haue taken the height, [...]urne your Astrolobe (the Athelida standing as before) not remouing your foote frō that standing, then looking thorowe the sightes, turning your face directly from the Steeple, then whereas your eye dooth rest, there set a marke: then there is no doubtes but that you shall take the true height and distaunce, dooyng this at euery standyng, your grounde beyng plaine and leuell.
¶ The fourth Chapter sheweth howe for to take the parte of any height as the length of a wyndow or such lyke.
NOw furthermore to take the part of a height, you may in like manner, doyng as afore is rehearsed in all poyntes, and also you maye with the Scal of the Astrolobe take the length of a pinacle or a windowe or windowes, the one aboue the other, you may take the measure between them as thus. Set your Athelida to the part .12. then goe backewardes or forwardes, tyll that your sightes doo agree with that thing that you woulde take measure of, letting your Athelida stande still at the part .12. Then in lyke maner take the other ende of that thyng whose length you doo meane to take, then take your sight agreeing wyth the other ende of the pinacle, then measure the grounde betweene the .2. standings: that shalbe the length of the pinacle, windowe, or crosse, as by this figure it may more plainely appeare, as for ensample this.
[Page] First I did set the Athelida vppon the part .12. and doyng as before is sayd: and tooke the vpperside of the windowe, and at my foote made a marke,Ens [...]mple in the taking of the poynt of a height. then I went nearer the Steeple, and tooke the lower ende of the windowe as you may see at the letter. A. then I measured the ground betweene the .2. standings, and founde it 20. foote, so I doo conclude the window to be .20. foote long. Thē in lyke manner I tooke the Pinacle, dooyng as afore is rehearsed, first at the toppe, and then at the foote, the Athelida standing still on the part .12. and founde the measure betweene the .2. standings .15. foote, the iust length of the pinacle, as by the .2. lynes B ▪ it doth appeare, then betweene the .2. crosses, dooyng as before is sayde, and founde the distaunce betweene the .2. standings .10. foote; the length betweene the .2. standings as by the .2. lynes C, it dooth appeare, and so doo by all other small partes.
¶ The fifth Chapter sh [...]weth howe to knowe the distance of many things that is from you, and also whether any other towre be higher or lower then the towre that you be vpon.
YEt furthermore by the Scal of the Astrolobe, you may know when you be on the toppe of a Towre, or toppe of a Castle, howe farre many thinges bee from you, and in lyke manner the height of an other Towre that shall stand neare vnto you. And also howe much that one Towre is higher then another, with diuers profitable thinges more, as this: First if you know not the height of the Towre that you be on, then take a lyne, hanging a Plomet of leade or some other suche thyng, then let it downe ouer the wall to the ground. Thē by the length of the lyne you shal know the height of the Towre or wall that you be vpon, then when you know the true height of the wall or Towre, then take your Astrolobe, hanging it vpō your thombe by the ring, as afore is declared, then looking thorowe the sightes in order, as afore is rehearsed. So shall you fynde the distaunce, as this: first, at the part .12.How to know distance by the shadowe. looke what the height of the wall is from the ground, so farre it is to the marke that you do see thorowe the sightes of the [Page 9] Athelida, turning your astrolobe that the sightes may goe downewardes, then the Athelida on the parte .6. of contrary shadowe, the thing that you shall see thorowe the syghtes shalbe .2. times the height of the Towre or wall: then on the part .4. of contrary shadowe, that thing that you doe see thorowe the sightes shallbe 3. tymes the height of the Towre of Castle, then on the part .3. i [...] shalbe .4. tymes the height of the wall to that thing that you shall see thorow the sightes. Then on the part .2. that thing that you shall see thorow the sightes, shalbe .6. tymes the whole height of the Towre or Wall. Then the Athelida on the part one, that thyng that you shall see thorowe the syghtes, the distance wyll be 12. tymes the whole height of the Towre or Castle, or wall, as for an ensample by this figure following.
By a Towre beyng founde to bee .60. foote hyghe, at the part 12. the shadowe to runne downewardes, it is .60. foote of,An ensample. at the parte .6. the sightes dyd shewe you that thyng that was 120. foote of, that is .2. score, at the parte .4, 180. foote of, that is .3. score, at the parte .3. the sightes shewe you .240. foote of, that is 4. score, at the parte .2. all thinges seeme from the toppe of the Towre thorowe the syghtes, as .360. foote of, that is, 6. score of. Then at the parte one, all thynges seene thorowe the [Page] sightes from the toppe of the Towre shall bee .12. tymes so farre from the wall, as the wall or Towre is in heyghte, that is .720. foote from the Wall, and that maketh .12. score. Nowe if that there were another Towre or Wall neere vnto you, you maye knowe howe manye foote that it is hygher then that whiche you bee on, as thus. First dooyng as afore is declared, you shall know how many foote that the Towre is hygh, thus by this afore rehearsed, you shall knowe howe farre that the other is from you. Then set your Athelida to the lyne of Leuell, so shall you see whether that the other Towre bee hygher then that whiche you bee on, then to knowe how much that the other Towre is hygher then that you bee on, doo this: First looke howe manye partes that there is from the foote or base of that Towre that you woulde knowe howe muche that the one is hygher then the other, to the ryghte lyne called the lyne of Leuell, then turne the Athelida tyll that you doo see the toppe agree wyth the .2. sightes, holdyng the Astrolobe by the ryng vppon your thombe, as before is rehearsed, as thys: The foote of the next Towre seene thorowe the sightes at the parte .12.To know how much the one Towre is higher or lower than another. then you shall deuyde that height of the Towre that you bee on, into .12. partes. Then looke howe manye feete that there commeth vnto a parte, then turne your Athelida tyll that you maye see the toppe of the nexte Towre, and looke howe manye that commeth vnto, adde so manye foote of the measure of your owne Towre, to the other Towre. Then at the parte .10. if you doo see the foote of the nexte Towre, deuide the heyght of the Towre that you bee on, into .10. partes, then looke howe many partes, that the other Towre is hygher then yours, adde so manye foote more to the heyght of the other Towre as the partes of feete dooth answere of your owne Towre, then in lyke manner, if you see the foote of the Towre at the parte .6. deuide the heyght of your owne Towre into .6. equall partes: then looke howe manye partes that the other Towre is hygher then yours that you bee on, adde so manye foote to the heyght as those partes [Page 10] dooth come vnto: and if you doo see the foote of the other Towre, at the parte .3. then deuide the heyght of that Towre that you bee on into .3. equall partes. Then looke howe manie partes that the other Towre is hygher then your Towre, adde so manye foote as those partes dooth come vnto the other Towre, as thys for an ensample, by a Towre that is 60. foote hyghe. Then I tooke my Astrolobe and turned the Athelida to the parte .4. Then I dyd see the base or foote of the other Towre, then that Towre that I was on, the toppe beyng .60. foote hyghe, I dyd deuide it into .4. equall partes, and that dyd aunswere to .15. foote a part: for this I am assured of, that when I dyd set the Athelida to the lyne of Leuell, that it was iuste the heyght of my Towre, that place whiche I dyd see vppon the other Castle.
[Page] Then I dyd turne the Athelida styll aboute,Ensamples. seekyng where I myghte see the toppe of the Castle: then at the parte one and a halfe, I myghte see it iustlye with both the sightes, then dyd I adde .15. foote and a halfe .15. that is .7. and a halfe, and those .2. summes make .22. foote and a halfe, and then put .22. foote and a halfe, to .60. foote, maketh .82. foote, and .½. the whole heyght of the other Towre or Castle. Yet for more playnenesse, lye another Towre of .50. foote hygh which I was vppon, I tooke my Astrolobe, and dyd as afore is sayde, and I sawe the base or foote of the other Towre at the parte .10. then I dyd deui [...]e the heyght of the Towre that I was on, into .10. equall partes, beyng .50. foote hyghe, and euerye one of those partes came to .5. foote. Then I dyd take the Astrolobe and turned the Athelida, tyll that I coulde see the verie toppe of the other Towre thorowe both the sightes: and then at the parte .4. I sawe that it was true. Then I dyd adde .4. of those partes, whiche was, 5. foote, to a parte, and that came to .20. foote. So that the one Towre was hygher then the other by .20. foote: so I dyd adde .20. foote to .50. foote, whych maketh .70. foote. So I doo conclude the whole heyght of the hygher Towre to bee .70. foote iust. Yet another emsample of .2. Towres: first, that Towre that I was on to bee .40. foote hyghe, and I sawe the base or foote of the other Towre at the parte .2. of contrarie shadowe. Then I dyd deuide that Towre that I was on, into .2. equall partes, and that dyd aunswere to .20. foote a parte. Then I turned my Astrolobe, and remooued the Athelida to the parte one. Then I sawe the toppe of the other Towre thorowe the .2. syghtes. Then dyd I adde one of these partes beyng .20. foote, to the heyght of the other Towre, which maketh in all .60. foote hygh, the true height of the other Towre, as by these .2. figures you may perceyue. [Page 11]
Now furthermore in lyke maner, if you be on the higher Towre,To know how much any Tower is lower then that you be on. you may know how much the lower Towre is shorter then the other. As this: first, knowing the height of your Towre that you bee [...]n: then take the foote, or base of the shorter Towre with your Astrolobe (as before is sayde,) then looke how many partes it commeth vnto, deuide the height of your Towre that you be [...]n, as you did before: then turne the Athelida, till that you may see the top of the shorter Towre, then looke at what part you may see the top of the shorter Towre: take so much away from the height of your owne Towre, as the partes doe come vnto: then that whiche shall remayne, shall be the height of the shorter Towre, as for ensample thus: By a Towre that you were on, being 63. foote hye,Ensampl [...] ▪ and you saw the foote of the other Towre, thorow the sights at the part 9. of contrary shadow, then deuide the whole height of your Towre that you be on, into 9. equall partes, and euery one of these parts commeth to 7. foote. Then turne the Athelida, tyll you may see [Page] the top of the shorter Towre agree with both the sightes, then at the part 2. you did see them, the one of those parts being 7. then 2. times 7. maketh 14. So that the lower Tower is 14. foote shorter then the other. Then pull 14. out of 63. foote, there remayneth but 49. foote, so you may see the whole height of the lower Tower to be 49. foote, and thus doe by all other Towers, Castles, Steeples, or Walles.
The 6. Chapter sheweth how for to knowe the height of a Hill, and also the distaunce vnto the toppe of any Hill with the Scall.
NOw furthermore, by the Scall of the Astrolobe, you may take the height of any Hyll, and also of the distaunce vnto the toppe of the Hyll, by the Lyne Hypothenasall, as though there were a Lyne made fast to the top of the Hill, as heereafter foloweth. First that Hyll that you doe require to know the height of it, or to know the number of the pace, or feete, that is aboue the grounde that you bee on: then seeke a plaine grounde neare about the hyll, there where you may see the top of the hyll, then doynge thus. First turne your Athelida, tyll that you may see the toppe of the hill thorow both the sights, your Astrolobe hanging vpright, the Ring being vpon your thumbe, then looke at what parte that the Athelida standeth on, then accordingly as you dyd see before, by the taking of the height of Steeples, Towers, or Wals, meating the ground betweene the 2. standinges, to be the height of the hill, as you may know by this ensample.
To knowe the height of a hill.First I seeking out my grounde meete for my purpose, to bee as playne as I can fynde it, first, at the part 6. I set the Athelida, and so dyd I see the top of the hyll, for nearer I coulde not see it: then I dyd turne the Athelida too the parte 4. and then where I saw it agree with the sightes of the Astrolobe, there I began for to mete how many pace, that it was betweene the parte 6. and the [Page 12] parte 4. the measure of ground was 100. pace: so I dyd conclude that the height of the hill was 100 pace hye, that is 500, foote. and then I must needes say, that from the part 4. to the Center or top of the hyl, if there were a perpendiculer lyne let downe as low thorow the middle of the hyll till that it were leuell with the sighte of mine eye, then it were to the ende of the perpendiculer Lyne 300. pace iust. Then for to know the iust distaunce to the top of the hyll, by a right Lyne, as though there were a Lyne stretched from the top of the hyll to mine eye, which is the Lyne hypothenusall: Then must I bee perfect in the seconde parte of Arithmetyke,To know the length of the Hipothenusall Lyne by the extracting of the roote. (that is to say) the extraction of rootes, and there will I doe thus: I must multiply the whole distance in it selfe, which is 300. times 300 pace, and of that multiplycation commeth 90000. Then in lyke maner I multiply the height in it selfe, which is 100. tymes 100. and of that multiplication commeth 10000: then I doe adde both those numbers together, & that maketh in number 100000. then this being done, I doe extract the square roote of both these numbers added together (that is to saye) 100000, and then there will stande in the quantytie Lyne .316. and wyll remayne 144. whiche is 18/79. Therefore I doo conclude that the Lyne shoulde bee stretched from the toppe of the hyll downe tyo the sightes of mine eye which is the Lyne Hypothenusal, to bee 316 pace, and one foote and better, the iust length of the hypothenusall Lyne, as by this Ensample it doth more playnely appeare.
So by this Hyll you may see that the height of the Hyll was aboue the grounde, that it was taken vpon 100. pace: that is 500. foote, and that maketh 8. score, and 20. foot: & the distaunce to the Center, or perpendiculer, or plumbe Lyne imagined into the Hil to be 300. pace, & that is 1500. foote, which maketh 25 score, and the Hipothenusall Lyne, from the top of the Hill to the standing, at the part 4. is 316. pace, & neare 2. foote, which is in feete 1582. and in scores, 26. and 22. foote, as the figure afore made doth represent. And thus doe by all other hilles, whether that it be a part of a Hill or a whole Hill, all is one matter.
The 7. Chapter sheweth you by the Skall of the Astrolobe, to know the true wydenesse of any water, or how farre that any ship is of from you, or to take any great distance by laying the Astrolobe flat before you with the Scall vpwardes.
YEt furthermore, by the Scall of the Astrolobe you may know the widenesse of Waters, and the distaunce from place too place all alonge the water syde, and also how farre that any Shippe doeth ryde from the shoare syde, and also how farre the Shippe is from you: whereby you may make a perfect shot, very profytable for Gonners to haue the vse of, as heereafter followeth.To knowe the widenesse of waters. Fyrst, take your Astrolobe, and sette the same vpō some steadye thinge, layinge that flatte with the Scall vpwardes: Then turne the Astrolobe tyll that the Lyne of leuell doeth stande [Page 13] as the shoare side, as those that you should set the Athelida with the line of Leuel, to looke al alongest the waters side: then shall the plumbe lyne of the Astrolobe stande directly crosse the water, then al thinges seene right with that line to be right ouer the water: then your Astrolobe lying styl, turne the Athelida to the part 12. then looke what marke or banke that you see hard to the waters side, through the sight of the Athelida, marke it: then take your Astrolobe going directly by the waters side, tyll you come directly right against the marke taken vpon the other side of the water, setting your Astrolobe as before is rehearsed. Then if the perpendiculer lyne doo directly poynt to the marke afore taken, then the measure betweene the two standinges, shalbe the true breadth of the water.
Furthermore, the Astrolobe standing as afore is rehearsed, setting the Athelida vpon the part .6. of the right shadowe, then double that measure betweene the .2. standinges, that shalbe the breadth of the water, then the Athelida vpon the part .4. of right shadowe, the Astrolobe set as afore is rehearsed, then the measure betweene the .2. standinges, shalbe the .3. part of the breadth of the water, and so foorth to the part .3. to the marke right ouer the water, shalbe the one quarter of the breadth of the water, then .4. tymes the whole measure shalbe the breadth of the water: for to take the breadth of waters with the Skal of the Astrolobe, is no other thing in the dooing of it, but as you doo take the height of Walles or Towres in al poyntes, sauyng that in the taking of heigthes, you doo hang your Astrolobe by the Ryng vpon your Thumbe: and for to take the breadth of waters, you must laye your Astrolobe steedy afore you, and the line of Leuel to stande al along the waters side, as circumspectly as you may or can: then you must make your measure al alongest by the waters side, as by this ensample folowing, of a water that is measured, and is .36. score ouer it.
An ensample.First I take my Astrolobe, and come to the waters side, and laye my Astrolobe vppon some steedye thing, and laye the lyne of Leuel all alongest by the waters side, then the thwart lyne of the Astrolobe poynted iust thwart or crosse the waters side, neare to the Church ende: then I turned the Athelida to the part .12. so I sawe a polled tree through the sightes: Then I tooke vp my Astrolobe, and beganne to goe, measuring the ground by pase, two steppes to a pase, and that made .5. foote, which is a Geometrical pase: and .12. of those pases make a score: And then I came right against the tree, prouyng it with my Astrolobe, and found that the measure was from my first standing, tyl I came right against it, 432. pases, and that maketh .36. score. So I dyd conclude the breadth of the water to be .36. score, from banke to banke.
[Page 14]Then furthermore I turned the Athelida to the parte .6. and then I sawe a polled tree at the house ende: then I went measuring the grounde, and founde that the grounde was .216. pases, and then I was right against the marke, and that was .18. score: then two tymes .18. is .36. Then I turned the Athelida to the part .4. of right shadowe, and measured the grounde, tyll I came right agaynste the marke taken through the sightes of the Athelida, and founde the measure betweene the first standyng, and the next, one hundred fourtie and foure pases, that is, twelue score: then three tymes twelue score, is thirtie sixe score. Then the Athelida standing vpon the parte .3. I measured the grounde betweene the two standinges, and founde it to be .80. pases, that is .9. score, and the fourth part of the breadth of the water, for foure tymes 9. is .36. Then the Athelida vppon the parte .2. Alwayes prouided that you doo as before is rehearsed, measuryng the grounde tyll you come directly agaynste the marke taken, shalbe three score and twelue pases, that is, sixe score: then sixe tymes sixe, is .36. For vppon the parte .2. the grounde betweene both the standinges, is but the sixt parte of the wydenesse of the water. Then at the parte one, the ground betweene the two standinges, shalbe but the twelfth parte of the breadth of the water, that is .36. pases, and that maketh three score: then .12. tymes three, is .36.
Nowe furthermore, if you wyll knowe the length of any of the Hypothenusal or slope lynes, then extracting the roote,To knowe the length of the slope lyne, by the extract of the Roote. the length of that lyne shall appeare: so that with the Skal of the Astrolobe, you maye knowe any distaunce, being sure that you doo make a square Angle, by laying the Astrolobe flatte afore you, euen accordyng vnto the Conclusions, when that you doo hang the Astrolobe.
And also you maye take a greater distaunce, and also a larger station, whereby you maye woorke more exactly, by laying it, then by hangyng of it. For that there is seeldome any ground, but that it is higher or lower in one place, then it is in another, & that maye breede a notable errour, if it be not well considered of. But if you doo laye the Skall flat before you, considering well [Page] the conclusions, you may commyt no great errour, being sure, that in your remouyng, you doo make a square Angle, and then measure the distance of grounde truely, for thence are many folde notable conclusions to be donne with the Skal, as by this you maye knowe howe farre of that any Shyp dooth ryde at an ancore in the Sea, or in any Baye, or Ryuer: you may knowe certainely howe farre shee is from you, so that shee be not moueable: And also you being besieged in a Towne, may knowe howe farre any thing is from you: And also if you be without any Towne, you may knowe by the S [...]al of the Quadrant or Astrolobe, howe farre any Towre, Balwarke, or Steeple is of from you. &c.
The eight Chapter sheweth vnto you, if that you doo know the dystance, then you may know whether that it be hygher ground or lower ground then the place that you are vpon, and howe much, both By the partes of the Scal, and by the degrees: and also you may know whether that one shippe be higher then an other &c.
And furthermore, you knowing the dystance vnto any place assygned, then you may know the height of any Hyl or Steple or Towre, or the deepenesse of any valley by the parts of the Scal, as thys: The dystance being known, if that it be hygher or lower by one of the parts & the Scall to be deuided 12.To know howe much any place is higher or lower then the placeth it you are on, whether that it be on Towre, Steeple, [...]l, Clyffe, of valley. &c. partes: then the thinge is higher or lower by the .12. parts of the distance, & if it be higher or lower by two of those partes, then the thyng is higher or lower then the place that you doe stande vpon by the sixt part of the distance. And if the thyng be higher or lower by .3. of those partes, then the thynge so taken, shall he hygher or lower by the .4. parte of the dystance: and if that it be higher or lower by the .4. part, then the thyng shalbe higher or lower by the third part of the distance: and if that the thing be higher or lower by the .6. part of the Scal, then the Hyl or valley shall be higher or lower by halfe the distance. &c. As [Page 15] for an insample this: I laying the Skall flat, toke a marke vpon the top of a Hyll, or in the botome of a valley: and so workyng as is declared in the Chapter going before, and founde the dystance to be .24. score from me, and then I desire to knowe howe much that the Hyl was hygher groūd, or the valey lower ground, then the place that I stoode vpon. And then I tooke the Astrolobe and hung it vpon my thombe, and so I sawe that the Hyll was hygher by the one part. Therefore I dyd conclude that it was .2. score higher, that is .120. foot hygher groūd then the place that I stode vpon, for that the dystance is .24. score: and the .12.An ensample. parte of 24. is .2. Wherfore yf that it were a valley, then it were .120. foote lower then the ground that I stoode vpon. &c. And then if that it were hygher or lower by the .2. part of the Skall, then it should be hygher or lower then the place that you stoode vpon, by the .6. part of the distance, that is .4. score, and that maketh .240. foote. And furthermore, if that it were hygher or lower by .3. of the partes of the scall: then the ground should be higher or lower by a quarter of the distance, that is .6. score: and that contayneth 360. foote. And furthermore, if that it were higher or lower by .4. of the partes of the Scal, then it should be higher or lower by the third part of the distance, that is .8. score: and that contayneth .480. foote, &c. And this I do take to be sufficient for an ensample. And nowe furthermore, if that the dystaunce were very farre, and also the Scal deuided but into .12. partes, yet you myght know the height of a Hyll, or the deepnesse of a valey,To know howe much any place is hygher, or lower by degrees. An ensample of shyps on the water. by the degrees of your Astrolobe, or Quadrāt, as this: the distance being knowen vnto any marke vpon a Hyll, or in any valley, if that it were one degree higher or lower then the place that you do stand vpon, then the thing shoulde be higher or lower grounde by the .60. part of the distance. If .2. degrees, then it should bee higher or lower by the .30. part of the dystance: if .3. degres, higher or lower, then the ground shoulde be higher or lower by the .20. part of the distance: yf .4. degres, then the grounde should be higher or lower by the .15. partes of the dystance: if .5. degrees, then the ground should be higher or lower by the .12. part of the distance: and thus farre the degrees will serue exactly yenough, [Page] but not vnto many moe degrees, for that they be the diuisor of a circle. But vnto .5. or .6. degrees they wyll serue the the turne very wel. And now for your better vnderstanding, I wil make an ensample vnto .5. degrees according vnto the dystance before rehersed,An ensample. that is, at, 24. score from you, the grounde being higher or lower by one degree, the thing is higher or lower by the .60. part of the dystance, that is .24. foote, whether that it be any marke vpon a Hyll or valley, or the height of any Towre or Steeple. &c. Yf that it be .2. degrees higher or lower, then the marke shall be higher or lower then the grounde that you doo stand vpon, by the .30. part of the distaunce: and the distaunce being .28. score, the Marke shall bee higher or lower by .48. foote.
And Furthermore, if that the marke bee higher or lower by. 3. degrees, then the thynge shall be higher or lower then the grounde that you doe stande vpon, by the .20. part of the distance: that is .72. foote. And Furthermore, if that the marke be higher or lower by .4. degrees, then the thing shall be higher or lower by the .5. part of the dystance, that is .96. foote. And further more, if the thinge be higher or lower by .5. degrees, then the thing so taken, shall bee higher or lower then the grounde that you stande vpon by the .12. part of the distance: that is .120. foote. &c.
And furthermore, by this meanes or order, you may knowe the distance vnto any shyppe vpon the sea, or Ryding in any Hauen or Harborowe you knowing the hight of any Towre or Clyffe, or any Hyll vpon the sea Coste, howe many foote that is higher then the water: and you may knowe it eyther by the partes of the Skall, or els by the degrees, as for an ensample, the Towre or Hil, or Clyffe to be .60. foote higher then the superficiall of the water, and the .60. foote is one score.
An ensample of shyps on the water.And if you do se the shipe at one degree lower then the horizon then it shall be .60. score vnto the ship: and if at .2. degrees, then [Page 16] it shallbe .30. score vnto the ship, if at .3. degrees, then it shal be .20. score vnto the ship, if at .4 degrees, then it shall be .15 score vnto the ship: if .5. degrees then it shalbe .12. score vnto the shippe: if .6. degrees, then it shall be .10. score vnto the shyppe: but if the shyppe be nearer, the degrees wyll serue no turne, but wyll be erronious. Wherefore you must vse the partes of the Scall, as .5. degrees and the part one is all of lyke dystance: for the hyght of the Towre, Clyffe, or hyll beeing .60. foote in hyght aboue the shippe, that is iust one score: at .5. degrees, the dystance vnto the shyppe is .12. score. And also at the parte one, the distance is .12. score in lyke maner &c. and at the parte .2. the dystance vnto the shyppe is .6. score: and at the part .3. the dystance vnto the shyppe shalbe .4. score: and at the part .6. but .2. score: and at the part .12. the dystance from the foote of the Clyffe or Towre, vnto the shyppe, shalbe but one score, that is iust the heyght of the Towre or Clyffe. &c.
Furthermore you may knowe, if that you be on the sea, whither that one shyppe be hygher or lower of borde,To know whether my shyp be higher or lower of boord, then another, and whether the one dooth ouertop the other, and howe. then the other shyppe, and howe much: and also whither the one shyppe dooeth ouertoppe the other shyppe, you may knowe howe much: so that shee bee not aboue a myle from you, as thys, by the lyne of the horizon lacke, what place so euer that you doo see iust with the horizon, is equall in height with your eye, neyther higher nor lower, whither that you bee one the Sea, or vpon the lande: and then you being in a shippe on the Sea, and you do desier for too knowe whither that the other shyppe be higher or lower of borde then that shippe that you are in, then looke Vppon the other shpppe, at what place that the horizon quoteth: and if you doo see the horizon ouer the other shyppe, then your shippe is higher of borde then the other ship: and if that you woulde knowe howe muche, then goe too a lower place in your owne shyppe, vntill suche time that you doo see the Horizon [Page] iust with that part that you doo desire to knowe the heigth of, and then standing styl, looke what part of your owne ship that the Horizon quoateth, that part of the ship is iust equal with the other shyp, neither higher nor lower: then to knowe whether that the other shippes top of her Mast be higher or lower then your ships, then goe vp, or sende one to the top, and if that the other ships top be higher then the Horizon, then the other ships top is higher by so muche as you doo see aboue the Horizon: but if that you doo see the Horizon ouer the top of the other ship, then your ship is the higher: and then to knowe howe much, come downe lower, vntyll you doo bring the other ships top vnto the Horizon, then at the iust heigth of your eye, is the true heigth of the other ships top, neither higher nor lower: and then looke howe much it is higher then your eye vnto the top, so much your top is higher then the other ships top. &c.
And also you being on the lande, you may knowe whether one ship be higher of boorde then the other, and also whether the one ship dooth ouertop the other ship, as this, by the quoting of the Horizon vpon both the ships, as this, If you be either in a Towre, or any high house, neare the sea coast, or els at the foote of any hyl eyther.
Then if that you desyre for to know which of the shyppes be the higher of boord, or els the hygher topped, then ascende or descend, vntil that you doo see the horizon iust with the hygher part of the ship, and then looke vpon the other shippe, and then if that the other ship be hygher then the Horizon, then that ship is so much hygher of borde from the quotyng of the Horizon vpwards, and then if that you would know how many foote, then ascend vpwards vntil that you doo see the vpper part of the ship iuste with the horizon, then looke how many foote and ynches that you were hygher then you were before, and so many foote the Ship is higher then the other ship iust.To know howe much one house, ship, towre, or hyl is higher then the other. And by this order you maye knowe howe muche one ship is higher topped then the other.
And by thys order you maye knowe whether one Towre is higher then another, or one house higher then an other: And also whether that one hyl be higher then another. &c.
[Page 17]And furthermore, by this meanes you doo knowe whether that one shyp dooth ouertop the other: then you may knowe how many foote it is from the top of any ship, vnto the water, by the heigth of your owne shippes top, and the heigth being knowen, then you may knowe the distance vnto any ship sailing on the sea, so that shee be not too farre of, by the partes of the Skal, and also by the degrees, as before is rehearsed, going so lowe as you can in your owne ship, and then to consider howe muche that you are aboue the water, &c. And thus I doo ende the conclusion of the Scal, and nowe dooth folowe the conclusion of the Crosse staffe.
The nienth Chapter sheweth the making of the Crosse staffe, that in some cases is better then the Skall of the Astrolobe, or Quadrant. &c.
NOwe furthermore as concernyng the making of a Crosse staffe, that serueth the Towne in diuers respectes, muche better then the Skal of the backeside of the Astrolobe, and specially for to take the length of the Cortane of the wall of a Towne, or the distance betweene two Townes, or any two markes standing directly against them, very profitable for al seruitours, or other, for to haue the vse of. And nowe foloweth the making of a Crosse staffe, as much as shal serue landmens turnes. First take a peece of good, fine, and wel seasoned wood, and let it be wel playned, and very streight, of [...]ue foote long, and then let it be diuided into .60. equal partes or ynches, and then you may graue in it .1.2.3. and .4▪ and so tyl you doo come to the ende at .60. And be sure that you make euery ynche or part note, the one to be bygger or lesser then the other. Then if you wyl, you may make at the ende of euery .12. ynches, a roundell or circle, and at the ende of euery .6. ynches, halfe a circle:The ma [...]ing of the Crosse staffe. then at euery .3. ynches, s [...]me marke or crosse, and then your long staffe is finished. Thē in like maner you shal make an other short staff, called a Transuastorie, of two foote long, and in the very myddle of it you shall make a square hole, suche a one as shal goe close to the [Page] longer staffe without any swaruing, and then shall you make .2. wings or plates of brasse, one for the one end, and the other for the other ende, then shall you make a chace or rygall on the one side of the Saffe, that the wynges may be rem [...]ued at your discretion: & then at .6. ynches from both the endes you shal make a marke: And then there will bee .12. ynches betweene the 2. markes. Then in lyke maner, you shall make .2. other markes 9. inches from both the endes, and there will bee .6. inches beetwene the .2. markes.
And then in like maner, you shal deuide the rest of the middle of the Transuastorie into ynches equal partes, and then it is finished, sauing that in the middle of the Transuastory you shall put a little peece of brasse into the hole or socket that the longer Staffe doth go thorowe, and then you shall make a little vice or worme, to the ende that you may make the Transuastory to stand fast at your descretion: as these .2. figures doo represent both the staffe and the Transuastorie, and the vppermoste, the longest staffe
¶The tenth Chapter sheweth howe for to vse the Crosse staffe, for to knowe the length of any Wall, or the distance betwene any two marks, and also the distance from you, vnto any Wal or Marke.
NOwe when so euer you list for to take the length of any cortaine of a Wall, or the widenes betwene two marks, or any other thing what soeuer it be, then shall you take the longer staffe, set out with equall partes, and put the Transuastorie vppon it, through the hole in the myddle of the Transuastorie: and then if you would know the wydenesse betweene anye two Markes, or the length of the cortaine of any Wall,How to vse the Crosse staffe to take the widnes and the distance of any thing. and the distaunce vnto them: then shall you doo thus: Firste, set the ende of the longer Staffe, harde vnde [...] one of your eyes, wynkyng with the other eye.
Than your Transuastorie standyng at .24. ynches from the ende of your long Staffe, whiche is the whole lengthe of your Transuastorie: Then goe forewardes or backewardes, standyng vpright with your bodye, and heade, and both your feete togeather: then goe forwardes or backewardes, lookyng towarde your Marke, tyll both the endes of your Transuastorye do agree with your two Markes iustly. If it bee a Wall, measure the grounde iust to the myddle of the Wall, and that shalbe the true length of the Wal.
But if there bee a Ditche betweene you and the Wal, then remooue your Transuastorie at the seconde standyng, his whole length further forewardes, that is, two foote: and then goe backwardes, tyl that you maye see againe, both the endes of the wal agree with the two endes of the Transuastorie. Then measure the grounde betweene the two standinges, and that shalbe the iust length of the wal. And then the distaunce vnto the wal, shalbe [Page] twise the length of the wal. Then if that the distaunce be further then the Transitorie wyl take, and the wal too shorte: then remoue the Plattes or wynges of the Transitorie, to the markes, sixe ynches from both the endes of the Transitorie: and then the two Plattes or ryngs wyl be but twelue ynches asunder.
Then take the wydenesse betweene the two markes, or the two endes of any wal iustly with the outsydes of the two Plattes or Ringes: then with the myddle of your foote, there make a marke: then remooue your Transitorie forewardes or backewardes, the length that the Plattes or Ringes be asunder, as you haue grounde: and then goe forewardes and backewardes, tyll that your two Plattes or Ringes doo agree againe with both the endes of the wal: and then there make an other marke at your feete. Then measuring the gr [...]unde betweene the two standinges, it shalbe the length of the wall.
And then for to knowe the distaunce vnto the wall, you shal doo thus: Looke howe many tymes that the Transitorie is from the ende nexte towardes you, and especially the distance betweene the two Plattes or ringes: so many tymes the length of the wal, shalbe the distaunce vnto the marke: as for ensample thus, By the wal of a Cortaine of a towne betweene two Turrettes, and my desire is to knowe the length of the Cortaine of the wal: and then I hauyng the Transitorie vpon the long Staffe, I could not come so neare the towne as I woulde. Then I remooued the Plates or wynges of the Transitorie, to the diuision of sixe ynches from both endes, that was, twelue ynches asunder: then I goyng forewarde, tyl that I dyd see both the Turrettes with the two Plates or wynges of the Transitorie: and then at my feete I made a marke, and then in like manner I remooued my Transitorie twelue ynches forewarde, and then I went backewardes, tyl [...]hat the two endes of the wal dyd agree agayne with the two Plates or wynges of the Transitorie, and there is made an other Marke.
Then I measured the grounde betweene the two standings, and founde it tenne score: then I dyd conclude, that the length of the Cortayne of the wal, was tenne score from the one towre to [Page 19] the other. And nowe I knowing the length of the wal, I maye easily knowe the distaunce vnto the wal, as thus: Nowe I doo looke howe many tymes twelue ynches that the Transitorie was from the ende nexte vnto me, and it was foure and a halfe: that is, 54. ynches.
And nowe, because that the Plates or wynges of the Transitorie were twelue ynches asunder, and .54. maketh foure tymes and a halfe twelue, and the length of the wal, tenne score. Therefore I doo conclude, the distaunce vnto the wal, from the place of the last standyng, to bee foure tymes and a halfe tenne score: that is, fourtie and fyue score: as by the ensample of the figure folowing it is declared.
[Page 20]Nowe furthermore, if the distaunce be further, then the two Plates or wynges maye bee remooued nyene ynches from the two endes, that is, but sixe ynches asunder: Then in like manner if that be too wide, you may remoue the two plates or wynges ten ynches from both the endes, and that is but foure ynches asunder. Then in like manner, if that the distaunce bee verye farre of, and the length of the wall bee shorte, then maye you remooue the Plates or winges of the Transuastorie, eleuen ynches from both the endes: that is, but two ynches asunder: And then, dooyng as before is rehearsed, to take two standynges, that shalbe the mydenesse betweene any two markes.
Prouided alwayes, that you remooue the Transuastorie at the seconde standing, either forewardes or backewardes, so many ynches, as the two Plates or wynges be asunder, iustly, and no more, and then you shall knowe the distaunce vnto any Marke or wall.
When you doe knowe the length of the wall, (and that is knowen, as afore is saide, by the measure betweene the two standinges) then looke howe many ynches that the Transuastorie is from the ende of the long Staffe nexte to your eye: then looke howe many ynches that the Plates or wynges of the Transuastorie are asunder, so many times the length of the wall shalbe the distance vnto the wal.
As for ensample thus: By the Cortaine of the wal afore named, being ten score long, & the Transuastorie to be set at .48.An other ensample. ynches from the ende. First, the two winges stoode at the very vtter ende of the Transuastorie, that is .24. ynches asunder: then the measure vnto the wal, shalbe twise ten score, and that maketh .20. score, because there is twise .24. in .48. Then in like manner the Plates or wings were set .12. ynches asunder, and the Trāsuastorie .48. ynches from the ende. Then there is foure tymes .12. in .48. then you may conclude, that that is foure tymes ten score vnto the wal of the towne, that maketh .40. score. Then in like manner the Plates or wynges being set but sixe ynches asunder, then there is eight tymes sixe in .48. which maketh eight tymes ten score: that is .80. score. Furthermore, if that the wynges [Page] were but foure ynches asunder, the Transitorie being .48. ynches from the ende, there is .12. tymes foure in .48. So the distance vnto the wall is .12. tymes .10. score. that is .120. score. Then furthermore, the winges standing but .2. inches a sunder, but then it is an hard matter for to take it perfect: then there is .24. tymes .2. in .48. so that maketh .24. tymes .10 score: which maketh .240. score. Now furthermore, in lyke maner if that it fa [...] not right iust measure, then if that there be but halfe the measure betweene the winges, then for that, take halfe the length of the wal, and adde it vnto the rest of the measure: and if that it bee three quarters, then three quarters of the measure, and for a quarter, one quarter. &c.
The eleuenth Chapter sheweth you howe for to take the length of a wall, when that you haue not grounde large yenough for your two stations or standynges.
NOwe furthermore, if that you haue not grounde for to goe forewardes or backewardes, so much as that the quantitie of the wydenes of the Cortaine, or the distāce between any two markes shal come vnto, there is a remedie for that, as this: Looke at what length you haue set the distance between the two Plates or wyngs: then remoue the Tranceuastory of the long staffe, but halfe the length betweene the two Plates or wyngs, at the second standing, and then the grounde betweene the two standings shalbe but halfe the length of the wal, or distance betweene your two markes: then double the measure that shalbe the length of the wal: then hauyng not so much ground, remoue the Transitorie but the thirde part of the measure betweene the two wynges of the Transitorie, and then the grounde betweene the two standings, shalbe but the third part of the length of the wal, and three tymes that measure, shal bee the whole length of the Cortaine of the wall.
[Page 21]Then hauing not so much ground, then remoue the Transitorye but one quarter of the measure of 2. plates or winges, and then the measure betweene the 2. standynges shall be but one quarter of the length of the Wall: and then 4. times that measure shall be the whole length. Thē in like maner you may remoue the Transatory but the 6. part of the measure & there Transitory the betweene the 2. standyngs shall be but the 6. parte of the length of the Wall: and so foorth to the 12. parte or more, as you haue Grounde or roome.
But heere is one thinge by the way, neuer take a short station betweene the 2. markes, as longe as you may haue a large: for that a lyttle errour often times multyplyed, becommeth a great and myraculous errour in the ende, yea an vntollerable fault.Ensample. And now for your better Ensample of all those questions afore rehearsed of the length of a Brickwall 12. score longe, fyrste I tooke my crosse Staffe, and sought out my grownde ryght against the middle of the Wall: and because I coulde not come so neare as I woulde, I remoued the 2. plattes or winges 6. ynches from the 2. endes of the transatorye that was 12. ynches asunder, and set the transatorye 36. ynches from mee: and then there where the 2. Plates or Winges dyd agree with the two endes of the Wall, there at my feete I made a marke: then I had not grounde ynoughe neyther for to goe forwardes nor backwardes: therefore I remoued my Transitory but 6. ynches forwardes, that is at 42. ynches, and then I went backwardes tyll that the 2. plattes or winges dyd agree agayne with the ende of the Wall, and there I made another marke. Then I measured the grounde betweene the 2. standynges, and founde it but 6. score: then that beinge halfe the length of the Wall, 2. times 6. score maketh 12. score.
Then I hauinge not so much ground, remoued the Transitory the thirde parte but 4. ynches forwarde, that is, at 40. ynches. Then measurynge the grounde betweene the 2. Standynges, was 4. score: then three times 4. score maketh 12. score: then hauynge not so much grounde, remoue the Transitory but one quarter forwards, that is 3. ynches forwardes, that maketh 39. ynches: [Page] and then the grounde betweene your two standynges shall bee but three score: and foure times three score maketh twelue score. Then in lyke case yf that you haue not so much grounde, you may remoue the Transuastorye but the sixt parte of the measure betweene the two Plates or Winges, that is two ynches forwardes, and that maketh .38. ynches: & then the measure beetweene the two standynges is but two score: and syxe times two score maketh twelue score, and so foorth to the twelfe parte of the measure betweene the two Plates or Winges of the Transuastorye, as by this Example.
The 12. Chapter sheweth you how to know the distaunce vnto any two marks, or to the two endes of any wall by the extracting of the square roote.
NOwe furthermore, whensoeuer you haue taken the wydenesse betweene any two markes, then you doe knowe the iust widenesse, but not the true distaunce, except it were a Wall, you doe know the true distaunce vnto the middle, but not to the ende.To know the distaunce vnto any two marks by the extracting of the square roote.
Now therefore whensoeuer you woulde know the distaunce vnto the endes of any Wall, or vnto a Churche, and a Tree, or whatsoeuer that you haue taken the wydenesse betweene them, then how farre so euer that they bee asunder, deuide the measure into 2. equall partes. Then take the Lyne of the distaunce vnto the middle of the marke, and fyrste multiplye the distaunce in it selfe: then in lyke manner multyplye the halfe widenesse in it selfe: then part both the numbers of the multiplycation, and adde them both together: then extract the roote of both the numbers, and it shall bee the distaunce of both the endes of the Wall, or any other 2. markes, as now for example thus: by a Church and a Bulwarke. And my desyre is to know the wydenesse betweene them, and first I take my crosse Staffe and set the Tranceuastorye 24. ynches from the ende: and the 2. plats or winges stoode at the harde ende: and then I tooke my fyrst standing, as afore is declared, holdynge the longe Staffe hard vnder the side of mine eye, and then I seing the Bulwarke & the church agreeing with the 2. ends of the trācevastory, there at my first standing I made a marke, and then I remoued the Tranceuastory 24. ynches forwardes, and that maketh 48. ynches, and there where the two markes dyd agree agayne at the 2. endes of the Tranceuastorye goynge backwardes, there I made an other marke, and then I measured the grounde beetweene the 2. standyngs, and founde it 24. score.
[Page 23]Then I did conclude the wydenesse betweene the Church and the bulwarke, was .24. score: then it must needes bee sayd, that the distaunce to the myddle waye betweene the Bulwarke and the Churche at the first standing to bee .24. score: because that the Transitorie was once his whole length from the ende nexte vnto mee, and then at the second standing the distaunce must needes be 48. score, because that the Transitorie was twice hys whole lēgth from the ende nexte vnto mee, beyng .24. ynches. And nowe for to knowe the distaunce vnto eyther the Bulwarke or the Churche, then shall you doo this: and for the neerest standing, when that the Transitorie was once his whole length from the ende, and the distaunce vnto the myddle .24. score, then I dyd multiplye .24. tymes .24. and that maketh .576. And then from the myddle betweene the Bulwarke and the Churche, was .12. score to the bulwarke, and .12. score to the Churche. And then .12. score multiply squarely, that is to say, 12 tymes .12. and that maketh .144▪ Then adde both your numbers together, that is to saye, 576. and .144. and that maketh .720. Then extract the roote of the number, and then there wyll stande in the quantitie lyne .26. and .44. wyll remaine ouer. So that you may conclude, that from the neerest standing, to the Bulwarke or to the Churche, it is .26. score, and 11/13. parte of a score, that is more neere .51. foote: and nowe from the furthest standing, and the distaunce vnto the myddle .48. score. Nowe multiplie .48. tymes .48. and that maketh .2304. Then multiply .12. tymes .12. for the halfe wydenesse, that is .144. and that added vnto .2304. maketh .2448. so extracting the roote, there will stande in the quantitie lyne .49. and then wyll remaine ouer .4. which maketh .47/98. parte, that is, neere halfe a score, beyng .29. foote. So I doo conclude, that from the further standing to eyther the Churche or Bulwarke, it is .49. score, and neere 29. foote.
The thirtienth Chapter sheweth howe to knowe the distance vnto any marke with the crosse staffe, without the extracting of the roote, and also howe to take the height of any thing with the crosse staffe.
NOwe furthermore for your more ease, whensoeuer that you woulde knowe howe farre it were to any marke or place by [Page 24] the helpe of two markes,To knowe the distance vnto any marke with ye Crosse staffe without the extracting of the roote. with not knowing the length of the slope lyne, then shall you doo thus: First, stande ryght agaynst the marke that you doo desyre to knowe the distance vnto, then seeke out your marke, and be sure that the other marke make a square Angle vnto that marke that you desyre for to knowe the iuste distance vnto: then remoue one of the plates or wyngs of the Transuastorie to the verye myddle of the Transuastorye: then when soeuer you list to knowe the distance, first at your fyrst standyng, then make a marke: then for your next standyng, remoue the Transuastorye, but so muche as the dystaunce is betweene the .2. plates or wynges, beyng sure that you take the marke that you doo desyre the distance vnto, with that plate or wyng of the myddle of the Transuastorye: then (as afore is declared) looke howe many ynches that the .2. plates or wynges be the one from the other, so manye tymes the measure that the distance is betweene the .2. markes, shall be the dystance vnto that thyng that you haue taken with the middle of the Transuastorie. And so foorth in al poyntes as afore is rehearsed: as for ensample thus, by a towre that I doo requyre the distance vnto,An ensample. and then I standyng wyth my face right agaynst the towre, then I sought a tree that stoode right besyde the towre, that made a perfecte square Angle to the tower and vnto mee: then because that the dystance was somewhat farre of, and the tree somewhat neare vnto the towre, therfore I set one of the plates or winges .6. ynches from the ende, and the other wing right with the middle of the Transuastorie. Then I set the ende of the long staffe harde vnder one of myne eyes, and tooke the measure true betweene the tree and the towre, with the plates or wings of the Transuastorie, the Transuastorie standing .48. ynches fom the ende. And then I remooued the Transuastorie .6. ynches forwardes, because that the .2. plates or wynges were but .6. ynches asunder, and that made .54. ynches: and then I went backwardes and made my seconde standing, and then I measured the grounde betweene the .2. standings, and founde the grounde .4. score, then I knewe that the tree was .4. score from the towre.
[Page]And then I looked howe manye ynches that the Transitorie was from the ende, and founde it .54: then in lyke manner I looked howe many tymes .6. there was in .54. and founde .9. times .6. Then I must needes conclude, the distance vnto the Towre to bee .9. tymes .4. score, that is, 36. score: as by ensample of these figures following.
The whole distaunce vnto the Towre is .36. score. Nowe furthermore, you may take the height of any wall, or Towre, or Steeple, or any other thing, so that you set one of your plates or wings with the very middle of your Transitorie,As touching the taking of heightes with the crossestaffe. & with the myddle plate be sure to take the foote or base of the Towre, Steeple, Wall, or tree: or else you may commit errour. And by the staffe you may knowe the wydenesse of waters, with diuers other most necessarie thinges, as this: When that you bee in a towne, for to knowe the distaunce of any place whose length or wydenesse that you doo knowe, as by the length of a pyke, or the wydenesse or distaunce betweene .2. Bushes or .2. stones, or any other thing, beyng sure that you take your sight true vppon your markes holding your handes steedie tyll you may see your .2. markes, ende wyth your 2. plates or .2. endes of your Transitorie, setting the ende of your long staffe close to the vtter parte of your eye, winking with your other eye, standing vpright with your necke and heade: and thys dooyng, you shall not fayle of the truth. For if that you erre, the fault shall bee in your selfe, for that you haue not taken it truely. [Page 25] Therefore that is very good to haue a rest to laie your long staffe on, & for to take a hey [...]u [...], you mu [...]t turne the Transuastorie one ende vpwardes, and the other ende downewardes, and then you must holde the ende of the long staffe close to the corner of your eye.
¶The fourteenth Chapter sheweth vnto you, how that you shall knowe the di [...]taunce of any shippe from you, and you beyng in another shippe, and both the shippes vnder sayle, and goyng by the Crosse staffe. &c.
ANd furthermore, by the Crosse staffe you maye knowe the distaunce vnto any shippe sayling on the Sea, very exactly, you beyng in another shippe sayling after them, or before them, or beside them: although that diuers men are not of that opinion, for that both the markes are moueable, whereby they cannot get any certaine station or standyng, as this is declared in the eight Chapter goyng before, how to knowe whether that one shyppe doth ouer toppe the other, by the sending of one vp vnto the toppe of the shippe, to looke how the Horizon cutteth vpō the toppe of the other shippe: and by that he dooth knowe whether that the other shippe dooth ouertoppe or vndertoppe the shippe that he is in: and then you knowing how many foote that your owne shippes toppe is in height from the toppe downe vnto the water, then you may knowe by that howe many foote the other shippes toppe is in height in lyke maner from the water very exactly.As touching the knowing the height of any shippes toppe. But if that you doo not knowe the iust height of your owne shippes toppe vnto the water, then you may knowe it thus, by send [...]g one vp vnto the toppe, with a leade or a Plomet made fast vnto a lyne, and so let downe vnto the superficiall parte of the water: and then measuring the lyne, you may see the height of the shippes toppe that you are in, downe vnto the water: and then by the height of your owne shippes toppe, you may iustly knowe the true heyght of the other. &c. And now to knowe the distaunce vnto the other shippe with the Crosse staffe, you must doo this:How to know the d [...]stance vnto any ship. take your Crosse staffe, and remoue the two plates or winges of the Transuastorie [Page] vnto the myddle of the staffe, and set them at a knowne distaunce betweene the two winges or plates, as at an ynche or halfe an ynche a sunder at your discretion, and that beyng done, then set the long staffe harde vnto the corner of your eye, wynking wyth your other eye, & then remouing the Transuastorie forwardes or backwardes vnt [...]ll that you may see and serue it truely, the toppe of the shippe iust with the vpper plate, and the lower part [...]f the shippe harde vnto the water with the edge of the lower winge or plate: and that doone, then looke howe many times the wydenesse betweene the two plates that the transuastorie is from the end next vnto your eye, so many times the height of the toppe downe vnto the water as that commeth vnto, shall bee the true distaunce betweene the two shippes: which you shall worke in this manner: First, the number of feete that the other shippe is from the toppe vnto the water beyng knowne, then looke howe many tymes the distaunce of the two wynges or plates bee a sunder, then looke how many times that quantitie the Transuastorie is from the ende nexte vnto your eye, then doo thus multiplie the number of feete from the toppe vnto the water, by the number of the distance betweene the two plates or wynges from the ende nexte your eye: and then looke what that number commeth vnto, and then deuide that by .60. and so many scores the two shippes bee a sunder iustly.An ensample. As for an ensample thus: by a shippe that was founde by the order before rehearsed, to bee .65. foote from the toppe of the toppe Matte vnto the water, and the two winges or plates were set iust an ynche asunder. And then in the obseruyng the Transuastorie was remouyng forwardes and backwardes vntyl that he dye see the toppe of the Maste, and the lower parte of the shippe harde vnto the two plates or winges: and that doone, then he looke [...] how many ynches the Transuastorie was from the end nexte vnto his eye, and founde it .54. ynches iust. Wherefore he multiplyed .65. by .54. for that .65. foote was the height of the toppe vnto the water, and the plates or winges were iuste one ynche asunder, and the Transuastorie .54. ynches from the e [...]e [...] and of that multiplication there commeth 3510. Wherefore deuide that .3510. by .60. and that will shewe vnto you the number [Page 26] of scores, and that .3510. deuided by .60. there will stande in the quantiue lyne .58. and .30. remayneth ouer. So that you may conclude, the distaunce betweene the two shippes to be iust 58. score and .½. and by this order you may know the true distance betweene any two shippes. &c. And yet for your better vnderstanding, I will giue a second ensample more easier to be vnderstood,Another ensample. by a shippe that was iust .60. foote from the toppe vnto the water, that being a iust score and no more, the two winges or plates being iust one ynche a sunder, and the shippe being obserued and was founde to bee where as the two plates did agree with the toppe and the lower part, that the Transuastorie was .40. ynches from the ende. Therefore they maye conclude that the distaunce betweene the two shippes was iust .40. score, for that the toppe of the maste vnto the water was iust one score: that is .60. foote, and the two plates or winges iust one ynche a sunder, and the Transuasitorie .40. ynches from the ende. &c. And also by this order you may knowe the distaunce of any shippe from the lande. &c. And thus I doo ende the conclusions of the Crosse staffe. &c.
¶The fifteenth Chapter sheweth vnto you, howe you shal make an instrumēt wherby you may describe a Region or Countrey, which you may call an Horizontall Sphere: and also howe to take the plat of any ground. &c.
NOwe furthermore, I thinke it conuenient to shewe vnto you the making of an instrument, whereby you may describe a whole Countrey at sundry stations or standings: which is verie meete and necessarie for all men that doo seruice to theyr Countrey, and principally for Generalles and Captaynes, and especially for all them that take [...]harge t [...] [...]ee leaders of men. The instrument is muche lyke [...]o the backside of an Astrolobe, but that it hath no Scal, and yo [...] shall make it in this manner. First, take a peece of well seasoned bordes ende [Page] of a foote square,The making of an instrument to describe a Countrey. & thē make it round: or else you may make it in metall, the larger the better, making it perf [...]t rounde. And then deuide the circumference or edge into .360. degrees or equall partes: and then in like manner deuide it into .32. equall partes, & name them as you do the .32. poyntes of a sea mans Compasse, and then make a hole in the center of the instrument, and thē make an Athelida with .2. sightes, such a one as an Astrolobe hath in all poyntes, and there make it fast with a pinne to the middle hole of the instrument, and then in one of the sides eyther to the North or South poynt, place a needle, such a one as a Dyall hath, and this instrument is finished. As by this figure following is represented.
[Page 27] Now foloweth the vse of this instrument, which is, for to describe a Region or Countrye, and for to knowe the distaunces from one place to an other: very meete for Cherography or Topography, to make a Carde or Mappe for any Countrye, or to know the dystaunce from one Towne to an other, and also to know towardes what part the Towne or Village doth beare from the one to the other, by the help of two stations or standings, made vppon some high grounde, as some Hill or some high Towre, where that you may see all the coste of the Countrye rounde about you, as thus: Fyrst, take the instrument and goe vppe vnto some high Hill or Towre, where that you may see all the Countrye rounde aboute you, and then draw into a peece of paper a Circle with a payre of Compasses, and then draw a Meridian Lyne, and then deuide the Circle into 32. equall partes as the instrument is, and then laye the instrument vpon some stoole or thing flatte afore you, and then set it with the needle due North and South, and so let the instrument stande without any remouinge: then turne the Athelida or Rule with the two sightes, to such Townes or Villages or hils, or Churches, as are within the Argle of sight, and looke thorow both the sightes of the Athelida, and see what Towne or marke that you doe see.
Then resort to your Paper, and looke vpon the instrument at what poynt and degree the Athelida is standyng on, then vpon the point and degree of the Circle wryte the name of the towne, or Village, or Hyll, then turne the Athelida to the next marke: and so foorth, tyll you haue taken all the townes and Villages rounde about the Countrye or Coastes that be within the Angle of sight, and write the names of all those townes at the poynte and degree that the Athelida doth stande vpon, at the tyme of the takyng of them with the 2. sights.
And furthermore, write in the paper the 4. principall windes, as easte, weste, northe, and southe. Euen as the coaste of the countrye dothe stande: and then drawe righte lynes from the Center of the Circle too the Circumference, to the place where the names of the townes were written, and so passinge right to the edge of the Paper.
[Page]And thus doe by euery towne written on the edge of the Circle, and then that station is finished. And then furthermore, looke to what place that you doe meane for to goe vnto for to make your seconde station, beinge one of those that you haue obserued afore. For the fyrst obseruation is to no purpose: so that you must of force haue 2. And then vpon that Lyne that the name of the towne or Hyll that you doe meane to goe vnto, sette one of the feete of the compasses, and with the other foote of the compasses make an other circle in lyke maner: then draw an other Meridian Lyne, and be sure that both the Meridian Lynes doe agree the one with the other, and so deuide that circle into 32. equall partes, as the other was in all poyntes: and then goe vp vnto some high place that was the marke before, and then lay your instrument afore you agayne, setting it by the needle due South and North, and so let the instrument stande.
The second obseruation.And then turning the Athelida to suche townes as were taken before, looking thorow both the sights were where the Athelida doth stand, and write the names of those townes agayne vpon the edge of that circle at the poynt and degree that the Athelida doth stand vpon: and doe thus tyll that you haue taken all the townes that were obserued at the fyrst standings: and then drawe right lynes from the Center of that Circle, by the edge of the Circle, to the names of those Townes that were written, and so the lynes for to runne right to the sides of the Paper. Then looke where that the lynes doe crosse, there make a marke: for there standeth the Towne or place that you haue obserued.
And now in lyke maner, yf you lyst, you may know the distaunce from one Towne to an other, as thus: fyrst, you must measure the distāce betwen any one towne to another: & that groūd being measured,To know the distaunce vnto any place. you must make a Scal or tronke of mesure on the side of the paper, and then measure the distaunce betweene those 2. Townes in the paper: then according to that proportion of measure make your myles in the Scall or tronke of the Carde or Mappe: and that beynge doone, you may knowe the distaunce with a payre of Compasses betweene any one Towne or Townes to the other, by the Scall of the Carde: and then this beyng doone, you may make [Page 28] that fayre in an other thing without lynes, and bewtyfye that at your pleasure, as for example thus, by the partes or countrye about Grauesende.
Fyrst, I tooke the Instrument, and then in lyke maner I made a Circle in a sheete of paper: then I drew a Meridian lyne,An Ensample. that is to saye, a lyne from the South to the North: and I deuided the Circle into 52. equall partes, and then I wrote the 4. principall windes in the foure sydes of the paper: that is to saye, the East, West, North, and South: and then I went vp to a Hyll that standeth besyde Grauesende, called Ruggon Hyll, and there besyde the Myll I made my fyrste standinge: and then I obserued al those Townes and places folowing: Fyrst Clyffe Church, and that I tooke Northeast and by East, and the sixt part of a poynte to the Eastwarde: the next was West Tilbrye Churche, North, and ¾. of a poynt to the Eastwardes, and then I tooke the Bulwarke of West Tilbrye, North, and ¼. of a poynte to the Westwardes: and then I tooke Brauesende Churche steeple, North and by West, and ⅔. partes of a poynte to the Westwarde: and then I tooke little Thurrock, Norwest and by North, and the 6. parte of a poynt to the Westwarde: then I tooke Grayes Thurrock Northwest, and the 6. part of a poynt to the Westwarde: & then I tooke Sainct Clements Churche, West, Northwest, and ¼. to the Northwardes: then I tooke North fleete Church, West and [...]/4;. partes of a poynt to the Northwards: then I tooke Swankam Churche, due West: then in lyke maner I tooke the Vinyard Mill, West, Northwest, and ¼. parte of a poynt to the Westwardes: then I tooke Mappam Church Southwest, and ⅕. part of a poynt to the Westwardes: then I tooke Cobbam Churche, Southea [...]t, and by South, and ⅕. parte of a poynte to the Southwardes: then I tooke Shorne Myll, East, and by South, and ⅖. partes of a poynte to the Southwarde: Then I tooke Chaulke Churche, East, and ⅖. of a poynte to the Southwardes: and so I make an ende of that standing.
And now I chose out for my secōd stāding, West Tillary church, & I dyd draw a Lyne frō the Center of the Circle to the Circumference [Page] of the Circle, to the title of Tilberye Churche beinge North, and ¾. of a poynte to the Eastwarde. the Lyne passynge ryght to the edge of the paper. And then I tooke a payre of compasses, and set the one foote of the compasses vpon that Line, and with the other foote I made a Circle: and then I made an other Meridian lyne by the other in the other Circle, so that the one dyd agree with the other: and then I deuided the Circle into 32. equall partes, and then I went ouer the water to West Tilbery Church, and then I layde my instrument before me, and set it due North and South, and there I obserued al the townes and places before named: as Cliffe, East and 1/ [...]. parte to the North: Shorne Myll, and Chaulk Church, South East & by South, and ½. parts to the Southward. Cobbam Churche, South and by East, and ⅙. part to the Southwards.
Ruggon Hill, the Mille South, [...] ¾. to the Westwards. Mepham Church, South and by West, and ½. to the Westwarde. Tilberye Bulwark and Grauesend, South, Southwest, and ½. to the Southwardes. Northe Fleete Churche: Southwest, and ¼. to the South. Swanskam Churche, Southwest, and ¾. to the Westwarde. Saint Clements church, west, and by South, and ⅛. parte to the West. Grayes thurrock, West, and ⅔. partes to the South. Litle Thurock, West, and ⅖. partes to the Southwarde. The Vineyarde Mill, West, and ⅕. part to the Southwarde. And so I make an ende. And then I drew lynes from the Center of the Circle to the Circumference, to the title of the names of the Townes, and so I passed by the right lynes to the furthest partes of the paper, fyrst vpon the one Circle, then vppon the other, tyll that I had drawne so many Lines as that there were Townes in both Circles: and there where that the Lynes dyd crosse the one the other, I made a marke: For there standeth the Towne, as by this Ensample it doth appeare.
The .16. chapter sheweth you how for to make a Trouke or skalle of measure in a mappe or Carde, whereby you may know the distance in myles that it is from one towne to an other.
Now this being done, you may know the distance from any one towne to an other. For as many townes as you haue obserued, and if you lyst you may goe from place to place, tyll that you haue obserued and taken all the Townes in a whole region or countrie, as thus: first measure the distance in myles frō any one towne to another, then that distance being knowne, make a Tronke or Skall of measure with a pare of compasses, according to the distance taken with the compasses betwene those .2.How to make a tronck or Skal of measure to know the distance frō any one towne vnto another. townes in the paper. Then that being truly diuided into myles and halfe myles, and quarters of myles, then you may know the distance from one towne to an other thorowe all a whole region or countrye, by the replying it with a payre of compasses, as you maye perceaue by the rule or Skall made vppon the other side of the paper: and the roundles with the prickes in the middle, be myles: and the prickes measured betwene them, is one quarter of a myle: as ensample, for the makyng of a Tronke or Skall. First, I measured the distaunce between Northfleete Church & Grauesend Church, & found the measure vpon the right lyne a myle and halfe a quarter: and then I made a Tronke of Skall in the card, as thus: then I toke a payre of compasses, and measured the distance from the crossing of the .2. lynes of the .2. circles of the Tytle of Grauesende, and the Tytle of Northefleete: and then I finding the measure to be a myle and .⅛. partes of a myle, I did rebate the .8. part of a myle: and then that which did remayne was iust a myle: and then according to that proportion of measure, I made a Skall or Tronke of measure on the side of the .2. Circles, and deuided it into .4. equall parts, and euerie one of these parts to be one quarter of a myle, as by the demonstration afore made, it doth appeare. Now whensoeuer that you do desire for to know the distance from any one [Page] towne to an other,An ensample how to reply a payre of compasses to know the distance vnto any town assygned in any carde or Map. then take your compasses, and open the compasses to the widenesse betwene the .2. townes, that the one foote might stande vpon the one Towne and the other vpon the other. Then set your compasses to the Skall or Tronke of measure: there shall you see the distance of myles open with halfe myles and quarters of myles: as for ensample this, by certayne places afore named, which is (Clyffe Church, and the vinyarde mylle,) and the third to be Grauesende. And the vinearde mille, and Clyffe church, the one beareth from the other by a right lyne East & west. Clyffe Church a quarter and halfe a poynt to the Northe of the East, and the vinyard mille a quarter of a poynt to the South, of the west, and the distance betwene them by a ryght lyne, ouer the water and the land .8. myles and .⅖. partes of a myle: and Clyffe Churche beares from Grauesende, East, Northeast, and to the North: and the distance ouer the water and the lande by a ryght lyne, 4. myles and ⅙. part of a myle. Then the vinyarde mill bare from Grauesende, West and by North, and part of a poynt to the North: and the distance to the mill from Grauesend .4. myle and .¾. partes of a myle: as by this ensample it dothe appeare. And now you knowing the distance vnto any place assygned, you may know the height of any hill, or the deepnesse of any valley, by the order declared in the Chapter there by the Scall, or els by the degrees. &c.
The vinyard myll.
The .17. Chapter sheweth vnto you how you may make a carde or mappe for any countrie, placing in it the true Longitude and the true Latitude: And also how for to know the true longitude and the true latitude.
NOw furthermore, if that you liste, you may make a carde, & bewtify it at your pleasure, & make it fairer, & you may drawe the longitude and the latitude of euery place, as thus: first, you may take the distance of euery Towne and Village, and Hill, or any other notable marke whatsoeuer it be, and then make a marke for the name of such a Towne, according to the obseruation that you haue obserued afore: bothe the distance, and towards what coste of the contrey the Towne doth declyne, according to the crossing of the .2. lynes, placing in it the principal ryuers or waters: and then in the very midle of the mappe or carde make a Meridian lyne, to the intēt for to rule al the rest of the work. And then in the margent of the card, from the South to the North,How to make a carde or pl [...] Tipograph [...]e and to place the longitude and the latitude in it. vpon both of the edges of the mappe or card, place the latitude of the country, (that is to say) at how many degrees that the pole Artick is lyfted aboue your Horizon, as you may know it by your Astrolobe, by the altitude of the same vpon the Merydian lyne, knowing what declination, the Sun hath vpon that day of the moneth that you take the height of the Sunne.How to take the latitude of any place. And then if that the Sunne hath North declination, you must substract or pull away the Suns declination with degrees and minutes: & if South declination, you must adde or putte to the Sunnes declination with degrees and minutes: and then that which shal remayne shall be the altitude of the Equinoctial. Then pull that sūme out of .90. degrees, with degrees and minuts: the remaynder shalbe the height of the North pole Artick aboue the Horizon.
And furthermore, you may know the latitude of any Towne or Countrey by the starres of the South, or starres of the North, knowing there iust declination from the Equinoctial, dooing by them as you doe by the Sunnes declination in all poyntes. And then if that they bee Northern Starres, you mu [...]t knowe the distaunce [Page] from the pole, and then if that the starre be aboue the pole then you must pull that sūme away with degrees and minutes. And if the starres at the time of your taking of them, be vnder the North pole, then put to that which is the distance of the starre from the pole, vnto the height of the starre: and that in lyke manner shall shew vnto you the true height of the North pole Artick aboue the Horizon. And then in the margine of the mappe of the East syde and of the weast side, you may write the latitude directly, in that East and west lyne of that place which you haue obserued the latitude of the North pole: and then that being truly knowen, you may knowe the true latitude of all the townes in a whole countrie or Region, knowing the distance to euery towne or place, as thus. Euery .60. myles going directly South and North, doth answere vnto one degree.
And then further, if that you would place the longitude, and that you cannot get without a globe, or else a Carde Cosmographye, or else you must followe some author who hath written thereof, and bycause you cannot get the longitude with no instrument, for that the whole frame of the firmament with all the lightes therof be caryed round about in 24. houres, so that there remaineth no marke nor lyght that standeth still, but onely the two poles of the worlde: therefore I will shew vnto you how that you may get the longitude with a globe or Carde Cosmographye, so that it be truely placed in it.
How to know the longitude.First you must measure the longitude from the Meridian of the Canarie Ilands, or other wise called the fortunate Ilands, and so take the number of degrees from that place vnto any other that hath that same Meridian that your Towne or place hath: and that shalbe the number of the degrees for your place.
And then you hauing one place true, you may finde the iust longitude in a whole region or countrye.
But there is one speciall thing to be noted, and that is this: The degrees of longitude be not so many myles in length as the degrees of latitude. For as those places that be to the south partes of thys syde or vnder the Equinoctiall be as longe as the degrees of latitude, so that to any of the 2. poles shorter & shorter, [Page 31] as I haue declared in the .16. Chapter of my booke called the Regement for the Sea, as by this Ensample it doth appeare, by the Realme of Englande.
Nowe whensoeuer that you doo desire to knowe the longitude and the latitude of any towne or place in a carde, after that the Mappe or Carde is drawne, then doo this: First, by the ensample afore made, holde a lyne or a string,How to know the longitude & the latitude in a Carde or Mappe. the Map lying flat & playne vpon a table before you. And first for the latitude, holde the lyne East and West ryght ouer the towne and place, then by the ensample afore made, you doo see the latitudes be vpon the East side, and vpon the West side: then by the lyne you shall know how many degrees and partes of degrees, the Pole is raysed aboue the Horizon. And then in like manner for to knowe the longitude of any towne in a Mappe or Carde, then hold the lyne due South [Page] and North right ouer the towne or place whose longitude you doo desire for to know: and for to hold it due South and North, which is called your Meridian lyne, you must doo this: For that the degrees be shorter to the North partes, then they be to the Southe side or partes of the Mappe or Carde, therefore you must seeke the number of degrees both at the South side and at the Northe side all at one time: holding the lyne proportionable right ouer the towne: that is to say, halfe degree for halfe degree, and quarter for quarter, and so forth to the least part of a degree.
The eighteenth Chapter sheweth vnto you how you may place all the principall riuers or waters truely in anye Carde or Mappe.
NOw furthermore, as it is sufficiently declared before, how for to describe or draw a Map or Card, for a whole region or Country, and also how to fynde the distaunce from one Towne to an other: therfore for that it is one of the speciall matters, in lyke maner to drawe or describe the principall ryuers or waters within a Region or Countrye into a Mappe or Carde: therefore after that you haue obserued all the notable Townes and places worthy of memory, then yf you canne take a Boate and so go all the whole length of the water or riuer in the very midle betweene both the landes, and then with a Maryners Compasse you may see how that the riuer doeth trent or turne: then you hauyng the obseruation about you, then you may knowe how long that the water doth trent by that poynt, or winde by the markes of the lande,How to place the riuers or waters in a Carde or Map whiche you haue afore obserued: and then so often as the water doth turne or Compasse about, you shall see by your Sea mans Compasse, and howe muche: and still you shall know the length by the marke vpon the shore.
And then you must draw a crooked lyne into the Paper that you haue noted those Townes and places, in the Region where that the pryncipall places be, according to the crossing of the 2. lynes, [Page 32] in euerye place the crooked Lyne to bee made accordinge to the trentinge of the Riuer or Water, and euery treminge to bee according vnto that poynt or Wynde that the Compasse dyd shewe to you: and this being done, you may knowe the wydenesse of the Water by the obseruation afore taken, and then you may draw your Plates, and so bewtifye it at your pleasure, takinge the crooked Lyne from the verye middle of the Water.
❧A Table of the Contents of the first part of this Booke called a treasure for Trauailers.
FIrst to the Reader of thys first part.
The firste Chapter of the first parte conteyning the makyng of the Quadrant with the Skall, whereby you may knowe the height or lownesse of any thinge.
The Seconde Chapter is of vpright shadow, that is to saye, to knowe the heighte of all thinges taken within the length of the thinge.
The Thirde Chapter sheweth howe for too knowe the heighte of anye thinge with the Skall by contrarye shadowe, that is to saye, without the length of any thinge so taken.
The Fourth Chapter sheweth howe to take the part of any height, as the length of a window or such lyke.
The fyfth Chapter sheweth howe for to knowe the distaunce of manye thinges that is from you, and also whether any other Towre be higher or lower then the Tower that you be vpon.
The Sixte Chapter sheweth howe for to knowe the height of a Hill, and also the distaunce vnto the top of any hyll with the Skall.
The Seuenthe Chapter sheweth you by the Skall of the Astrolobe to knowe the true wydenesse of any Water, or howe farre that anye Shyppe is of from you, or to take anye great distaunce by layinge the Astrolobe flatte beefore you with the Skall vpwardes.
The Eight Chapter sheweth vnto you if that you doe knowe the distaunce, then you maye knowe whether it bee higher grounde or lower then the place that you are [Page] vpon, & how much, both by the partes of the Skall, and by the degrees, and also you may know whether that one Ship be hygher then another.
The ninth Chapter sheweth the makinge of a Crossestaffe that in some cases is better then the Skall of the Astrolobe or Quadrant.
The tenth Chapter sheweth how for to vse the crossestaffe, for to knowe the length of any wall or the distaunce betweene any 2. markes, and also the distance from you vnto any wall or marke.
The eleuenth Chapter sheweth you how for to take the length of a wall when that you haue not grounde large yenough for your .2. stations or standings.
The twelfe Chapter sheweth you howe for to know the distaunce vnto any 2. markes, or to the 2. endes of any wall, by the extracting of the square roote.
The thirteenth Chapter sheweth howe for to knowe the distaunce vnto any marke with the Crossestaffe, without the extracting of the roote, and also howe for to take the height of any thing with the Crossestaffe.
The fourteenth Chapter sheweth vnto you howe that you shall know the distaunce of any shippe from you, and you being in another shippe, and both the shippes vnder sayle and goyng, by the crosse staffe.
The fifteenth Chapter sheweth vnto you, how that you shall make an instrument whereby that you you maye describe a region or countrey whiche you may call a Horizontall, and also howe for to take the plat of any ground.
The sixteenth Chapter sheweth you howe to make a Trounke or Skall of measure in a Mappe or Carde, whereby you maye knowe the distaunce in myles that it is from one towne to another.
The seuenteenth Chapter [Page] sheweth vnto you howe you may make a Carde or mappe for any countrey, placing in it the true longitude, and the true latitude, and also howe for to knowe the true longitude, and the true latitude.
The eyghteenth Chapter sheweth vnto you, howe you may place all the principall riuers or waters truely in anye Carde or Mappe.
The Argument of the seconde Booke, of the Treasure for Trauailers.
The second booke of the Treasure for Trauaylers, shewing howe by the longitude and latitude of any Cytye, Towne or place, for to knowe the distance in myles vnto them, and also by what poynt or winde of the compasse they be from you. And also there is shewed in this booke, how dyuers notable Cyties, Townes or places, doe beare from the Citie of London, both in Europe, Africa, Asia and America, with sundry principall Ilands in the sea, both by what distance they be in myles from London, and what winde or poynt of the compas they are frō Londō, & also theyr longest day, & the diuersitie aspect, that is to say, howe much the Moone shal chaūge rather or later, then it doth at the Cytie of London: being very necessary for all sortes of traualers eyther by Sea or by Lande: Written by william Bourne.
¶To the courteous Reader.
FRiendely Reader, there is conteyned in this seconde Booke, how by the longitude and the Latitude, to knowe the distance vnto what quarter of the worlde that anye place assigned is from you: that is to saye how many miles, (according vnto our english accoumpt) and by what poynt of the Compasse anye Citie or Towne, or any other notable Place is from you wheresoeuer you bee, vppon the face of the whole Earth.
And for that the Citie of LONDON is the most notable, & the famousest place heere in ENGLANDE, therfore [Page] I haue thought it good, to assigne the Citie of London to be the place appoynted, how farre sundrye notable Cities and Townes, and other places worthy of memorye are from the citie of Londō, both their distance in miles, & vnto what quarter of the world they doe beare from the Citie of London, according to their longitude and latirude, accordingly as sundrye authors haue set downe their longitude and latitude: and also there is contayned in this second Booke, the diuersitie aspecte, that is to saye, how much that the Moone shall change rather or later, then it doth at London, according vnto the Longitude of the places that are mentioned in this second Booke: and also the length of the longest Sommer day at the places named in this secōd Booke, according vnto the latitudes of the places sette downe in this seconde Booke. And for that there is no person that hath trauailed generally through the face of the whole earth, therefore they must needes of force folowe such authours, as haue written therof, whether they be true or not: and therefore you must needs take thē as they be, for otherwise I know not how it is possible for to doe it, but onely to folowe the best and most Learned authors that haue written in those causes. And yet the learned men that haue bene afore time, must of force folow those that haue giuen vnto them the notes of the longitude and the Latitudes of any places that they haue not bene at them selues, whether they be true or not. And there bee a number of persons, who if they doe fynde but a small fault in any Booke, then by that meanes they will goe about to discredit the whole matter, often repeatinge the matter, yf they doe fynde any errour in it: as who shoulde saye, what a cunning man he is, although in all the rest of the whole booke, hee is not able to say any thing thereunto. And it may bee possible, that hee may haue no iudgement in the rest of the causes how necessarie so euer the rest of the substance of the matter is.
Wherefore (gentle Readers) if you doe finde any fault in [Page 2] this Booke, then gently geue me warning thereof: and if you doe amende the faultes therin contayned, then I shall bee the more beholding vnto you &c. For as touching the longitude and the latitude of places, men must credit those that haue beene there, for the trueth of the matter: and yet euery man that hath bene at any place, cannot do it, for the .100. person that hath trauailed vnto places, is not able to take the true latitude, but much lesse the longitude of any place. And furthermore, as touching the true distaunce vnto any place assigned, that cannot bee by any one poynt of the Compasse, as is declared in this Booke. &c. And thus (gentle Readers) I betake you vnto the almightye God for euermore.
¶The second booke of the treasure for Trauaylers.
The first Chapter of the Second booke, shewing you how for to know the distance vnto any Towne vpon the face of the earth, and what is to be considered in the doing thereof. &c.
NOwe beginneth the second booke, shewing by longitude and by latitude the dystance vnto any Towne, or Citie, or place vpon the face of the earth, keping one poynt or winde ouer the Sea and LANDE, although that it be not the very nearest way, for the very nearest way ouer the Sea and Land can not be by one poynt of the Compasse, except it be vpon the Meridian lyne, that is, due South or due North from you: or being vnder the Equinoctial, to be due East or West. But if it be in any other place from vnder the Equinoctiall, although it be due East or West,The nearest way ouer the Sea and Land is not by any one poynt of the compasse. both the places to be vnder one Paralell: yet in the going due East and West, is not the nearest way ouer the Sea and Land, but the next way ouer the Sea and Lande is, by diuers wyndes or poyntes of the compasse: and the further frō the Equinoctial to eyther of the two poles, the greater chaunging of the poyntes of the compasse. For the next way ouer the Sea and the Land, vnto any place, is to goe by the great circle which is equall vnto the Equinoctiall or the Meridian circle, which will not be according vnto any one poynt of the compasse, but vnto dyuers: as for proofe thereof you shall haue this for an ensample thus:An ensample. that in the latitude of .60. degrees that there were two Townes or places in that paralell, the one being opposite or right against the other, that is .180. degrees, and a degree in that paralel doth containe .30. myles. And nowe [Page 3] to goe iust East or West in that paralel, to come vnto the place assigned, it is .5400 myles: as for proofe therof, multiply .180. tymes .30. but that is not the next way vnto the place assygned: but the next way is to goe by the Merydian lyne, that is to say, to goe due North, vntill you do come ryght vnder the pole, and then to goe by that Merydian, due South, tyll you haue that latitude agayne: and then it is but .3600. myles, as you may knowe by playne multiplycation, as it is from the latitude of .90. degrees, vnto the pole, to go due North .30. degrees, and from the pole, Southward agayne, other .30. degrees, that is in all .60. degrees: and then to multyply .60. tymes .60. it sheweth the true dystance, which is but .3600. myles. And to goe by the paralell lyne, that is due East or West, then it is .5400. myles, that is halfe so much more, as by playne proofe you may know. But if the two places be both vnderneth one paralel, & be shorter thē 180. degrees asūder, thē it requireth to go by diuers points of the compasse, and not by the Meridian,The greatest compasse of the earth, 21600 myles according vnto the passing of the great circle, which doth conteine in circumference 21600. myles, which is the greatest compasse of the earth, and not according vnto moe paralels then one, which is the Equinoctial, nether vnto no one poynt of the compasse: for any poynt of the Compasse will bring you vnto the poles of the worlde, or verye neare, excepte those that be pararel, which is East or West,Al the points of the compasse wil bring you vnto the pole of the world except the East or West. as all ryght lynes drawe being extended, exceptynge lynes paralell, will Crosse the other in the ende: so all the poyntes of the Compasse doe winde vntyl they doe come vnto the poles or very neare the poles of the world, as they be all Hilicall or Spherall lynes.
Wherefore there is no one poynt or wynde, that can be prescribed to be the next way by that poynt vnto any place assygned, but onely the Meridyan lyne or lynes: and to goe East and West, then to be vnder the Equinoctiall, for the nexte way els is by sundry poyntes of the compasse &c.
Wherefore I omitte to say any more thereof, but onely to shew vnto you, how for to know the dystance vnto any Towne or place situated vpon the lace of the whole earth, by any one assygned [Page] poynte of the compasse, then for to knowe the true distaunce ouer the Sea and the lande. And I doo shewe it thys waye,You cannot passe the nearest way for it is thorow the frosen zones. for two causes, the first is this, for that it is not possible to passe the next way, by the meanes of the frozen Zone. Wherfore it is supposed, that it is not nauigable in those Seas, neyther passageable by lande in those Countreys: and the seconde cause is this, as before is declared, in the goyng the next waye, it dooth require to goe by sundry poyntes of the compasse, which woulde be but a confused matter, for the most part of those persons that doo desire to knowe the distaunce vnto any place assigned, neyther shall he knowe so readily which way it standeth, or beareth from him.
A confused matter to say a place dooth stand by diuers poyntes of the compasse.And furthermore, in the knowing the distaunce vnto any place assigned, and by what poynt of the compasse it beareth, this is to be considered, that the Longitude dooth begin at the Meridian of the Cannary Iland, and so to follow vnto the Eastwardes, and so ending at .360. againe at the Cannary Ilandes, as I doo shewe in my booke called the Regiment for the Sea.
The second Chapter sheweth vnto you, howe you may knowe the distaunce vnto any Towne situate vppon the face of the whole earth, so that you do [...] knowe the true Longitude and the true Latitude of them.
NOw furthermore, if that you doo know the Longitude and the Latitude of any towne or townes, situate vppon the earth, you may know the distaunce vnto them, as before is declared, as thus: If that the towne be iust East or West from you, that is to say, that your towne or place is vnder the Paralel that the other towne is,To know the distance of any towne from you, if that both the places are in one Paralel. that is to say, that the Pole artike of that towne or place is so manye degrees aboue the Horizon as your towne is, both in degrees and minutes: then shall you seeke how many degrees of Longitude, the other towne dooth differ frō yours: then you shall seeke how many myles that one degree shal answere vnto it, in that paralel, and then you shall multiplie the [Page 4] one by the other, that is to say, the degrees by the myles: and that summe which commeth of that multiplication, shalbe the distance betweene the two townes: as for ensample, thus: by the Citie of London & Answerpe in Brabant, which differeth but .4.An ensampl [...]. minutes in Latitude: for at London, the Pole is raised .51. degrees & .32. minutes, and at the Citie of Antwerpe, the Pole is raised .51. degrees .28. minutes, therefore we be both vnder one paralel. Now the Longitude of London is from the Cannarie Ilandes .19. degrees, and .54. minutes, and Antwerpes Longitude is .26. degrees & .36. minutes, so that Antwerpe standeth East from London .6. degrees .42. minutes. Now must I know how many miles a degree conteineth in that paralel, (and of that I doo make mention in my booke called The Regiment for the Sea, in the .16. Chapter) and that I doo finde to be .37. myles to one degree. Thē I multiplie .6. times .37. because that it is .6. degrees & .37. myles to one degree: and of that multiplication there commeth .222. Then there is .42. minutes more, and that .42. minutes conteineth neare .26. myles: so that the whole summe of myles from London to Antwerpe, by a right East line ouer the Sea, and the land, is .248. myles. Now furthermore, if that towne or place haue that Longitude that your towne hath, and hath another Latitude,To know the distance if that both the places are in one Merydian. that is to saye, that it dooth stande due South or North from you, hauing all one Meridian lyne, then must you looke howe manye degrees the other towne is Southe or Northe from your towne: and then you knowyng that, you maye knowe the distaunce to any Towne or place that standeth vnderneath your Meridian, allowyng .60. myles for euery degree of Latitude, as for ensample thus: by the Citie of London, and Roane in Normandie,An ensample. which hath in manner all one Longitude, as the Citie of London hath .19. degrees .54. minutes of Longitude, as afore is declared: so hath the Towne of Roane .20. degrees .3. minutes, which differeth 6. myles to the Eastwardes of the Meridian of the Citie of London, and as it is afore rehearsed, that the latitude of London is .51. degrees and .32. minutes, the Latitude of Roane is 49. degrees and .10. minutes: so that Roane standeth .2. degrees & .22. minutes to the Southwardes of the Citie of London.
[Page]And then multiplie .2. tymes .60 which maketh .120. and then there is .22. minutes more, then that commeth to .22. myles, so that .120. myles, and .22. myles, maketh in al .142. myles, the distance betweene the Citie of London and Roane, [...]uer the sea & land, by a ryght lyne betweene them. Now furthermore, if so be that any towne or countrie hath an other longitude and an other latitude, then yours hath, then to knewe the distance betweene thē, you must woorke thus: First, looke what latitude that your towne hath, and then looke the latitude of the other towne that you woulde knowe the distance vnto,Howe to know the distance, if that both the places doth differ both in longitude and in latitude, that is to say, yt is neither vnder your parallel nor Meridian. then that being knowne, you must seeke the longitude of the other towne howe muche it doeth differ from yours: then looke howe many myles of the latitude wyl answeare to one degree: then that number beyng multiplied, the number of degrees by the myles, and that sheweth howe many myles that it is from the Meridian of your towne to the Meridian of the other towne. Then the other towne hath an other latitude then yours hath, and if the towne bee to the Northwardes of your towne, then the degrees of that paralell, shall bee shorter then the degrees of your paralell, and if the latitude of the towne bee to the South partes of your towne, then shal the degrees of the parallel be longer then the degrees of the parallel of your towne. Then in like manner as you haue multiplied the number of myles by the degrees of your towne, so in like manner you shall seeke howe many myles wyll annsweare vnto one degree in that parallel: Then multiplye the degrees by the myles, and it wyll shewe vnto you the distaunce of myles from the other towne too the Meridian of your towne: then the distance of the Southermost towne, from the Meridian, is moe myles then the other towne is.
Therefore you shal adde or pull both your nūbers together, and then take halfe that for your East and West line, then shall you multyply the number of myles in it selfe, and keepe it in memorye: then you knowing the number of myles of Latitude, that the one Towne doth differ from the other, then in lyke maner you shall multyply that number in it selfe, then the multiplycation of [Page 5] both the numbers you shall adde together, then you shall by extraction of Rootes, seeke the square Roote [...] that being knowne, shall be the iust distaunce by that poynte or right Lyne ouer the Sea and the Lande, from the one Towne to the other: as for ensample thus:
By the Citie of London,An Ensample by Hierusalem and the Citie of London. and the Citie of Hierusalem nowe being destroyed, whiche was somtime the most famous Citie on earth, and the Latitude of London, as afore is declared, beinge 51. degrees 32. minutes, and euery degree of our paralell is 37. myles: and the Latitude of Hierusalem is 31. degrees, and 22. minutes, then for euery degree in that paralell, shall be 51. myles. Then I knowing the Longtitude of the Citie of London for to bee 19. degrees and 54. minutes, then I doe seeke the Langtitude of Hierusalem, and I finde it for to bee 65. degrees, and 45. mynutes. Then I doo pull away 19 degrees 54. minutes, out of 65. degrees 45. minutes, and then remayneth 45. degrees 51. mynutes, and so many degrees and minutes is Hierusalem Easte from the Citie of London. Then first I doe multiply the miles in a degree of our paralell, as this: beinge 45. degrees and 37. miles to one degree. Therefore I doe multiply the one by the other, that is 45. times 37. and of that multiplycation commeth 1665. then 51. minutes more, and that commeth neare vnto 32. miles: then put 32. vnto 1665. that maketh 1697. and so manye miles it is from the Citie of London vnto the Meridian lyne of Hierusalem.
And now you must multiplye the number of degrees into myles for the latitude of Hierusalem, whiche is 51. myles to one degree in that paralel, and the degrees be in number 45. degrees 51. minutes: Therfore I doe multyplye 45. by 51. and of that multyplycation there commeth 2295. Then there is 51. minutes more, and that commeth neare vnto 44. miles: and put 44. vnto 2295. and that maketh 2339. and so manye myles it is betweene Hierusalem and the Meridian lyne of the Citie of London. Then this being done, I doe adde both the numbers together, that is to say, the number of miles in the paralel of London betweene both [Page] the Meridians, the one being .1697. and the other for to be 2339. then addynge both these numbers together, maketh 4036. then take halfe that number for your true East and West lyne, whiche wyll be 2018. myles: then I doe seeke the diuersitie beeweene the 2. paralels as thus.
The pole artick of London is raysed 51. degrees and 32. mynutes, and the pole artick of Hierusalem is raysed 31. degrees and 22. minutes. Then I doe substract 31. degrees 22. mynutes, out of 51. degrees 32. minutes, the remainder is 20. degrees 10. minutes: then I doe multiplye the number of degrees by myles, 60. miles to one degree, because that they bee degrees of Latitude, thus .20. times 60. & of that multiplication commeth .1200. and then there is 10. mynutes more, and those 10. minutes commeth to 10. miles: so that the whole summe of myles from the paralel of London to the paralel of Hierusalem, is 1210. myles. And now for to fynde the true distance ouer the Sea and the land by a poynt or lyne: you must doe thus by the exctactions of rootes. Fyrst, you must multiplye the Longitude and the number of myles in it selfe, as it is afore rehearsed: the halfe of the miles of the distaunce betweene the 2. Meridians of both the Latitudes added together, that is to saye, as afore is rehearsed .2018. times 2018. and of that there commeth 4072324. Then multiplye the distaunce betweene the 2. paralels in it selfe, that is to saye, 1210. times 1210. & of that multyplycation there commeth .1264100. Then I must adde or put both these nūbers together, and these 2. numbers being both together,From Hierus [...] lem vnto London 2352. myles. and 25 26. are 5536424. This beinge done, you must extract the square roote of this number, and the square roote of 5536424. maketh 2352. And 4520/4704. parte, and that doeth contayne in myles from Hierusalem to London by a right lyne ouer the Sea and the Land 2352 miles, and neare 25/26. partes of a myle, the iust distaunce betweene Hierusalem and the Citie of London.A second Ensample by Venice and London. So that the longitudes and the latituds be true.
Yet furthermore, for your better Ensample, by the Citie of Venice, as the longitude of London is 19. degrees and 54. minutes, the longitude of Venice is 35. degrees 30. minutes. Therefore [Page 6] substract or draw 19 degrees 54. minutes out of 35. degrees .30. minutes, the residue shalbe 15. degrees, 36. minutes. Then Venice is 15. degrees .36. minutes, to the Eastwarde of London, then the latitude of London being 51. degrees and 32. minutes, the latitude of Venice is 44. degrees and 45. minutes. Then take 44. degrees 45. minutes out of 51. degrees 32. minutes, the remnaunt shall be 6. degrees 47. minutes. So that Venice is 6. degrees 47. minutes to the South part of London. Then you shall multiply the number of degrees of longitude into miles, and fyrst for the paralell of London, as afore is declared .37. myles to one degree: and the degrees of longitude being .15. degrees .36. mynutes, you shall multiplye 15. times 37. and that commeth to 555. Then there is 36. minutes more, and that commeth to 22. miles more. Then put .22. vnto .555. and that maketh .577. myles, the distaunce betweene London, and the Meridian of Venice. Then you must seeke how many miles wyll answer to one degree in the paralel of Venice, that commeth to 43. miles to a degree. Then multiply the degres of longitude by the number of miles in that paralel, that is 15. times 43. and that commeth to 645 then the 36 minutes more commeth vnto neare 26. miles.
Then put .26. vnto .645. and that maketh .671. so that it is .671. miles from Venice vnto the Meridian of London. Then put both these numbers together, that is to say, the distaunce betweene the Meridian of London and the Meridian of Venice, in the paralell of London, and the paralell of Venice, the one beinge 577. myles, and the other 671. miles: and those 2. numbers being both together, maketh 1246.
Then take halfe that number for your East and West line, & that commeth vnto 623. And now I doe conclude, that Venice is East from London 623. miles. Then you must multiplye the degrees of latitude into miles 60. myles to one degree, and the Latitude of Venice being 6. degrees to the South parte of London: therfore I multiply .6. times .60. and that commeth vnto .360, then there is 47. minutes more, and that maketh .47. miles: then put 47. vnto 360. then it wyll be 407.
[Page]This being done, multiplye the myles of longitude in it selfe, as 623. times 623. and that commeth vnto 388129. Then multyplye the latitude in it selfe, that is to say, 407. times 407. and that commeth vnto 165649. then adde or put both these numbers together, that is to saye, 388129. and 165649. and that maketh 553778. And now you must seeke the square roote of both these nū bers added together by extracting of rootes, & that wil be 744 & [...]2/744. part, and that it is neare ⅙. part of a myle. So I doe conclude that the distaunce from Venice to London, by a right lyne ouer the Sea and Lande, is 744. myles, and ⅙. part of a myle: so that the longitude and the latitude be truly taken.
And thus may you doe by all other Townes and places situate vpon the face of the whole earth, whether that the distaunce bee much or litle: so that you may knowe the true longitude and the true latitude, and so resort to the true length of the Paralel as afore is declared.
The thirde Chapter sheweth how for to knowe vnto what quarter of the World any place doth stande from you, that is to saye, by what poynte of the Compasse, you knowinge the true Longitude and the true Latitude &c.
ANd furthermore, you knowinge the true longitude and the true latitude of any Towne vpon the face of the whole earth, then you may know vnto what quarter of the worlde it doth beare or stand from you: that is to say, by what poynt of the Compasse, as this: If athat any two places haue both one longitude, that is to say, one Meridyan line, & hath an other latitude, that is to say, that the North pole is raised more degrees then yours is, then it is North from you: if fewe degrees, then that beareth South from you.
[Page 7]And also if that it hath your longitude, and haue the South pole,North or South. aboue the Horizon, then in lyke manner the place is due South from you &c. And furthermore, if any two places haue all one latitude, and hath another longitude, being both in one paralel, and if that it haue more degrees in longitude, then your towne hath, then that Citie, towne or place, is vnto the Eastwardes of you. If fewer degrees in longitude, then your Towne hath,East or West. then it is West, from your Citie, Towne, or place, as in the Chapter going before is declared. If that it be more degrees in longitude then your Citie, Towne, or place hath, by .180. degrees, then that place is West from you, although both the places haue one latitude, that is to say, in one paralell. And then to knowe how many myles, you must first note the degrees of longitude that it hath from the Meridian of the Canary Ilande:Note. and then rebate that out of .360. and then adde or put vnto that number of the longitude of your owne place: and so multiply the number of myles in that paralel, & that shall shew vnto you the nūber of myles, that the Citie, Towne, or place is vnto the Westwarde of your place, and the reason thereof is this, for that the circumference of the earth is to goe from the East vnto the West, is .360. degrees: and halfe that number is .180. degrees. And then if that it be more degrees then it is Westwardes from you,360. degrees is the Compasse of the earth. and if that it be but iuste 180. degrees, then it is opposyte or ryght against your place that is neither East nor West, nor no poynt of the compasse els, if that both the places were vnder the Equinoctiall, or els if that the one haue the North pole, and the other haue the South pole, both of one altitude, or heyght aboue the Horizon. For then the one should be Antipodies the one vnto the other, that is to say,What Antipedies are, that goe foote vnto foote▪ the one to goe foote vnto the foote of the other, the one of the one side of earth, and the other on the other side of the whole earth, & to haue the whole thicknes of the earth betweene them. &c. And furthermore for to knowe by what other poynt or wynde of the Compasse that any place dooth bears, then that is thus knowne: the two townes or places to differ both in longitude and in latitude, then as in the Chapter going before is declared, it is knowen, by this order following. If that it haue fewer degrees in longitude then [Page] your place hath, and fewer degrees in latitude in lyke manner, then it is according vnto the degrees, and especially vnto the number of myles, as thus: If the place be shorte in longitude, and also in latitude, and both in lyke quantitie, that is to say, in the iust number of myles, that it bee no more myles from the Meridyan of the two places then that it is from the paralell of the two places,In the Southwest quarter. then that place is Southwest from you iust. And furthermore, if that the distaunce in myles betweene the two paralelles be .5. times the distance between the two Meridians, then that place is South and by West. And furthermore if the distance in miles, between the two paralelles of any place assigned, be two times & a halfe so many myles, that is to say, ⅖. part of the distāce between the two Meridians, thē that place is Southwest frō your places. And if that the distance between the two Meridians be .3. quarters of the nūbers of myles between the two paralelles, then that place is Southwest & by South from your place. And if that the distance between the two paralels, be but .3. quarters of the nūber of miles between the two Meridiās, thē that place is Southwest & by West from your place. &c. And furthermore, if that the nūber of miles between the two paralelles be but .⅖. partes of the number of miles between the two Meridians, than that place is West Southwest frō your place. And furthermore, if the distance between the two paralels of any place assigned, be but the .5. parte of the nūber of miles between the two Meridians, that is to say, that the nūber of miles be .5. times that nūber of miles betweene the two paralelles, thē that place is West & by South from your place. &c.
And furthermore, if that any Cities, townes, or places, bee more degrees in longitude thē your Cities townes or place is, & fewer degrees in latitude, thē al those places shalbe in the Southeast corner, as al the other before rehersed, were in the Southwest corner,In the Southeast quartes. as thus: The degrees multiplied into myles, both the longitude & the latitude, as in the chapter goyng before is rehearsed, then if that the nūber of miles of the distance between the two parallels be equal vnto the nūber of miles between the two Meridians, thē that place shalbe iust Southeast frō your place. And furthermore, [Page 8] if that the distāce of miles betwen the two Meridiās, be but the .5. part of the nūber of miles between the two paralelles, then that place is South & by East frō your citie, towne, or place. &c. And if to .5. partes, that is to say, that the nūber of myles between the two paralelles is more then the nūber of miles betwene the two Meridians, by double & halfe so much more, thē that place is South, Southeast frō your place. &c. And furthermore, if that the nūber of miles between the two Meridians be but .3. quarters of the nūber of miles between the two paralelles, thē that place is Southeast & by South frō your place. &c. But if that the nūber of miles between the two paralelles be but .3. quarters of the nūber of miles between the two Meridians, thē that place is Southeast & by East frō your place. &c. And if that the number of miles between the two paralelles be but .⅖. parts of the nūber of myles betwen the two Meridiās, thē that place is east, Southeast frō your Citie, towne, or place: &c. If but .⅕. part of the nūber of miles between the two Meridians, then that place is East and by South from your place. &c. And furthermore, if that any place be more degrees in longitude, & also in latitude, then your place is, then those Cities townes or places are in the Northeast quarter.In the Northeast quarter. And (as before is rehearsed) if that the nūbers of myles, be equall both betweene the two paralelles, & the two Meridians, thē that place is Northeast from you. And also if that the number of miles between the two Meridians be but the .5. part of the nūber of miles between the two paralelles, then that place is North & by East: if ⅖. parts, then North Northeast: if ¾. then Northeast & by North. &c. And if the number of miles betweene the two Meridians bee more then the number of myles between the two paralelles, that is to say, the number of myles to be but .⅓. part, then that place is East and by North: if .⅖. partes, then East Northeast: if .¾. then Northeast and by East from your place. &c. And furthermore, if any place hath more degrees in latitude and fewer degrees in longitude then your place, then those places be in the Northwest quarter.In the Northwest quarter, And (as before is rehearsed) if the number of myles bee equall both betweene the Merydians and the parallelles, then that is but Northwest: and if the number of myles be lesse [Page] betweene the Meridians, then it is betweene the paralelles, then (as before is sayde) if it be but .⅕. parte, then it is Northe and by West: if .⅖. partes, North Northwest. If . [...]/4. partes, Northwest and by North. But if it be not so many myles betweene the two paralelles, as it is betweene the two Meridians, if .⅕. partes, that place is West and by North: if .⅖. partes, West Northwest: if ¾.An ensample by Rome and London. then Northwest and by West frō your place. &c. And for your better instruction, you shal haue ensample by the Citie of London and Rome: and as before is declared, in the Chapter goyng before, that the latitude of London is .51. degrees .32. minutes, and the longitude .19. degrees .54. minutes, and the latitude of Rome 42 degrees iust, and the longitude .36. degrees .40 minutes. And (as in the Chapter goyng before is shewed) in the knowing of the distaunce is to rebate the lesse from the more: wherefore [...]ebate the longitude of London out to of the longitude of Rome, as thus: Rome being .36. degrees 40 minutes, in longitude: so London is .19. degrees .54. minutes. So that there is .16. degrees .46. minutes, betweene the Meridians of Rome and London. &c. And the latitude of London beyng .51. degrees .32. minutes; the latitude of Rome is .42. degrees iust. Wherfore rebate .42. degrees iust, from .51. degrees .32. minutes: then .9. degrees .32. minutes remaineth: so that there is iust .9. degrees .32. minutes betweene the two paralelles. And now to knowe by what poynt of the Compasse, doo this: Rome is to the East wardes of London .16. degrees .46. mi. for that it is more degrees in longitude. Wherfore you most seeke howe many myles that it is, first in your paralell, and heere at London .37. myles dooth answere vnto one degree: therefore multiply .16. times .37. and that commeth vnto .592. and then there is .46. minutes more, and that commeth vnto .28. miles, and better. Then put .28. vnto .592. and that maketh .620. so that you may conclude that it is .620. myles from London vnto the Meridian of Rome in the paralel of London. And nowe the latitude of Rome is .42. degrees, and then .44. myles maketh a degree in that paralel. Wherefore multiply .16. times .44. and that maketh .704. and then there is .46. minutes more, and that maketh .33. myles and better. Wherefore adde .33. vnto .704. & there [Page 9] it will be .737. so that you may conclude that it is from Rome vnto the Meridian of London .737. myles. Wherefore adde or put both these two numbers toge [...]her, that is to say, 620. and .737. and that maketh .1357. And nowe take halfe this number, and that will shewe vnto you howe many myles that Rome is to the Eastwardes of London, and that is .678. myles and a halfe: and nowe there is .9. degrees .32. minutes betweene the two paralelles, and 60 myles make a degree. Therefore multiply .9. times .60. and that maketh .540. and then take .32. myles more for the .32. minutes, & .32▪ put vnto .540. maketh .572. so that Rome is .572. miles vnto the Southwardes of London, and nowe for that Rome is more degrees in longitude then London, and fewer degrees in latitude then London, therefore then Rome must needes be in the Southeast quarter: and to knowe iust by what poynt, then looke what both the numbers be, as thus: Rome is vnto the Eastwards of London 678. myles and ½. and vnto the Southwardes of London .572 myles, then vewing the two numbers .572. is more then ¾. of 678. Therefore you may conclude, that Rome dooth stande from London, Southeast and by East, and somewhat declinyng or leaning more vnto the Southwardes: and if that the numbers had been equall, then it had been due Southeast. &c. And to knowe howe many myles by that poynt of the Compasse, that is shewed in the Chapter goyng before, and by this order you shall kn [...]w by what poynt of the Compasse that any place dooth beare from you. &c.
¶The fourth Chapter sheweth the Longitude and the Latitude, and by what poynt of the Compasse, that sundrye places within England and Scotland, and Ireland, and also of certayne Ilandes, neere vnto them, dooth beare from the Citie of London, and what distaunce of miles that they are from London, by the poynt of the Compasse ouer the water and ouer the lande. And also there is shewed howe muche that the Moone shall chaunge, rather or later then it dooth at London, and [Page] also it dooth shewe the length of the longest Sommers day, for as many places as be named.
NOwe furthermore, in so muche as I haue shewed vnto you how by the longitude and by the latitude, you maye knowe by what poynt of the Compasse that any place assygned beareth from you, and also at anye place assygned for to knowe the distance by that poynt of the compasse, that is to say, howe many myles that it is from you: so in like manner I thinke it good for to shewe the longitude and the latitude of sundry principall places vpon the face of the whole earth, according vnto diuers Authours that haue written thereof, and also for that the Citie of London is the principall and most famous place here in England,London is the principallest and the most famous place of England. I will declare or shew vnto you, by what poynt of the Compasse that any of those places doo beare or declyne vnto, from the Citie of London, and also howe many myles by that poynt ouer the Sea and London by that ryght lyne or poynt of the compasse. And also I doo thinke it good for to shewe vnto you the diuersitie aspect of all those places by the Citie of London,The diuersitie aspect at London. that is to say, howe much that the Moone shall chaunge rather or later then that it shall doo at the Citie of London, whereby maye be knowne the time of any Eclipse eyther of the Moone or Sunne, and also the aspectes of the Moone with the other planets, you knowing at what houre or tyme that it wyll happen or be at London.
And also I doo thinke it good for to shewe vnto you the length of the longest Sommer day in all those places that shall be named accordyng vnto the longitude and latitude,The length of the day. and then the length of the shortest Wynter daye is soone knowne: and the daye is ment to bee, from the Sunne rysing vnto the Sunne setting. For the latitude of places dooth alter the length of the daye, and the longitude dooth alter the tymes of the Eclipses eyther of the [Page 10] Sunne or of the Moone, wyth all the other aspectes, that the Moone hath with the Sunne or any other of the Planets. &c.
And nowe shall followe the longitude and latitude and the other things before rehearsed, of certaine places, and first for England, and Scotlande, and Ireland, with some Ilandes belonging thereunto.
And for that London is the assigned place the longitude therof from the Canarie Ilande beyng 19 degrees 54. minutes,London the assigned place. and the latitude or eleuation of the Pole beyng 51. degrees 32 minutes:S Michaelmount in Cornwall. and first this S. Michaels muount in Cornewall hath longitude .14. degrees .20. minutes, and latitude 30. degrees 40. minutes, and is West and by South from the Citie of London .210. miles, and the Moone shal chaunge rather then at London by .25. minutes, and the longest Sommer day is .16. houres .20. minutes long. &c.
Doner in Kent, the longitude .21. degrees .15. minutes,Doner in Kent. the Latitude .51. degrees .20. minutes, and is East and by South from the Citie of London .49. myles, and the Moone shall chaunge later then at London .5. minutes, and the longest day in Sommer is .16. houres .25. minutes. &c.
Barwick, the Northermost part of England,Barwick. standing vpō the edge of Scotland, the longitude .20. degrees .24. minutes, the latitude .55. degrees .58. minutes, and is North and a little declining vnto the Eastwardes .267. miles, and the Moone shall chaunge l [...]t [...]r then it doth at London .2. minutes: and the longest Sommer day is .17. houres .24. minutes long. &c.
The Citie of Yorke hath longitude .20. degrees,The citie of Yorke. and latitude 54. degrees .2. minutes, and is in manner due North from the Citie of London .150. myles, and the Moone chaungeth later then at London .7/5. part of a minute, and the longest Sommer day is neere 17. houres long. &c.
Carlell in Cumberland, the longitude .17. degrees .48. minuts,Carlell. the latitude .55. degrees .2. minutes, and is Northe, Northwest, 224. myles from the Citie of London, and the Moone chaungeth rather then it doth at London .9. minutes, and the longest daye in Sommer is .17. houres long. &c.
[Page] Edenborowe in Scotland.Edenborowe in Scotlande, the longitude is .19. degrees .50. minutes, and the latitude is .57. degrees iust, and is due Northe from the Citie of London .328. miles, and the Moone chaungeth neere about that time that it doth at London, and the length of the longest Sommer day is .17. houres .40. minutes long.
Catnes poynt.Catnes poynt the Northermost part of Scotland, the longitude .20. degrees the latitude 62. degrees, and is in manner due Northe from the Citie of London .628. myles, and the Moone chaungeth neere about that time that it dooth at London, and the longest Sommer day is 19 houres .25. minutes.
The Southwest part of Ireland.The Southwest parte of Irelande hath longitude .6. degrees, and latitude 52 degrees, and is West and somewhat vnto the Northward from the Citie of London .518. myles, & the Moone chaungeth rather then at London .55. minutes, and the longest Sommer day is .16. houres .30. minutes.
The Northpart of Irelande.The Northermostpart of Ireland hath longitude 13. degrees, and latitude .58. degrees 10. minutes, and is▪ Northwest and by North, & to the Northwardes 462. miles, and the Moone chaungeth rather then at London .27. minutes, and the longest Sommer day is .17. houres .55. minutes.
The citie of Deuelinge.The Citie of Deuelyng in Irelande, hath longitude .12. degrees .40. minutes, and latitude 54. degrees .40. minutes, and is Northwest and by West .296. miles, and the Moone chaungeth rather then at London .29. minutes, and the longest Sommer day is .17. houres .15. minutes long.
Sainct Patrikes porcatorye.Saint Patrickes Porcatorie hath longitude .8. degrees .42. minutes, and latitude .56. degrees .50 minutes, and is Northwest and by West .415. myles, and the Moone dooth chaunge rather then at London .45. minutes, and the longest Sommer day is 17. houres and .4. minutes long.
The Ile of Man.The Ile of Man hath longitude .15. degrees, and Latitude 56. degrees .4. minutes, and is Northe Northwest, and somewhat declyning vnto the West .358. myles, and the Moone chaungeth rather then at London by .20. minuts, and the longest Sommer day is, 17. houres 30. minutes.
[Page 11]The Ilandes called Sylley, hath longitude .12. degrees .24.The Ilandes called Silley. minutes, and the Latitude 50. degrees 54. minutes, and is West and by South from the Citie of London .278. myles, and the Moone chaungeth rather then at London .30. minutes, and the longest Summer day is 16. howres long 20. minutes. &c.
The fifth Chapter sheweth the longitude and the latitude and the other thinges before rehearsed of certaine of the principallest places in Europe, as in Spaine and Portugal, and Fraunce, and Italie and Germanie. &c.
ANd now shall folow the longitude and the latitude with the other thinges before rehearsed, of Europa, as Portugall, Spayne and France, and Italy, and Germany. &c.
And first Lyshborne in Portugal:Lyshborne in Portugall. and that hath longitude 5. degrees, and latitude 38. degrees 50. minutes, and is South Southwest 985. myles, and the Moone shall chaunge. rather then at the Citie of London neare an howre, and the longest Summer day is 14. howres 45. minutes.
Cape Saint Vincent in Portugall, the longitude .4. degrees 58.Cape Sainct Vincent. minutes, the latitude 35. degrees 36. minutes, & is South Southwest .1092. myles from the Citie of London, and the Moone chaungeth rather then at London, one howre: and the longest Sū mer daye is .14. howres .30. minutes. &c.
Cape Saint Mary, the longitude is 5. degrees .10. minutes,Cape Sainct Mary. the latitude .36. degrees .45. minutes, and is South Southwest 1089. myles from London, and the Moone chaungeth rather then at London .58. minutes, and the longest Summer daye is .14. howres 30. minutes. &c.
Cape Finester in Galeza, the longitude 4. degrees 50. minuts,Cape Finester. the latitude .43. degrees .10. minutes, and is Southwest and by [Page] South .788. miles, and the Moone chaungeth rather then at London one howre, and the longest Summers day is .15. howres 20. minutes.
Bayone.Bayone in Galeza, the longitude is 5. degrees 40. minutes, the Latitude .42. degrees .40. minutes, and is Southwest and by South 800. myles from the Citie of London, & the Moone chaungeth rather then at London 57. minutes.
S. Iames.Sainct Iames of Compostella, the longitude 7. degrees, the latitude 42. degrees 15. minutes, and is Southwest and by South 810. miles, and the Moone chaungeth rather then at London .56. minutes, and the longest Summers day is 15. howres 4. minutes. &c.
Bylbow.Bylbow in Bysley, the longitude .11. degres .45. minutes, the latitude .43. degrees .35. minutes, and is South Southwest .578. myles, and the Moone chaungeth rather then it doth at London .33. mynutes, and the longest Summer daye is .15. howres .30. minutes long.
S. Sebastins in Byskey.S. Sebastians in Byskey, the longitude is 15. degrees, the latitude .43. degrees, 30 minutes, and is South and by West .572. myles from the Citie of London, and the Moone chaungeth rather then at London 18. minutes, and the longest Summer day is 15. Howres 30. minutes.
Tolledo in Castell.Tolledo in Castell, the longitude 10. degrees .49. minutes, the latitude 37. degrees, and is South and by West 934. myles from London, and the Moone chaungeth rather then at London 36. minutes, and the longest Summer daye is 14. howres .36. minutes &c.
The Citie of Ciuell.The Citie of Ciuell in Andelazia, the longitude 7. degrees, the latitude 38. degrees .5. minutes, and is South & by west .950. myles, and the Moone chaungeth rather then at London 52. minutes, and the longest Summer day is 14. howres 40 minutes.
Gibaraltarre.Gibaraltarre, the longitude .7. degrees .30 minutes, the latitude 36. degrees 4. minutes, and is South and by West 1066. miles from London, and the Moone changeth rather then at London 49. minutes, and the longest Summer day is 14. howres .25. minutes.
[Page 12]Granmaliga, hath longitude 8. degrees .50. minutes,Granmaliga the latitude 37. degrees 30. minutes, and is South and by West 960. myles from London, and the Moone chaungeth rather then at LONDON .35. mynutes, and the longest Summer daye is .14. howres .4. mynutes.
The Citie of Granado hath longitude .9. degrees .5. minutes,Granado. and latitude .38. degrees .20. minutes, and is South and by West .911. myles from London, and the Moone chaungeth rather then at London 45. minutes, and the longest Summer daye is 14. howres 43. minutes.
Burdeux in Fraunce, the longitude .17. degrees .54. minutes,Burdeux in Fraunce. the Latitude 45. degrees .45. minutes, and is South and somewhat to the West 36. myles from London, and the Moone changeth rather then at London .8. minutes, and the longest Summer day is .15. howres 25. minutes.
Paris in Fraunce, the longitude is 23. degrees .30. minutes,Paris in Fraunce. the latitude is 48. degrees 40. minutes, and is South Southeast, .215. myles, and the moone chaungeth later then at London .13. minutes, and the longest Summer daye is .15. howres .57. mynutes.
Roane in Normandye, the longitude 20. degrees 30. minutes,Roane. the latitude .49. degrees .10. minutes, and is South and a litle to the East 142. myles, and the Moone chaungeth later a lytle then at London, and the longest Summer daye is .16. howres 4. mynutes. &c.
Calyce in Fraunce, the longitude .22. degrees .15. minutes,Calice. the latitude .51. degrees .15. minutes, and is East and by South 86. myles from the Citie of London, and the moone chaungeth later then at London 9. minutes, and the longest Summer day is 16. howres 25. minutes.
Brydges in Flaunders, hath longitude .24. degrees .30.Bridge [...] in Flaunders. mynutes, the latitude .51. degrees 20. mynutes, and is East .162. myles, and the Moone chaungeth later then at LONDON 16. mynutes, and the longest daye is .16. howres .16. minutes. &c.
[Page] Gaunt.Gaunt in Flaunders, the longitude .25. degrees .30. minutes, the latitude 51. degrees 15. minuts, and is East 209 miles, the moone chaungeth later then at London 20 minutes, and the longest day is 16. howres 13. minutes. &c.
Midleborow.Midleborow in Walkerlande, one of the Ilandes of Zelande, the longitude 25. degrees 26. minutes, the latitude 51. degrees 48. minutes, and is East 205. miles, and the moone chaungeth later then at London 20. minutes, and the longest day is 16. howres 30 minutes, &c.
Antwerpe in Braband.Antwerpe in Braband, the longitude is .26. degrees 36. mynutes, and the latitude 51. degrees 28. minutes, and is East, and somwhat bending vnto the South 248. myles from London, and the Moone chaungeth later then at London 24. minutes, and the longest Summers day is 16. howres 28. minutes. &c.
Amsterdam in Holland.Amsterdam in Holland, the longitude 27. degrees 5. minutes, the latitude .52. degrees .20. minutes, and is East and by North 266. myles from London, and the Moone chaungeth later then at London 28. minutes, and the Longest day is .16. howres .40. minutes. &c.
Lucke.Lucke, the longitude 29. degrees .30 minutes, the latitude 50. degrees, and is East 333. myles from London, and the Moone chaungeth later then at London 30. minutes, and the longest daye is 16. howres &c.
Gulder.The citie of Gulder in Gulderlande, the longitude 27. degrees 48. minutes, the latitude 51. degrees .42. minutes, and is East 296. myles, the Moone chaungeth later then at London .28. minutes, and the longest day is 16. howres 30. minutes. &c.
Cleue.Cleue in Cleueland, the longitude is .28. degrees .6. minutes, the latitude is 52. degrees, and is East 303 miles from London, and the Moone chaungeth later then at London .32. minutes, and the longest day is 16. howres 30. minutes. &c.
Collyne.Colline hath longitude 29. degrees 45. minutes, the latitude 52. degrees, & is East and by North 360. myles, and the Moone chaungeth later then at London 39. minutes, and the longest daye is 16. howres 34. minutes. &c.
[Page 13]The Citie of Mentz in high Germanye, the longitude .31. degrees 15. minuts, the latitude 50. degrees, and is East 420. miles,The Citie of Mentz. and the moone chaungeth later then at London .45. minutes, the longest day is 16. howres 25. minutes. &c.
The Citie of Spiers, the longitude 31. degrees 30. minutes,Spiers. he latitude 49. degrees .15. minutes, and is East and by South 430. myles from London, and the Moone chaungeth later then it doeth at London .46. minutes, and the Longest day is .16. howres 2. minutes. &c.
The citie of Strawsborow, the longitude 30. degrees 15.Strawsbrow. mynutes, the latitude .48. degrees .45. minutes, and is East and by south, and to the south .432. myles frō Londō, the Moone changeth later then at London .41. minutes, and the longest daye is 16. howres .0. minutes. &c.
Franckforde, the longitude .31. degrees .40. minutes,Francford [...]. the latitude .50. degrees, 10. minutes, and is east & to the south a litle, .448. myles from London, and the Moone chaungeth later then at London 47. minutes, and the longest daye is 16. howres 15. mynutes. c&.
The Citie of Prage, the longitude .38. degrees 20. minutes,Prage. the latitude .50. degrees, 6. minutes, & is East and a lytle to the south 700. myles from London, and the Moone chaungeth later then at London 1. howre 14. minutes, and the longest day is .16. howres .15. minutes. &c.
The Towne of Hambrough, the longitude 34. degrees,Hambrough. the latitude is 54. degrees, 30. minutes, and is East Northeast & to North .538. miles from London, and the Moone shall chaunge later then at London .56. minutes, and the longest daye is .18. howres iuste, &c.
Elson More in Denmarke, the longitude .32. degrees .30.Elson in Denmark. minutes, the Latitude .58. degrees 20 minutes, and is Northeast 577. myles from London, and the Moone chaungeth later then at London .50. minutes, and the longest daye is 18. howres 0. minutes. &c.
The North Cape, whiche is the Northermost parte of all Norwaye, hath longitude .39. degrees .30. minutes, and latitude [Page] .71. degrees 20. minutes, and is North Northeast 1308. myles, and the Moone chaungeth later then at London 1. howre 15. minutes, and the Sunne setteth not in the time of .78. dayes and nightes, that is 10. Weekes, when our dayes bee at the longest: and in lyke manner the Sunne wyll not rise in the tyme of .78. dayes and nyghtes in Winter in lyke manner. &c.
Iseland.Iselande vnder the King of Denmarke, an Iland, the myddle of it hath longitude 7. degrees, the latitude 65. degrees .30. minutes, and is North Northwest, 930. myles from LONDON, and the Moone Chaungeth rather then at London .52. minutes, and the longest daye is 21. howres 44. minutes. &c.
The Citie of Rome.The Citie of Rome in Italye, the longitude is 36. degrees 40. minutes, the latitude 42. degrees, and is Southeast and by East, 887. myles, and the Moone chaungeth later then at London .1. howre .7. mynutes, and the longest day is .15. howres .4. minutes.
Florance.The Citie of Florance, the longitude is 34. degrees 15. minuts, the latitude 24. degrees .45. minutes, and standeth from London Southeast a ly [...]le vnto the Eastwardes 802. myles, and the Moone chaungeth later .57. minutes, and the longest daye is .15. howres 10. minutes.
Pisa.Pisa, the longitude .33 degrees, the latitude is 42. degrees 15 minutes, and is Southeast 741. myles from London, and the Moone chaungeth later then at London 53. mynutes & the longest daye is 15. howres 6. minutes.
[...]nice.The Citie of Venice, the longitude is .35. degrees .30. minutes, the Latitude .44. degrees .45. minutes, and is East Southeast and too the Southwardes, 744. myles from LONDON, and the Moone chaungeth later then at London 1. howre 3. minutes, and the longest daye is 15. howres 20. minutes.
Millayne.The Citie of Myllayne, the longitude is .31. degrees .45. minutes, the latitude 44. degrees 15. mynutes, and is Southeast [Page 14] and somewhat to the Eastwarde 645. myles from London, and the moone chaungeth later then at London .48. minutes, and the longest day is 15. howres 22. minutes.
The Citie of Naples, the longitude is 38. degrees,The Citie of Naples. 50. mynutes, the latitude is 39. degrees .55. minutes, and is Southeast and by East 1051. miles from London, and the Moone chaungeth later then at London 1. howre 16. minutes, and the longest daye is .14. howres 50. minutes.
The Citie of Philippos in the kyngdome of Macedonia, the longitude 50. degrees 45. minuts, the latitude is .41. degrees,Philippos in the kingdome of Macedonia. 45 minutes, & is East Southeast 1395. myles from London, and the Moone chaungeth later then at London 2. howres 3. minutes, and the longest day is .15. howres .10. minutes. &c.
Constantinople that is now the Turkes, the longitude is 56. degrees, the latitude is .43. degrees .5. minutes,Constantinople that is the seate of the Turk [...]. and is east Southeast 1547. myles from London, and the Moone chaungeth later then at London 2. howres 24. minutes, and the longest daye is 15. howres 15. mynutes. &c.
Athens, that hath bene sometime a famous Citie, but now destroyed the longitude 52. degrees 43 mynutes, the latitude .37.Athens. degrees, 15. minutes, and is Southeast and by East .1624. myles frō Londō, the Moone changeth later then at London 2. howres 11. minutes, and the longest daye is 14. howres .40. minutes. &c.
Danswicke, latelye vnder the Kinge of Polonia, hath longitude .46. degrees, and latitude .54. degrees .55. minutes,Danswick. and is East Northeast 961. miles from LONDON, and the moone chaungeth later then at London 1. howre .44. mynutes, and the longest day is seuenteene howres fyue minutes. &c.
The kingdome of Swethen,The kingdome of Swethen. the mydle thereof hath longitude 42. degrees, and Latitude .64. degrees, and is Northeast from London 1040. myles, and the Moone chanugeth later then at London.
[Page].1. howre .28. minutes, and the longest daye is .20. howres .30. minutes &c.
The Citie of Muscouia in Rosey.The Citie of Muscouia in Rosey, hath longitude 69. degrees, the latitude 57. degrees, and is East and by North 1747. myles from the Citie of London, and the Moone chaungeth later then at London, 3. howres .16. minutes, and the longest daye is 17. howres .40. minutes. &c.
And thus I ende the discription of the Cities and Townes of Europe.
The Sixt Chapter sheweth the longitude and the latitude and the other things before rehearsed, of certayne of the principallest places of Africa, and of certayne Ilandes nearer thereunto.
AND now shall folowe the longitude and the latitude, and the thing [...]s before rehearsed, of some of the Cities and Townes, and Ilandes of Afryca.
Morocus in Barbary.And fyrste, the Citie of Morocus in Barbary, the longitude 5. degrees 5. minutes, the latitude 30. degrees 4. minutes, and is South Southwest and somewhat in the Westwardes 1449. miles from London, and the moone chaungeth rather then at London .59. minutes, and the longest daye is .14. howres.
S. Cruce rode.S. Cruce Rode, the longitude 2. degrees, the latitude .30. degrees, and is South Southwest and to the Westwards 1440 myles from London, and the moone chaungeth rather then at London .1. howre, and the longest Summer daye is .14. howres. &c.
Fesse.The Citie of Fesse, the longitude .10. degrees, the latitude 30. degrees, and is South Southwest 1365. myles from London, & the moone changeth rather then at London 39. minutes, and the longest day is 14. howres.
[Page 15]Tangie is a holde that the King of Portugall keepeth in Barbarie, and hath longitude 6. degrees 30. minutes,Tangie. and latitude .35. degrees 40. minutes, and is South Southwest .1113. myles from London, and the Moone chaungeth rather then at London .53. minutes, and the longest Sommer day is .14. houres .25. minutes.
Abilles, a Hill commonly called Cappe Hill,Abilles. ryght against Iuberaltare, and is one of Hercules pyllers, the longitude .7. degrees, the latitude .35. degrees 40. minutes, and is South Southwest .1116. myles from London, and the Moone chaungeth rather then at London 52. minutes, and the longest day is .14. houres .25. minutes.
Argeyll, the longitude .18. degrees, the latitude .37. degrees,Argeyll. and is South .872. miles from London, and the Moone chaungeth later then at London, and the longest day is houres minutes. &c.
Alexandria in Egipt, the longitude .60. degrees, 30. minutes,Alexandria in Egipt. the latitude .31. degrees, and is Southeast and by East .2169. miles from London, and the Moone chaungeth later then at London .2. houres 42. minutes, and the longest day is .14. houres. &c.
The mouth of Nilus that emptieth himselfe in Mari Mediterraneo, the longitude .62. degrees,The mouth of Nilus. the latitude .31. degrees 30.. minutes, Southeast and by East .2200. myles from London, the Moone chaungeth later then at London 2. houres 48. minutes, and the longest day is, 14. houres 8. minutes. &c.
The North ende of the Red Sea next vnto the middle earthe Sea, the longitude 64. degrees, the latitude 30. degrees,The North ende of the Red Sea. and is Southeast and by East .2345. myles from London, & the Moone chaungeth later .2. houres .56. minutes, and the longest day is .14. houres .0. minutes. &c.
Cape Deuaca in Ginney, the longitude 2. degrees .20.Cape Deua [...] in Ginney. minutes, the latitude .14 degrees .50. minutes, and is South Southwest .2426. myles from London, and the Moone chaungeth rather then at London 1. houre 10. minutes, and the longest daye is but 12. houres 50. minutes.
[Page] The Castle Demine.The Castle Demine, a holde that the King of Portugall doth keep in Ginney, the longitude 24. degrees, the latitude .2. degrees 30. minutes, and is South, a lyttle to the Eastwardes 2940. myles from London, and the Moone chaungeth later then at London, 16. minutes, and the longest day is .12. houres 20. minutes.
The mouth of the Ryuer of Bynney.The Mouthe of the Ryuer of Bynney, the longitude .32. degrees, the latitude .5. degrees, and is South and by East, and to the Eastwardes 2885. myles from London, and the Moone chaungeth later then at London 48. minutes, and the longest day is .12. houres .20. minutes.
Cappe boon Sperance.Cappe boon Sperance, the Southermost parte of all Ethiopia, hath longitude .52. degrees, & latitude .35. degrees, 10. minutes, & is of the South pole called the pole Antartike beyond the Equinoctiall, and is South and by East, and to the Eastwardes 5382. miles from London, and the Moone chaungeth later then at London .2. houres 8. minutes, and their longest Sommer daye is in our Wynter, and is 14. houres long 20. minutes. &c.
Goia.Goia, a Citie in Ethiopia, the longitude is .60. degrees, 50. minutes, the latitude hath the South Pole eleuated 19. degrees 50. minutes, and is South Southeast .4685. miles from London, and the Moone chaungeth later then at London .2. houres 3. minutes, and the longest dayes are in our Wynter, and that is 13. houres 15. minutes.
Garma.Garma, another Citie in Ethiopia, and hath longitude .57. degrees, and the South Pole is 24. degrees aboue the Horizon, and is South Southeast .4528. myles from London, the Moone chaūgeth later then at London by 2. houres 28. minutes, and their longest daye is as before is sayde, contrarie vnto ours, beyng 13. houres 30. minutes long. &c.
The great Ilande of S, Laurence.The great Ilande of Saynt Laurence, on the East side of Ethiopia beyonde Cape boon Sperance, hath longitude 85. degrees 30. minutes, and the South Pole is eleuated 20. degrees in the myddle of the Ilande, and is Southeast and [Page 16] by South 5249. myles from London, and the Moone chaungeth later then at London 4. houres .20. minutes, and the longest daye is .13. houres .15. minutes in our Wynter. &c.
The Ilande of Saynt Thomas, hath longitude 30.The Iland of S. Thomas. degrees .30. minutes, and no latitude: for that the myddle therof is ryght vnder the Equinoctiall, and is Southe and somewhat to the East wardes .3696. myles from London, and the Moone chaungeth later then at London .42. minutes, and the daye is continually alwayes .12. houres longe, neyther more nor lesse, what declination soeuer that the Sunne hath. &c.
The Ilandes of Cape Deuarde, hath Longitude 356.The Ilandes of Cappe Deuade. degrees, the latitude .16. degrees among the myddle of them, and is South Southwest .2465. myles from London, and the Moone chaungeth rather then at London 1. houre .36. minutes, and the longest Sommer daye is but 13. houres 0. minutes. &c.
The Ilandes called the Canaries,The Canary Ilandes. and the byggest Ilande called the Grand Canarie, hath no longitude, for that it is the assygned place to begyn the Longitude: the latitude 28. degrees 30. minuts, and is Southe Southwest .1914. myles from London, and the Moone chaungeth rather then at London 1. houre 20. minutes, and the longest day is .13. houres 24. minutes, and is derectlye vnder the Tropicke of Cancer. &c.
The byggest Ilande of the Madera, hath longitude 358.The Madera Ilandes. degrees 40. minutes, for that it is more Westerly then the Grand Canarie, where that the Longitude begynneth by one degree and 20. minutes, the Latitude is .29. degrees and .30. minutes, and is Southwest and by South .1625. myles from London, and the Moone chaungeth rather then at London 1. houre 25. minutes, and the longest daye is .13. houres .54. minutes. &c.
And thus I do end the description of the Cities, Townes, and Ilandes of Africa.
¶The seuenth Chapter sheweth the Longitude, and the Latitude, and the other things before rehearsed of certaine of the principallest places of Asia and in the East India. &c.
ANd now shall followe the longitude and the latitude, and all the other things before rehearsed, of certaine of the Cities and Townes and other places of Asia as followeth.
Claudiopoles.And first of Claudiopolis in the countrey of Pontus and Bethania, where S. Luke wrate the Gospel, and the Actes of the Apostles, the longitude .59. degrees .30. minutes, the latitude .42. degrees 45. minutes, and is East Southeast 1697. myles from London, and the moone chaungeth later then at London 2. houres 38. minutes, and the longest day is 15. houres 8. minutes. &c.
Nicea.Nicea where Nicea Counsell was, the longitude 58. degrees, the latitude 42. degrees 15. minuts, and is East Southeast 1668. myles from London, and the moone chaungeth later then at London 2. houres 32. minutes, and the longest day is 15. houres 6. minutes. &c.
Troy.Troy that was destroyed, the longitude 55. degrees 50. minutes, the latitude 41. degrees, and is East Southeast .1605. myles from London, and the Moone chaungeth later then at London 2. houres 24. minutes, and the longest daye is .15. houres .0. minutes. &c,
Ephesus.Ephesus where Saint Iohn wrate the Gospell, the longitude 57. degrees 40. minutes, the latitude 37. degrees 40. minuts, and is East Southeast, and to the South partes 1808. myles from London, and the moone chaungeth later then at London 2. houres 30. minutes, and the longest day is 14. houres 40. minutes. &c.
Tralus.Tralus, the longitude is 58. degrees 40. minutes, the latitude 38. degrees .50. minutes, and is East Southeast, and to the South partes 1797. myles from London, and the moone chaungeth later then at London 2. houres 34. mnutes, and the longest day is 14. houres 44. minutes. &c.
Philadelphia.Philadelphia in Bothlydias, the longitude 59. degrees, the latitude 38. degrees 50. minutes, and is East Southeast, and to the [Page 17] Southwardes 1816. myles from London, and the moone chaungeth later then at London 2. houres 36. minuts, & the longest day is 14. houres 44. minutes. &c.
Olimpus a Citie in Lycia, the longitude 61. degrees 30.Olimpus. minutes, the latitude 36. degrees 10. minutes, and is East Southeast a lyttle to the South 1993. myles from London, and the Moone chaungeth later then at London 2. houres 46. minuts, and the longest day is 14 houres 30. minutes. &c.
Pompeiopolis a Citie of Galatia, and builded by Pompey,Pompeiopolis. the longitude .62. degrees, the latitude 42. degrees, and is East, Southeast 1814. myles from London, and the Moone chaungeth later 2. houres 48. minutes, and the longest day is 15. houres 10. minutes. &c.
Olbia in Pamphllia, the longitude .62 degrees,Olbia. the latitude 36. degrees .55. minutes, and is East Southeast .1989. myles from London, and the Moone chaungeth later then at London 2. houres 48. minutes, and the longest daye is .14. houres .36. minutes. &c.
Pargamus in the Countrey of Doris, the longitude .57.Pargamus degrees .35. minutes, the Latitude .39. degrees .45. minutes, and is East Southeast .1709.. myles from London and the Moone chaungeth later .2. houres .30. minutes, and the longest day is .14. houres 54. minutes. &c.
Cesaria in Capadocia, the longitude .66. degrees .30.Cesaria. minutes, the latitude .39. degrees .30. minutes: and is Easte Southeast .2064. myles from London, and the Moone chaungeth later then at London .3. houres .6. minutes, and the longest day is .14. houres .50. minutes. &c.
Nicopolis in Armenia the lesse, the longitude .69.Nicopolis. degrees 20. minutes, the latitude .41. degrees .40. minutes, and is East Southeast .2129. miles from London, and the Moone chaungeth later .3. houres .18. minutes, and the longest day is .15. houres .3. minutes. &c.
Antiochia in Cilicia, the longitude .64. degrees 40. minutes,Antiochia. the latitude .36. degrees 50. minutes. & is East Southeast .2078. [Page] myles from London, and the Moone chaungeth later then at London 2. houres 58. minutes, and the longest day is 14 houres 33. minutes. &c.
Geldia.Geldia in Albania parte of great Tartarie, the longitude 83. degrees, the latitude .46. degrees 30. minutes, and is East and to the Southwardes 2458. myles from London, and the Moone chaungeth later 4. houres 12. minutes, and the longest day is .15. houres 40. minutes. &c.
Bola.Bola in Armenia the greater, the longitude 76. degrees 10. minutes, the latitude 44.. degrees, and is East and by South 2294. myles from London, and the Moone chaungeth later then at London 3. houres 45. minutes, and the longest day is 15. houres 20. minutes. &c.
Alexandria in Siria.Alexandria in Siria, the longitude 69. degrees 30. mynutes, the latitude 36. degrees 10. minutes, & is East Southeast 2277. miles from London, and the Moone chaungeth later then at London 3. houres 18. minutes, and the longest day is 14. houres 30. minutes. &c.
Tripolis in Phenicia.Tripolis in Phenicia, the longitude 67. degrees 30. minutes, the latitude 34. degrees 20. minuts, and is East Southeast, and to the Southwardes 2314. myles from London, and the Moone chaungeth later 3. houres 10. minutes, and the longest day is 14. houres, 20. minutes. &c.
Barut.Barut, and is the Porte of Damascus, the longitude 76. degrees, the latitude 33. degrees 20. minutes, and is East Southeast, and to the Southwardes 2321. miles from London, and the Moone chaungeth later 3. houres 8. minutes, and the longest day is 14. houres 15. minutes. &c.
Antiochia.Antiochia the Mount Taurus, the countrie of S. Luke, the longitude 69. degrees, the latitude 35. degrees 30. minutes, and is East Southeast 2319. myles frō London, and the Moone chaū geth later then at London 3. houres 16. minutes, and the longest day is 14. houres 26. minutes. &c.
Damascus.Damascus, [...]ere Caine sleine his brother Abel, the longitude 69. degrees, the latitude 33. degrees, & is East Southeast and to [Page 18] the Southwardes 2404. myles from London, and the Moone chaungeth later 3. houres 16. minutes, and the longest day is 14. houres 15. minutes. &c.
Porte Iassa or Ioppa, the longitude 65. degrees 45. minutes,Port Iassa. the latitude .31. degrees 55. minutes, and is Southeast, and by East and to the Eastwardes 2338. myles from London, and the Moone chaungeth later then at London 3. houres .2. mynutes, and the longest day is 14. houres .6. minutes. &c.
The deade Seas or lake of Sodome, the longitude 66.The Lake of Sodom. degrees 50. mynutes, the latitude 31. degrees 10. mynutes, and is Southeast and by East and to the Eastwardes .2404. myles from London, and the Moone chaungeth later 3. houres 8. minutes, and the longest day is .14. houres 4. minutes. &c.
Bethsaida in Galilea, the longitude 57. degrees 5.Bethsaida. mynutes, the latitude 31. degrees 15. mynutes, and is Southeast and by East .2039. myles from London, and the Moone chaungeth later 2. houres 29. minutes, and the longest day is 14. houres 6. mynutes. &c.
Nicopolis in Samaria, the longitude 66. degrees 50.Nicopolis. mynutes, the latitude 31. degrees .50. mi. and is Southeast, and by East and to the Eastwardes .2382. myles from London, and the Moone chaungeth later 3. houres 8. mynutes, and the longest daye is 14. houres 10. minutes. &c.
Hierusalem in Iudea,Hierusalem sometyme the famous Citie on the earth, but nowe destroyed by Titus, in the tyme of Vaspatian the Emperour of Rome, the longitude 65. degrees 45. minutes, the latitude 31. degrees 22. mynutes, and is Southeast, and by East, and to the Eastwardes 2352. myles from London, and the Moone chaungeth later by 3. houres 3. minutes, and the longest day is 14. houres 8. minutes. &c.
Charan in Mesopotamia, where as Abraham dwelled,Charan in Mesopotamia the longitude 73. degrees 45. mynutes, the latitude 36. degrees, 10. mynutes, and is East Southeast .2466. myles from London, and the Moone chaungeth later by 3. houres 36. minutes, and the longest day .14. houres 30. minutes.
[Page] Babilon.Babilon where the Towne of Babel was, the longitude is 79. degrees, the latitude .35. degrees, and is East Southeast, 2724. myles from London, and the Moone chaungeth later by 3. houres .56. mynutes, and the longest day is 14. houres .25. minutes. &c.
Erupa in Arabia.Erupa in Arabia, the longitude .72. degrees 30. mynutes, the latitude 30. degrees 15. mynutes, and is East Southeast and to the Southwardes .2641. myles from London, and the Moone changeth later by 3. houres 30. minutes, and the longest day is 13. houres 56, minutes. &c.
The Red Sea.The Red Sea, the place whych Moyses and the Children of Israell went through, the longitude 63. degrees 30. mynutes. the latitude 29, degrees 50. mynutes, and is Southeast and by East 2336. myles from London, and the Moone chaungeth later 2. houres 54. minutes, and the longest day is 13. houres 56. mynutes. &c.
Mount Synai or Mount Oreb.Mount Synai or mount Oreb, where that Moyses receyue [...] the ten Commaundementes, the longitude 64. degrees, the latitude 30. degrees, and is Southeast, and by East 2344. myles from London, and the Moone chaungeth later then at London, by 2. houres 58. mynutes, and the longest daye is 13. houres 58. minutes. &c.
Michia.Michia in Arabia, where is the Sepulchre of the false Prophet Mahomet, the longitude 72. degrees 15. minutes, the latitude 23. degrees, and is Southeast, and by East, and to the East wardes 2954. myles from London, and the moone chaungeth later by 3. houres 29. minutes, and the longest day is 13. houres 25. minutes. &c.
The Citie of Niniuie.The Citie of Niniuie in Assiria where as Ionas the Prophet was sent, the longitude 78. degrees, the latitude 36. dedegrees, and is East Southeast .2635. myles from London, and the moone chaungeth later by 3. houres 52. minutes and the longest day .14. houre [...] 30. minutes.
Asia.Asia a Citie in Susana, the longitude .80. degrees 10. [Page 19] minutes, the latitude 31. degrees 40. minutes, and is East Southest 2923. myles from London, & the moone chaungeth later by 4. howres 1. minute, and the longest daye is 14. howres 8. minutes.
Arima in Persia, the longitude 87. degrees, 45. minutes,Arima. the latitude 33. degrees 50. minutes, and is East Southeast .3108. miles from London, and the Moone chaungeth later by .4. howres .31. minutes, and the longest daye is 4. howres .15. minutes. &c.
Alca in Media, the longitude is 86. degrees 15. minutes, the Latitude .41. degrees, and is East and South 2791. myles from London, & the Moone chaungeth later by 4 howres 25. minuts, and the longest day is 15. howres.
The Caspian Sea, the longitude of the midle thereof is .90.The Caspian Sea. degrees, the latitude of the midle therof is .45. degrees, 30. minutes, and is East and to the Southwards .2788. myles from the Citie of London, and the Moone chaungeth later then at London by 4. howres 40. minutes, and their longest daye is .15. Howres 30. minutes.
Arges in Carmania, the longitude .96. degrees .30. minutes,Arges. the latitude .23. degrees .30. minutes, and is East Southeast 3917. myles from London, and the Moone chaungeth later by .5. howres 6. mynutes, and the longest daye is .13. howres .25. minutes, &c.
The Citie of Hecatompilon in Parthia, whiche hath .100.Hecatompilon. gates, the longitude 93. degrees .20. minutes, the latitude 37. degrees, 50. minutes, and is East and by South 3714. myles from London, and the Moone chaungeth later then at London .5. howres .6. minutes, and the longest daye is .14. howres .38. minutes. &c.
Harcan in Hircania, the longitude .7. degrees 30 minuts,Harcan. the latitude .40. degrees .30. minutes, and is [...]ast and by South 3332. myles from London, and the Moone chaungeth later then at London by 5. howres .14. minutes, and the longest day is 14. howres .50. minutes.
Sena in Margiana, the longitude .102. degrees .30. minuts,Sena. the latitude .42. degrees .20. minutes, and is neare East and [Page] by South .3430. myles from London, & the Moone chaungeth later by 5. howres 30. minutes, and the Longest day is .15. howres 8. minutes.
Chomara.Chomara in Bactriana, the longitude .106. degrees, the latitude 40. degrees, and is East and by South 3635. myles from London, & the moone changeth later by 5. howres, 45. mynutes, and the longest day is 14. howres .50. minutes.
Prepsa.Prepsa in Sogdiana, the longitude 130. degrees, the latitude .45. degrees, and is East and to the Southwardes, 4389. myles from London, and the moone chaungeth later by 7. howres 20. minutes, and the longest daye is .15. howres 30. mynutes &c.
Aspabora.Aspabora in Scithia within the mount Emaus, the longitude 102. degrees, the latitude 44. degrees, and is East and by south, 3311 myles from London, and the moone chaungeth later by 5. howres 28. minutes, and the longest day is 15. howres 20. mynutes.
Issedon.Issedon in Seythia, without the mount Emaus in [...]hatay, and vnder the Great Chane Emperour of Tartaria, the longitude 150. degrees, the latitude 48. degrees .30. minutes, and is East and a lytle to the Southwardes 5008. miles from London, and the moone chaungeth later by 8. howres 40 minutes, and the longest daye is .15. howres 56. minutes.
Isadon.Isadon in Serica, the longitude 162. degrees, the latitude 45 degrees, and is East and too the Southwardes 5622. myles from the Citie of London, and in this Countrye of Serica, breed the Sylk Wormes, and the Moone chaungeth later then at London .9. howres 28. minutes, and the longest daye is .15. howres 30. minutes &c.
Alexandria maria·Alexandria Maria, the longitude 110. degrees, the latitude .36. degrees, and is East and by South 3937. myles from London, and the Moone chaungeth later by 6. howres iust, and the longest daye is 14 howres 30. minutes.
[Page 20]Asta in Drangiana, the longitude .107. degrees .30. minutes,Asta. the latitude 30. degrees, 40. minutes, and is East Southeast, 4087. myles from London, and the moone chaungeth later by .5. howres .50. minutes, the longest daye is .14. howres iuste &c.
Cuni in Gegrosia, the longitude .110. degrees,Cuni. the latitude 23 degrees 50. minutes, and is East Southeast .4461. myles from London, and the moone chaungeth later by 6. howres, the longest daye is 13. howres 30. mynutes.
Bardaxima in India within the riuer of Ganges,Bardaxima. the longitude .113. degrees, 40. minutes, he latitude .20. degrees 40. minutes, and is East Southeast 4735 myles from London, and the moone chaūgeth later by 6. howres 15. minutes, and the longest day is 13. howres 15. minutes.
Calicute the most famous Citie of marchandize in all India,Calicute. the longitude .112. degrees, the latitude .5. degrees, and is Southeast and by East and to the Eastwards .5224. miles from London, and the moone chaungeth later by .6. howres .8. minutes, and the longest daye is but .12. howres .20. minutes. &c.
Polibotra in Persia, the longitude 143. degrees,Polibotra. the latitude 27. degrees, and is East and by South and too the Southwardes 5710, myles from London, and the Moone chaungeth later by .8. howres 12. minutes, and the longest daye is 13. howres .45. mynutes.
Pentapolis in India without Ganges, the longitude .150.Pentapolis. degrees, the latitude .18. degrees, and is East Southeast 6337. myles from London, and the Moone chaungeth later by 8. howres .40. minutes, the longest daye is .13. howres .10. minutes. &c.
[Page] Thagora.Thagora in India without Ganges, the longitude 168.. degrees, the latitude 6. degrees, and is East South East 7680. myles from London, and the Moone chaungeth later by 9. howres 52. minutes, and the longest daye is 12. howres .20. mynutes,
Ciamfa.West Ciamfa in Chatay, the longitude .188. degrees, the latitude .37. degrees .15. minutes, and is East and by South 7205. myles from London, and the Moone changeth later then at London .11. howres .43. minutes, and the longest day is .14. howres 36. minutes.
Quinsay.Quinsay, the greatest Citie in the whole World, in Chatay, and vnderneth the Great Chaine Lord of the East and South Indians, the longitude .192. degrees, the latitude .37. degrees 40. minutes, and is East and by South .7272. myles from London, and the moone chaungeth later by 11. howres .28. minutes, and the longest daye is .14. howres .38. minutes &c.
G [...]iten.G [...]iten in the East India, in the Prouince of China, the longitude .183. degrees, and is neare vnto the South Sea, the latitude 25. degrees 15. minutes, and is East and by South 7312. myles from London, & the moone chaūgeth [...] then at Londō by 11. howres 12. minutes, and the longest day is 13. howres 35. minutes.
Ciamfa.East Ciamfa, the longitude .97. degrees, the latitude .32. degrees 5. minutes, and is East and by South, 7787. myles from London, and the moone chaungeth later then at London by .11. howres 48. minutes, and the longest daye is 14. howres 10. mynutes.
Tangury.Tangury in Mugi, the longitude .178. degrees, 15. minutes, the latitude 31. degrees, & is East & to the Southwards, 6980. myles from London, and the moone chaungeth later by .10. howres .28. minutes, & the longest day is 14. howres 5. minutes.
Thebet.The Prouince of Thebet, in whiche the great Chaine Lord of the East and South Indians hath his Courte, and all the Kinges of India are vnder hym, the longitude is 168. degrees, [Page 21] the latitude .3. degrees .20. minutes, and is Easte Southeast 7670. myles from London, and the Moone chaungeth later by 9. howres 44. minuts, and the longest daye is but 12. howres 10. minutes.
Cyamba, in this place they vse Coral in the steede of money,Ciamba and haue great plenty of most sortes of Spices, the longitude 199. degrees 10 minuts, the latitude .25. degrees .30. minutes, and is East and by South 7980. myles from London, and the Moone chaungeth later by .11. howres .48. minutes, and the longest day is 13. howres .36. minutes.
Barnia in the South India, the longitude .202. degrees .40.Barnia. minutes, the latitude .11. degrees .40. minutes, and is West and by South 8824. myles from London, and the Moone chaungeth rather by .11. howres 52. mynutes, and the longest daye is 12. howres.
Nar in Moaber, the Inhabitants doe worship Oxen,Nar. the longitude 196. degrees, the latitude hath the south pole 20. degrees, 10. minutes, and is Southeast and a litle to the Eastwardes 8512. myles from London, and the Moone chaungeth later by 11. howres .44. minutes, and the longest daye is in our Winter, and is 13. howres .15. minutes. &c.
Malaqua, the longitude is 189. degrees,Malaqua. the Latitude of the South pole is 15. degrees .30. minutes, & is Southeast and by East 8781. myles from London, & the Moone chaungeth rather by 11. howres 16. minuts, and the longest daye is 12. howres 56. minutes.
In the Kingdome of Lace there is a Citie called Lace,Lace. the longitude is .166. degrees 30. minutes, the latitude is 21. degrees, 40. minutes, and is East and by South .7047. myles from the Citie of London, and the Moone chaungeth later then at London by 9. howres 44. minutes, and the longest daye is .13. howres 24. minutes.
¶The eyght Chapter sheweth the Longitude, and the Latitude, and the other things before rehearsed, of certaine of the principallest places of America or the west Indies, that hath been founde within these 100. yeares, and not knowen vnto the olde writers.
ANd now shal folow the longitude, & the latitude, & al the other thinges before rehearsed of certayne Cities,The Streighte of Magellenos the southermost part of all America. & other notable places of America. And fyrst the Streightes of Magellenos the Southermost parte of all America, the Longitude .305. degrees, the Latitude is the Pole Antartick, or South Pole .25. degrees .30. mynutes, and is South Southwest, and too the Westwardes, and beyonde the Equinoctiall 7224. myles from London, and the moone chaungeth rather then at London by .5. howres .0. minutes, and the longest Summer daye with them is our shortest Winter daye, for that the pole Antartick or south pole is aboue the Horizon, and is .16. howres .36. minutes. &c.
The great Riuer of Platte.The great riuer of Plate, the longitude 327. degrees, the latitude is the South pole 35. degrees, and is South Southwest 5685. myles from London, and the Moone chaungeth rather then at London by .3. howres 32. minutes, and their longest summer day is in our winter. & is 14. howres .30. mynuts long.
Cappe Crusos the Eastermost part of America.Cappe Crusos the Eastermost part of all America, & is cōmonly called the cost of Brasell, the longitude 345. degrees, the latitude 5. degrees of the south pole, and is South Southwest 3792 myles frō London, & the Moone changeth rather then at Londō 2. houres 20. mi. the lōgest day is about .12. houres .30. minuts.
Cappe de Planco.Cappe de planco, the longitude .306. degrees, the latitude 5. degrees, & is southwest and by West 4547. myles from Londō, and the Moone changeth rather 4. howres .56. minutes, and the longest daye is about 12. howres 20. minutes &c.
Cappe Sainct Marthae.Cappe S. Marthae, the lōgitude .284. degrees, the latitude 12. degrees, and is west southwest & to the southwards 5103. myles from London, and the Moone chaungeth rather by 60. howres 24. minutes, and the longest daye is 12 howres 45. minutes.
[Page 22]Carthagena, the longitude .282. degrees, the latitude 10.Carthagena degrees .15. minutes, and is West Southwest and to the South 5316. myles from London, & the moone changeth rather by .6. howres, 32. mynutes, and the longest day is 12. howres .38. minutes.
Nomber de Deus, the longitude 276. degrees, the latitude 7. degrees, and is West Southwest 5685. myles from London,Nomber de Deus. and the moone chaungeth rather by 6. howres 56. minutes, and the longest daye is .12. howres 25. mynutes &c.
The great & famous Citie of Mexico, the principallest place in all America, the longitude .238. degrees, the latitude .21.The Citie of Mexico. degrees 30. minutes, and is West and by south, 6844. myles from London, and the moone chaungeth rather then at London by 9. howres 28. minutes, and the longest day is 13. howres 20. mynutes.
The riuer of Palme in Floryda, the longitude 260. degrees,The riuer of Palme in Floryda. the latitude 39. degrees .20. minutes, and is West and to the Southwardes 5034. miles from London, and the moone chaungeth rather then at London by 8. howres .0. minutes, and the longest daye is 14. howres 45. minutes.
The Cape of Cerra Floryda, the longitude .272. degrees,The Cape of terra Florida. the latitude 31. degrees, and is West and by Southe .4935. myles from London, and the moone chaungeth rather by 7. howres .12. minutes, & the longest daye is .14. howres .6 minutes. &c.
Perru in America, the longitude .290 degrees,Perru. the latitude hath the South pole 5. degrees, and is Southwest and by West .5528. myles from London, and the moone chaungeth rather then at London 6. howres 0. minutes, and their longest daye is but .12. howres .20. mynutes.
Pannama, a Towne or Citie vppon the Sea Coaste of Mare de Sur or South sea, the longitude .276. degrees,The porte of Pannama. the latitude .20. degrees 40. minutes, and is Southwest and by West, and to the Westwardes 5794 myles from London, and the Moone chaungeth rather by 6. howres 56. minutes, and the longest day is 12. howres 15. minutes.
[Page] Tumbes.Tumbes, a Port in the Prouince of Peru, vpon the cost of the South Sea, the longitude 276. degrees, the latitud 12. degrees of the Antartick pole, and is Southwest and by West 6045. myles from Londō, and the moone chaūgeth rather by 6 howres 56 minutes, and the longest day is but .12. howres 15. minutes in our Winter.
Baculaius. or new founde Land.Baculaius is on the Northeast ende of America, commonlye called the new founde Lande, the longitude of the midle of them is 320. degrees, the latitude of the midle thereof is .54. degrees, and is West and to the North partes .2200. myles from London, & the moone chaungeth rather by 3. howres .59. minutes, and the longest daye is 16. howres 58. minutes.
The land of Labrador.The Lande of Labrador, the longitude of the Eastermost Cape is 320 degrees, the latitude thereof 63. degrees, and the moone chaungeth rather by 3. howres 95. minutes, and is West Northwest and to the Northwardes .2768. myles from London, and the longest day is 20. howres 0. minutes longe.
And thus I doe ende the discription of the may [...]e, or firme land of America. &c.
The ninth Chapter sheweth the Longitude and the Latitude, and the other thinges before hearsed of certayne of the most principalle Ilands of Europe, within the midle earth Sea, and also of the moste principalle Ilands of Asia and America.
ANd now shall folow the longitude and the latitude, and the other thinges before rehearsed, of Certayne of the most notablest Ilands of all Asia and America, and also of Europe: and fyrst of certayne of the most principall Ilands in the midle earth Sea.
The Iland of Cicilia.And fyrst, the Iland of Cicilia, being the principallest Iland in all that Seas, the midle therof hath longitude 37. degrees, the latitude 36. degrees, and is Southeast and by South 1178. miles from London, and the Moone chaungeth later by 1. howre .8. minutes, and their longest daye is 14. howres .30. minutes. &c.
[Page 23]The Ilande of Corsica, the myddle thereof hath longitude 31.The Iland of Corsica. degrees, the latitude 40. degrees, & is Southeast and by South. 829. myles from London, and the moone chaungeth later by .44. minuts, and their longest day is 14. houres 50. minutes. &c.
The Ilande of Sardinia, the myddle hath longitude 31.The Iland of Sardinia. degrees, the latitude 38. degrees, and is South Southeast, and to the Eastwardes .932. myles from London, and the Moone chaungeth later by 44. minutes, and their longest day is .14. houres 40. minutes long. &c.
The Ilande of Maiorica, the myddle hath longitude .17.The Iland of Maiorica. degrees, the latitude 38. degrees 30. mynutes, and is South and a little to the Westwardes .792. myles from London, and the Moone chaungeth rather by 12. minutes, and the longest day is 14. houres 43. minutes. &c.
The Ilande of Minorica, the longitude .20 degrees,,The Iland of Minorica. the latitude 39. degrees, and is due South .752. myles from London, & the Moone chaungeth at that tyme that it dooth at London, and the longest daye is .14. houres .45. minutes. &c.
The Ilande of Candie, the longitude .55. degrees,The Iland of Candy. the latitude 35. degrees .20. minutes, and is Southeast and by East, and to the Eastwardes 1791.. myles from London, and the Moone chaungeth later then at London by 2. houres .20. minutes, and the longest day is .14. houres .25. minutes. &c.
The Ilands of Nigropant, the longitude .54. degrees,The Ilands of Nigropant. the latitude 38. degrees, and is East South and to the Southwardes 1643. myles from London, and the Moone chaungeth later by 2. houres .16. minutes, and the longest day is .14. houres .40. minutes. &c.
The Ilandes called Ciclades,The Ilāds called Cyclades. the myddle of them hath longitude .56. degrees 10. minutes, the latitude .37. degrees .20. minutes, and is East Southeast, and to the Southwardes 1545. miles from London, and the longest day is 14. houres .35. minutes, and the Moone chaungeth later 2. houres 24. minutes.. &c.
The Ilande of Ciprus, the longitude .65. degrees 30.The Ilande of Ciprus. minutes, the latitude .35. degrees 10. minutes, and is East Southeast. 2190 miles from London, and the Moone chaungeth later by 3. [Page] houres 2. mynutes, and the longest daye is .14. houres 20. minutes. &c.
The Ilande of Scoyra.The Ilande of Scoyra, the longitude 86. degrees, the latitude 12. degrees, and is Southeast and by East .3958. myles from London, and the Moone chaungeth later by 4. houres 24. minuts, and the longest day is 12. houres 45. minutes. &c.
The Ilande of Ormosa.Ormosa is an Ilande in the narrowe Persicke Seas, and hath longitude 99. degrees, the latitude .19. degrees, and is East Southeast 4070. myles from London, and the Moone chaungeth later by 5. houres 4. minutes, and the longest day is .13. houres 12. minutes. &c.
The great Iland of Tabrobannu.The great Ilande called Tabrobannu lying in the East Orean, the longitude 151. degrees, the myddle thereof hath no latitude for that it is directly vnder the Equinoctiall, and is East Southeast 7065. myles from London, and the Moone chaungeth later then at London 8. houres 44. minutes, and the daye is continuall 12. houres in length. &c.
The Iland of great Iaua.The Ilande of the greater Iaua, the longitude 179. degrees, the latitude hath the South pole Antarticke 7. degrees 30. minutes, and is East Southeast, & a lyttle to the South .8486. myles from London, and the Moone chaungeth later by 10. houres 36. minutes, and the longest day is but 12. houres 20. minutes. &c.
The Iland of the lesser Iaua.The Ilande of the lesser Iaua, hath longitude 188. degrees, and no lattitude for that it is vnder the Equinoctiall, and is East Southeast 8715. myles from London, and the Moone chaungeth later by 11. houres 12. minutes, and the daye is alwayes 12. houres long. &c.
The Ilande of Berno.The Ilande of Berno, hath Longitude 178. degrees, the latitude is of the South pole, and is .2. degrees .30. minutes, and is East Southeast .8320. miles from London, & the Moone chaungeth later by 10. houres 32. minutes, and the longest daye is 12. houres 8. minutes. &c.
The Ilands of Molucke.The Ilandes of Molucke that lye in the Southe Sea called Mare de Sur, the longitude 193. degrees, the latitude 9. degrees, and is East Southeast and a little to the Eastwards 8688. myles from London, and the Moone chaungeth later then at London [Page 24] by 11. houres 32. minutes, and the longest day is but 12. houres 35. minutes. &c.
The Ilande of Gelilo the greatest Ilande of al the Maiucke,The Iland of Gelilo. and hath longitude 204. degrees, the myddle thereof hath no latitude for that it is directly vnder the Equinoctiall, and is West, Southwest 9078. myles from London, and the Moone chaungeth rather then at London, for that it is vnto the westwardes, and is because that it is more to the Eastwardes of London, then 180 degrees which is more then halfe the Circumference of the two paralelles, that is to say, the paralell of London, & the paralell of the Ilande beyng the Equinoctiall,Gelilo is near [...] Antipode [...] vnto London. and if that it had the Southe Pole eleuated 51. degrees and a halfe, then it had been neare Antipodes vnto the Citie of London, and the Moone chaungeth rather 11. houres .44. mynutes, and the longest day is but 12. houres long. &c.
The Ilande of Iapan neare the coast of China,The Iland of Iapan. the longitude 198. degrees, the latitude 32. degrees, and is East and by South 7919. myles from London, and the Moone chaungeth later then at London by 11. houres 52. minutes, and the longest Sommer day is .14. houres 10. minutes. &c.
The Ilande of Stipango, the longitude 200. degrees 30.The Iland of Stipango. mynutes, the latitude 50. degrees, and is West from the Citie of London, for that it is more then .180. degrees vnto the Eastwardes, therefore the shortest waye is vnto the Westwardes, and is 6668. myles from London, and the Moone chaungeth rather then at London by 11. houres 58. minutes, and the longest day is 16. houres 4. mynutes. &c.
Cuba,The Iland of Cuba. one of the byggest Ilandes in the West Indies in the great Bay of America, and the myddle thereof hath Longitude .275. degrees, the latitude .23. degree .30. minutes, the verye myddle of the Ilande that is directly vnder the Tropicke of Cancer, and is West Southwest .5114. myles from London, and the Moone chaungeth rather 5. houres 0. mynutes, and the longest daye is .13. houres 26. minutes. &c.
[Page] The Iland called Hispaniola.The great Ilande called Hispanyola neare Cuba, the myddle thereof hath longitude 285. degrees, and the latitude is 20. degrees in the myddle thereof, and is West Southwest, and somewhat to the Southe .4805. myles from London, and the Moone chaungeth rather by .6. houres .20. minutes, and the longest daye is 13. houres 15. minutes.
Saint Iohns Ilande.Saint Iohns Ilande, the Longitude of the myddle thereof is 293. degrees .30. mynutes, the latitude of the myddle is 18. degrees, and is West Southwest .4536. myles from London, and the Moone chaungeth rather 5. houres .46. mynutes, and the longest daye is 13. houres 8. minutes. &c.
The Ilande of Iamica.The Ilande of Iamica, the Longitude is 276. degrees, the Latitude .16. degrees, and is West Southwest .5332. myles from London, and the Moone chaungeth rather 6. houres 56. minutes, and the longest day is .13. houres .0. minutes &c.
The Ilands of the Surres.The Ilandes called the Surres in our West Occean Sea, the myddle amongest them, hath longitude 344. degrees, and the Latitude amongest the myddle of them is .39. degrees, and is Southwest and by West 1674. myles from London, and the Moone chaungeth rather 3. houres 24. minutes, and the longest daye is .14. houres .45. minutes. &c.
And thus I doo ende the description of the principallest Ilandes of Asia, Europa, and America. &c.
¶The tenth Chapter is as touching certaine thinges in the knowing of the distaunce vnto any place assigned by Longitude and by Latitude. &c.
AND furthermore, insomuche as the shortest distaunce vnto any place assigned, cannot be by any one poynt of the Compasse, as is before declared in the first Chapter of this seconde booke, wherefore if that you doo desire for to knowe the distaunce ouer the Sea and Lande, the nexte way, and the shortest distaunce,If that you doo desire to know the shortest distance vnto any place, then you must do it with a Globe. then you must prepare a Globe terrestrial, and that the longitude, and the latitude of the Townes and Cities, and other notable places, to be truely placed on the Globe: and then take a payre of Compasses, and then looke those two places in the Globe, that you doo desire for to knowe the true distaunce vnto, and then open your Compasses, and set the one foote on the one place, and the other on the other place assigned, iustly: and that doone, then your Compasses standyng styffe and not remoued, set them vnto the Equinoctiall circle on the Globe, and that doone, then looke howe manye degrees that it is iustly betweene the two feete of the Compasses,How to know the true distance vnto any place by the Globe. and that beyng knowne, then multiply the number of degrees by 60. and that shall shewe vnto you the true number of myles, betweene any two places assigned, and this beyng doone precisely, taking the true number of degrees, & the partes therof, you shal not fayle of the truth, so that the Longitude and Latitude of the places be truely set vppon the Globe: and then 60. myles dooth aunswere vnto one degree both vnder the Equinoctiall, and the Meridians.The whole compasse of the earth is 28600 myles, no place can be no further distance from you th [...] 10800. myles. And in euery great Circle on the Globe of the Earth, whose whole circumference or compasse is 21600. myles, so that no two places assigned, cannot be further distaunce asunder then 10800. myles, and then the one must be opposit, or ryght against the other, being Antipodes, goyng feete vnto the feete of the other, and then as before [Page] is declared, it is neyther East nor West, nor no poynt of the Compasse else, for which waye soeuer that you doo goe by anye ryght lyne, the distaunce is all one, but if that any two places bee not directlye Antipodes the one vnto the other, then that is nearer one waye, then that it is another way: and yet it shall not bee by any one poynt of the Compasse, but by diuers poyntes of the Compasse, as before is rehearsed, except that the two places bee both vnder one Meridian, or else vnder the Equinoctiall. &c.
❧A Table of the Contentes of the chapters of the second part of this Booke called a treasure for Trauailers.
FIrst to the Reader of thys seconde part.
The firste Chapter of the seconde parte sheweth you how for to know the distance vnto any towne vpon the face of the earth, and what is to be considered in the dooynge therof.
The Seconde Chapter sheweth vnto you, howe you may know the distaunce vnto any Towne situate vpon the face of the whole erth, so that you doe know the true longitude and the true latitude of them.
The Thirde Chapter sheweth howe too knowe vnto what quarter of the worlde that anye place doth stande from you, that is to saye, by what poynt of the Compasse, you knowing the true longitude and the true latitude.
The Fourth Chapter sheweth the longitude and the latitude, and by what poynt of the compasse that sundry places within England and Scotland and Irelande, and also of certayne Ilandes neare, vnto them doth beare from the Citie of London, and what distaunce of myles they are from London, by the poynt of the Compasse ouer the water and the land: and also there is shewed how much the moone shall chaunge rather or later then it doth at London, and also it dooth shewe the length of the longest Summer daye, for as manye places as are named.
The fyfth Chapter sheweth the longitude and the latitude and the other thinges before rehearsed, of certayne of the principallest places in Europe, as in Spayne and Portugall, and Fraunce, and Italy, and Germany.
The Sixte Chapter sheweth [Page] the longitude and the latitude and the other thinges before rehearsed, of certayne of the principallest places in Africa, and of certaine Ilands neare therunto.
The Seuenthe Chapter sheweth the longitude and the latitude and the other things before rehersed of certayne of the principallest places of Asia, and in the East India.
The Eight Chapter sheweth the longitude and the latitude and the other thinges before specifyed, of certayne of the princpallest places of America or the West Indies, that hath bene founde within these hundred yeares, and not knowne vnto the olde Writers.
The ninth Chapter sheweth the longitude and the latitude and the other thinges be fore rehearsed, of certayne of of the moste principall Ilandes of Europe, within the midle earth Sea, and also the most principall Ilandes of Asia and America.
The tenthe Chapter is as touching certaine thinges in the knowyng of the distaunce vnto any place assigned by longitude and by latitude.
The Argument of the thyrde Booke, of the treasure for Trauailers.
¶The thirde Booke of the Treasure for Trauailers, conteyning some matters for the measuring of superfycialles, as Lande, Borde, Pauement, or Glasse, and also some matters as touching Solled bodyes, as Tymber, Stone, or such otherlyke: and also howe to alter the Tonnage, burthen, or bygnesse of shippes, and to keepe that moulde and proportion with other necessary thinges belonging thereunto. &c. Being very necessary for all sortes of people that trauaile eyther by Sea or Land, written by William Bourne.
To the Reader of this third Booke.
GEntle Reader, although Maister Leonard Dygges in hys Booke called Tictonicon, and also Maister Thomas Dygges his Sonne in another Booke, called Pantometry, hath shewed how for to measure al Superfycialles, as Land, Borde, Glasse, Pauement or any such other lyke, & also how to measure al maner of Solled bodies, as Timber, Stone, & such other lyke, yet notwithstandyng I haue written in this third Booke, a lyttle briefe note as touching those causes, and also how to buylde shippes for to make them of what tonnage or burthen that you lyst, and to keepe any forme in the mould or proportion that you lyste, whereby that any Mechanicall workemen by following the order in the Booke prescribed, may make any shippe the one lyke the other, and to make them of what bygnesse or smalnesse he lyst, and to keepe that forme and fashion in an poyntes, both in the moulde that is vnder the water, and also in the fashion aloft, aboue the water. And also there is conteyned in this third part, howe for to know the bygnesse of Ropes, whether that it be as byg agayne, or three tymes so bygge more or lesse, at your discretion, which in my opinion is very necessary to be knowne, both vnto Naupegers or shippe Carpenters, and also vnto all sortes of Sea men: and also there is other necessarie matters conteyned in this third Booke.
¶The thyrde Booke of the treasure for Trauaylers.
The first Chapter of the thyrde Booke, sheweth you howe for to caste the contentes of lande by Arithmeticke, and also by the husbands rule which is by the account of money. &c.
NOwe begynneth the thirde Booke, for that it is necessarye for to knowe how to measure all manner of plat formes and bodyes, both their superficiall contentes, and also there masey contentes. Therefore as briefly as I may I wyll shewe vnto you: yet there hath famous and wyse men written thereof in our Englishe tongue as M. Leonard Dygges, and M. Thomas Dygges, his sonne, & other notable men seene in the Mathematicall Sciences. Therefore I doo intend to treate the lesse thereof, and especially of those thinges that those haue written of, I wyll not meddle withall at this tyme, for that they haue sufficiently declared it, as this: for to know the contentes of Lande, to be measured in Triangles, beyng sure for to make a square angle and so forth, as M. Dygges dooth declare in hys Tictonicon, and for to cast the contentes therof, you shall doo this:To know the cōtentes of account of any peece of groūd by Arithmetike. When you haue found a length and a breadth of anye peece of ground, whose contentes in Acres you doo desire for to know, you shall do it by Arithmetike, as thus. You shal multiply the length with the breadth, then that number that commeth of that multiplication, you shall deuide by .160. and that shall shewe vnto you the true numbers of Acres, then if there bee any halfe roddes or quarters of roodes, if that they be in breadth, you shal adde then to the length, and if that they be in length, you shall account them in the breadth, and so foorth. Nowe I doo knowe that euery man hath not Arithmetike, therefore you shall make your account by this meanes, for to knowe the true contentes of the measure of [Page] any peece of Lande, when you doo know the length and the bredth thereof, as thus: by the account of money, euery marke for to conteyne one Acre,To know howe many acres there is in any peece of ground by the account of money. as thus, by the account of money, euery noble of money to conteyne halfe an Acre, and euery 3. shillinges and 4. pence, to conteyne a roode or a quarter of an Acre, and euerye groate or 4. pence to conteyne a dayes worke, and euery penny to conteyne a pearche, or as some terme it a roode, and for to cast the contentes of Land, doo this, as by ensample of a peece of Land that is 30. pearches long, and 24. pearches broade, the 24. pence is 2. shillinges, then beyng .30. roodes long, that is 2. tymes .30. shillinges, that maketh in money 3. pounde, and 3. pounde is .4. marke, and a noble, so that the peece of Lande that is .30. roodes long, and 24. broade, doth conteyne 4. Acres and a halfe. Yet furthermore for your better vnderstanding, where there is half pearches and quarter of pearches, both in the length and in the bredth, then you shall doo thus, by a peece of Lande that is 53. roodes long, and a halfe, and of bredth 42. and a quarter, then 42. pence maketh 3. shillinges and 6. pence: laye downe 3. tymes 53. shillinges, and that will be .7. pounde and .19. shillinges, and then ther is 6. pence more, in the bredth: and 53. halfe shillings maketh 26. shillinges and 6. pence, then laye that to the other summe, and then it maketh 9. pounde 5. shillings and 6. pence, then there is in the length halfe a roode more, therefore you must account it in the bredth, and 42. halfe pence maketh 21. pence. Then laye that to the sūme, then there is in the same bredth a quarter of a roode more, and that you must recken in the length: and 53. farthinges maketh 13. pence farthing, then laye the same to the rest, and it wyll make in money 9. pounde 8. shillinges and 4. pence ob. and that aunsweres to, in measure .14. Acres and 5. dares worke, and about halfe a pearche, for that you may knowe that .9. pounde is 13. markes and a noble, and there is 8. shillinges, & that is more then a noble by 4. grotes. Then put that noble to the other noble, then that maketh 14. markes, then the 4. grotes, put to the other 4. pence, maketh 5. grotes, and so that peece of lande which is 53. roodes long and a halfe, and 42. roodes broade and a quarter, shal be in measure 14. Acres 5. dayes worke, neere half a pearch. And [Page 3] by this account of money, you may know the contentes of anye peece of lande, better then you may knowe by any maner of table or tables, and this serueth both for the learned, and the vnlearned, and is generally called the husbandmans rule, for that he may as soone learne this or sooner, then he shall vnderstande the tables of measures, and that serueth but for a quantitie of measure, and thys serueth generally for all manner of measures, be it neuer so bygge or smal, being sure for to cast the money right.
The seconde Chapter sheweth how to measure board and Glasse, and to cast the contentes therof, with other necesary thinges belonging therunto.
NOw furthermore in lyke manner, for the measuring of boord or Glasse or any such other lyke, for that it is sufficientlye declared in tables, in Maister Digges his Tictonicon: yet notwithstandinge thus you may know the contentes without any tables, as thus.
Looke at what length your boorde is, multiplye the number of feete into ynches 12. ynches to the foote, then that beinge doone, multyplye the breadth with the length, that is to saye, the number of ynches of the length, with the number of ynches of the bredth, deuide that number by 144. and that shall shew vnto you the number of feete: then if that there remayne any thinge, euery 72. ynches maketh halfe a foote, and then euery 36. shall make ¼. parte of a foote, and for that euery man hath not Arethmetick for to cast it by, yet this is a ready way that many Carpenters doe vse, and is exact ynouth, as thus.
If that the Borde be more then a foote brode, then they doo looke how many foote long the Borde is: then [...]hey account that that there is so many foote of Borde as the length of the borde is, and then for the odde ynches and partes, they mete in the bredthe how much it is, and then with the rule, as often times as there is foote long in the Borde they doe measure or set it downe, and then they do measure how many foote longe it commeth vnto, and then they doe say that it is so many foote of borde more then the length [Page] of the borde is: and that is true without any fayle, as for ensample thus, by a borde of 10. foote longe, and 14. ynches and a halfe broade. Nowe for that the Borde is 10. foote longe, then at twelue ynches broade, there is 10. foote of borde, and then there is two ynches and an halfe more in the breadth, and for that with the ynche rule that is layde downe 10. times, for that the borde is 10. foote longe, and that beinge measured howe long it reacheth, it wyll be 25. ynches longe, that is .2. foote and 1. ynche, thē that 2. foote put vnto the 10. foote, it maketh .12. foot, so that you may conclude that a borde of 10. foote longe, and .14. ynches and ½. brode, that there is 12. foote and 1.12. parte of a foote of a borde, without any fayle, and thus you may doe, howe brode or narrow so euer that any borde or Planck is.
A note of measure.And furthermore, at one ynche brode, then 12. foote long maketh a foote of borde, at 2. ynches brode, 6. foote long to a foote: at 3. ynches broade 4. foote longe to a foote, at 4. ynches brode 3. foote long to a foote, then at 5. ynches brode 2. foote and 5. ynches long to a foot of borde: at 6. ynches brode 2. foote longe to a foote of borde, at 7. ynches brode 1. foote and 8. ynches and a halfe to 1. foote of borde, at 8. ynches brode, one foote and 6. ynches longe to one foote of borde: at 9. ynches brode 16. ynches long to one foote of borde: at 10. ynches brode 14. ynches longe and ½. to one foote of borde, at 11. ynches brode 13. ynches long and 1.11. parte of an ynche to 1. foote of borde: at 12. ynches brode 12. ynches long to one foote of borde, at 13. inches brode 11. ynches long and 1.13 parte to one foote of borde, at 14. ynches brode 10. ynches and 2/7. partes of an ynche longe to one foote of borde: at 15. ynches brode 9. ynches and 9.15. partes of an ynche long to one foote of borde: at 16. ynches brode 9. ynches long to one foote of borde, at .17. ynches brode 8. ynches and 1.2. long, to one foote of borde, at .18. ynches brode 8. ynches longe to one foote of borde, and for that there is no cōmō bords sawne aboue 18. ynches brode, therfore I leaue of to proceede any further, & if it chaūce for to be broder thē any of the measure afore named: then you shall take one of these measures afore, that is halfe the breadth, and then you shall take [Page 4] halfe the length for the true contents of the measure, and so foorthe at your discretion.
And furthermore,You may know by Arithmetick how many ynches in length wyll make a foote of borde whatsoeuer the bredthe is. you may know how many ynches long wyll make one foote of borde whensoeuer you do know the bredth, as this. Fyrst looke howe many ynches that the borde is brode, then deuide the bredth out of 144. and that shall shew vnto you the true contentes of inches, of length in one foote of borde, with partes of ynches adding the remainder vnto the bredth. And furthermore in lyke maner, for to knowe the contentes howe many feete there doth contayne in any great quantytie, as Pauement or Glasse, or Chamber floures, then multiplye the length with the breadth,By Arithmetick you may know how many foot there is in any great quantyty. and that sheweth vnto you the true contentes of the number of feete. Thus much haue I sayde for the measuring of all manner of plate formes, for that the common people fall into such a number of errours for lack of Geometry & Arithmetick, as thus. Some wil holde opinion that if any Square or Circle be as muche in measure more, they wyll say that it is but as bigge agayne, where that it must needes of force be 4. times so big, as for ensāple by a Pauement that is but 12. foote square euery waye, and an other Pauement (in lyke maner) 24. foote square euery way, now that Pauement being 12. foote square, contayneth 144. foote, and the other being 24. foote square euery way, contayneth .576. foote, that is 4. times so bigge as the other that is but 12. ynches square, as by this Ensample it doth appeare.
[Page] the one of these squares to be 12. foote square, and the other 24. foote square: for yf that you would haue a square the one to bee as bigge agayne as the other, then yf that it bee a square roote as these 2. figures afore made: Then looke how many foote it is from corner to corner, right agaynst it, passinge by the Center of the square, the length of that Lyne from corner to corner, shall make an other square vpon the foure sydes as bigge agayne as the other from corner to corner: as for ensample thus.
By the square afore made of 12. foote square euery waye, and the slope Lyne from corner to corner, is 17. foote, lackinge 1.33. parte of a foote, which is 16. foote and 32.33. parte of a foote. For as the square roote of 12. is 144. so the square roote of .17. is 289. swhich is more by one foote, then the double of 144. as by the enample afore made it doth appeare. And for your better ensample, beholde this Fygure with
the square roote of .12. is cutte from the one corner to the other corner, and the length of that lyne from the one corner to the other is 17. foote lackynge 1.33. parte of a foote, and yet for the more plainnes, you shal haue this ensample by the square afore made of .12. foote euery way, and so beinge cutte from corner to corner, it is 17. foote lacking 1.33. parte: and when you haue done, you shall put the 2. partes so cutte a sunder, together, laying the syde 12. vnto 12. and then it wyll make a Tryangle as bigge as the square: then adding so much more vnto it, wyll make a square roote iuste as bigge agayne, as by this ensample it doth appeare.
Now furthermore, the square roote of .17. lackynge one 33. part, will bee corner to corner 24. foote, and it is a square roote iuste as bigge agayne, as that of sixteene foote and a 23. parte of 33.
And now furthermore for Circles or longe squares, all is one matter, as for an ensample thus by a Circle of 12. foote broade, and the Compasse shall be 37. foote and 8. ynches and better, for this is generall for euer looke how many times 7. is in the Diameter, so many times 22. shall be the circumference. Or now contrarywise: Looke howe manye times 22. you haue in the Circumference so many times 7. shall be the Diameter.
Now to the purpose:An ensample in Circles. a Circle as much more in breadth or in Compasse, shal make a Circle foure tymes so bigge in measure as the other, and for to measure a Circle truly, doe thus. Fyrste, knowing the Circumference and the Diameter, multiply [...] the one by the other, that is to saye, the compasse with the breadth, and then take the fourth parte of the measure, for the true contentes of the Circle, or els take halfe the Compasse, and halfe the breadth: then multiply the one by the other, that being done, it sheweth the iuste contentes of the Circle, as for ensample thus.
By the Circle of 12. foote broade, and the Compasse 37. and 9. ynches, and halfe 12. is 6. and halfe 37. foote and eight ynches [Page] is 18. foote and 10. ynches, and it being multiplyed together, maketh 113. foote, the true contentes of that Circle afore named. And now there is an other Circle that is 24. foote broade, and that commeth vnto in Compasse 75. foote and 4. ynches. And then take halfe the Compasse which is 37. foote and 8. ynches and halfe the bredth, and that is .12. foote, and then multyplye the halfe Compasse with the halfe bredth, and that maketh .452. as by the ensample of these 2. Circles it doth appeare.
Now furthermore, yf that you woulde haue an other Circle to be iust as bigge agayne, or els in lyke manner the other beynge knowne, I woulde haue a Circle halfe so bigge, then bring your circle into a square roote, not reckoning the compassed parte, [Page 6]
and the length of the square shall make the Diameter of a Circle iust halfe so bigge, and that being doubled, it wyll make a Circle iust as bigge agayne as the other Circle, as by this ensample of a Circle of 24. foote broade, and the roundnes beyng cut a way,Ensamples of Circles. it will make a square roote of 17. foote square, lackinge 1.33. parte of a foote: and then you may knowe what a Circle of 17. foote of Diameter lacking 1.33. parte of a foote, wyl make an other Circle halfe so bigge as a Circle of .24. foote of bredth, and as big agayne as a Circle of 12. foote broade: and so foorth in all poynts whether that they be Circles or squares, as by the ensample of a longe square of 12. foote longe and 6. foote broade, and there is an other square of 24. foote longe and 12. foote broade.
Now the square of 12. foote longe and 6. foote broade,An ensample of long square [...] contayneth but 72. foote, and the other of 24. foote long & 12 foote brode, contayneth in feete .288. whiche is foure tymes so bigge as the longe square 12. foote longe and 6. foote broade.
[Page]And for to make an other square as bigge agayne as that of 12. one way and 6. an other way, that longe square shall bee 17. foote long, lacking 1.33. partes of a foote, and of bredthe 8. foote and 16.33. parte of a foote: as by these 3. figures it doth appeare:
the one 12. foote long and 6. foote brode, and the seconde .24. foote long and 12. foote brode, and the thirde 16. foote and 32.33. long, and 8. foote and .16.33. brode. And the length of the shippe lynes from corner to corner of that which is 10. foote longe and 6. foote brode, is 13. foote and 11.26. part of a foote: and that of 24. foote longe and 12. foote brode, shal be 26. foote and 11.13. parte of a foote, the length of the Hipothenusal lyne from the one corner to the other corner, and also the longe square of seuenteene foote long lacketh 1.33. parte and neare 8. ynches and 1.2. broade, the slope Lyne from corner to corner, shall be nineteene foote longe lackinge 1.36. parte of a foote, which is 18. foote and 35.36. part of a foote: and as it hath bene often declared in this woorke, howe too knowe the lengthe of the slope Lynes from the one corner to the other corner, beinge sure for to make a square Angle.
[Page 7]And then by extracting of the roote, as afore is declared, you may knowe the length of the Hipothenusall or slope Lynes, as by this ensample: if that your
square doo leuell, then you must bee sure to make it square to your grounde lyne, as by this ensample is doth appeare, by these 2. figures, and the pricked lynes doo make the leuelles a iust square Angle, both the sharpe Angle, and the broade Angle, as you maye see by these .2. figures afore made. And furthermore, for to knowe the proportiō, how much the one is bygger then the other of any superficial, whether that it be circles or square rootes, if that you doo knowe the contentes of the one, and would knowe howe much that the other is bygger or lesser, then you knowing the contentes of it alreadie, then multiply them both squarely, that doone,How to knowe the quantytie or proportion of any Circle or square what the one is biger then the other. then if that you doo know the contentes of the lesser, and would seeke the contentes of the bygger, then multiplye the bygger number by the contentes of the lesser, and looke what that commeth vnto, then deuide that same by the number of the lesser, and that wyll shewe you iustly, what proportion that the bygger is in quantitie more then the lesser. Nowe contrariwise if that you doo knowe the contentes of the bygger: and to knowe the contentes of the lesser, then multiply the contentes of the bygger, with the number of the lesser, and then deuide that same by the number of the bygger, and that wyll shewe vnto you the proportion of the lesser, and by thys order you maye knowe the proportion of any Triangles or longe square, or what forme soeuer that it hath, as it is more plainelye hereafter shewed in the 8. Chapter by the proportion of ropes.
The thirde Chapter dooth shewe howe for to measure Tymber, and to bring it to a square, aswell without Arithmetike as otherwyse, and also howe for to knowe the true contentes of anye peece of Tymber.
NOw furthermore, for the measuring of all manner of bodyes, as Tymber or stone, or any suche other lyke, Maister Dygges in his Booke named Tectonicon, hath made Tables of the squares of it: yet notwithstanding I will shewe vnto you, how that you shall knowe how many ynches long wyl make a foote of any portion of measure, as thus: first knowing the breadth and the thickenesse, and you woulde knowe how many ynches longe wyll make a foote, then looke howe manye ynches that the breadth of the Tymber is the broder waye, and then in lyke manner looke howe many ynches that it is in th [...]cke [...]sse the narrowest waye, then multiply the broader side, wyth the narrowe syde, then that number that commeth of that multiplication,How to knowe [...] many ynches long in Tymber wyll make a foote what square s [...]nes that it hath by Arithmetike. you must deuide that summe out of .1728. then that sūme that standeth before the quanti [...]ie lyne, shall be the number of ynches in length of one foote of Tymber or stone: and then if there remayneth any thing, then if that number which was the deuider if that it be halfe the number, then it is halfe an ynche more: if a quarter of the number, then one quarter of an ynche: and yf .3. quarters of the summe, then 3.4. partes, and so foorthe to anye parte or partes of the remainder. And then according to that, the proportion shall be so many partes of an ynche, as the remaynder dooth shewe, and thus you maye knowe howe many ynches long wyll make one foote of Tymber or Stone, without anye squaring of the Tymber. And as Maister Dygges in his Booke called Tectonicon, hath made Tables of the squares, that you may doo by extractions of the roote, as afore is declared in thys woorke. And nowe for bycause that euerye person that destreth for to knowe howe for to measure Tymber, or any other thyng, haue not all manner of Arithmetyke, therefore you shall haue a [Page 8] Table of the squares of Tymber,The length of a foote of Timber according vnto the square. howe manye feete and ynches wyll make one foote longe of Tymber from one ynche square, and so from ynche to ynche, tyll that you come to .36 ynches square, as by this ensample it dooth appeare, and the vppermost rowe of this table is the number of ynches of the squarenesse.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| 1 | 4 | 36 | 16 | 9 | 5 | 4 | 2 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 0 | 11 | 3 | 9 | 5 | 2 | 0 | 10 | 8 | 7 | 6 | 5 | 5 |
| 1 8 | 3 4 | 7 16 | 1 4 | 1 4 | 3 8 | 13 16 | 11 16 | 3 4 | 15 16 | 1 4 |
The seconde, how many foote long will make one foote of Tymber, the thyrd is ynch, the 4. is partes of an ynche, to bee added
| 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 |
| 4 | 4 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 3 4 | 5 16 | 7 8 | 9 16 | 5 16 | 0 | 3 4 | 1 2 | 3 8 | 3 16 | 1 16 | 7 8 | 3 4 | 11 16 | 9 16 | 1 2 | 7 16 | 5 16 |
vnto the number of feete, or ynches, as by these 2. Tables it doth appeare. And nowe for the measuring of Tymber or Stone, looke what that it commeth vnto in square number, then these tables afore made doo shewe vnto you, howe manye ynches and partes of ynches wyll make a foote longe of that squares: and for bycause that euerye peece of Tymber that is to be measured, is not equallye square, I wyll shewe vnto you howe that you maye square it wythout extracting of the roote, for that I knowe euery person hath not that kynde of Arithmetike.
And furthermore, for to make Tables thereof, it were but superfluous, for that Maister Dygges in hys Tectonicon, hath made Tables exact yenough for that purpose.
[Page]And furthermore this I am assured of, that the reason how for to square theyr tymber, may be as soone beaten into the common peoples heades, and sooner, then they will by instructions learne to vnderstande the tables of squares. And nowe to instruct them howe for to square theyr tymber whensoeuer that the Tymber is broder one way, then that it is another way, then doo thus. Fyrst looke howe many ynches that the Tymber is the broder way, and then looke howe many ynches that it is the narrowe waye, then when that you haue doone,How to square Tymber wythout [...]rithmetike or tables. recken howe many ynches that it is, more then the perfyte square, then take that number of ynches and put it into 2. equall partes: then that beyng doone, you shall lacke a certaine quantitie for to fulfyll one of the corners, and that quantitie you shall rebate vppon the .2. sides, concluding thus, that it is thus many ynches square, lacking so muche as the quantitie in the corner dyd shewe vnto you, vppon the 2. sides. And for your better instructions I wyll giue vnto you certaine ensamples,An ensample. as thus, for the fi [...]st ensample is by a peece of Tymber of 13. ynches one way, and 11. ynches another waye, and nowe you doo see that the broder side is .2. ynches more then the narrowe side: then deuide the .2. ynches into 2. equall partes, and that is one ynche to a part, and then you doo see that it is .12. ynches one waye, and .12. ynches the other way, sauing that it lacketh one ynche at one of the corners, and that one ynche wyl rebate vpon the 2. sides of 12. which is 24. ynches, a .1.24. part of an
ynche, as by this figure it is declared. And now I do conclude that this peece of tymber 13. ynches one way, and 11. ynches another waye, dooth make in square Tymber 11. ynches and 23.24. parts of an ynche, which is .12. ynches, lacking 1.24.The seconde ensample. part of an ynch. And now to the seconde ensample by a peece of Tymber, that is 12. ynches one waye, and 20. the other way. Nowe you doo see that the broder syde is 8. ynches more then the narrowe side: therefore I doo deuide the 8. ynches into 2. equall partes, and that is 4. ynches to a part, and [Page 9] then laye 4. ynches more to 12. ynches,
vpon the 2. sides, that maketh 16. ynches square, then theyr lacketh .4. ynches square at one of the corners, then multiply 4. tymes 4. and that is 16. and then the peece of Tymber beyng added vnto the 2. sydes 4. ynches vnto 12. it maketh 16. and 2. tymes 16. and that maketh 32. then that 16. ynches that lacketh in the corner beyng rebated from 32. wyll rebate halfe an ynche, for .16. whole ynches will make .32. halfe ynches. Therefore I doo conclude that the peece of Tymber that is 20. ynches one waye and 12. ynches the other way, wyll make in square Tymber 15. ynches, and ½. the true square thereof.The thyrde ensample. Now furthermore to the thyrde ensample by suche a peece of Tymber that is .23. ynches one waye, and but .7. ynches the other waye, then the broader square, is more then the narrower by 1 [...] [...]nches: then as afore is declared, deuide 16. into 3. equall par [...], and it wyll be 8. to euery part, and then put 8. ynches in breadth vppon the two sydes vnto 7. it wyll make 15. so
that it woulde make a square 15. ynches euery way, sauyng that it lacketh a great matche in one of the corners, then multiplying 8. times 8. it maketh 64 then you must rebate 64. ynches out of the 2. sides of 15. ynches, and 2. tunes 15. is 30. ynches, and thē the square is but 14. ynches: then 2 times 24. is 28. and when there is 30 pulled out of 64. then is there but 34. lefte: thē rebate 28. ynches more from the 2. sides, then the square is but .13. ynches square, and then .30. and .28. beyng taken out of 64. then there resteth but .6. and then at the .2. corners, as first at 30. and then at 28. you shal rebate one ynche at eche of the corners, one and 2. tymes one is 2 then put that 2. vnto the 6 and it maketh 8. and then the square Tymber is but 13. ynches, and .2. tymes 13. is but .26. and yet there is .8. ynches [Page] to be rebated of from .26. and it commeth vnto 4.13. parte of one ynche, & so muche the timber is lesse then .13. ynches square: therefore you may conclude that the peece of Tymber .23. ynches one way, and but 7. ynches the other way, shal make in square Tymber 12. ynches, and 9.13. parte of one ynche iust, and this is true, and thus maye you square any peece of Tymber, whatsoeuer that it be, without any tables or extractyng of the roote. And thus I make an ende of the ensamples, thynking this sufficiente yenough for instructions: and for to measure rounde Tymber, or Tymber that hath many square sydes, Maister Digges hath sufficienly declared in hys Tectonicon, sauing that for the measuring of rounde Tymber, you must allowe as I haue declared in this Booke: that is to say, euerye Diameter of .7. ynches, hath the circumference 22. ynches: and then to measure rounde Tymber, take halfe the circumference, called the compas, and halfe the Diameter, called the breadth, or thyckenesse: then squaring that, it shal shewe vnto you the true square of that Tymber, without any fayle.
The fourth Chapter sheweth howe for too measure all manner of bodies, as Tymber, or stone, cubes, or globes: and to knowe what proportion of measure or waight the one hath vnto the other.
NOwe furthermore, for the measuring of al manner of bodies, that lacketh parte of their forme, and other that be more then their forme, and other that be mixed bodyes, beyng in one place more then theyr forme, and in an other place lacketh parte of theyr forme, in the measuryng of them, you shal doo thus. And as it is declared afore, in the measuring of Tymber or Stone, or anye suche other lyke, if so be that it be equallie square or partilye square, all is one matter, or rounde, or many squares, Mayster Dygges hath sufficiently [Page 10] declared thereof, as touching the measuring of it,How to measure any thing that lacketh parte of hi [...] forme. for that it is a body properly of it selfe. Thē furthermore, there be bodies that lacke parte of theyr forme, as thus, there is is a peece of Tymber eyther rounde or square, that maye be hollowe in the core or middle, or els it may be hollow like a Trough or with hollowe natches into it, as by these ensamples it dooth appeare, and the blacke dooth sygnifye the hollowe: and for to measure them trulye, do thus.
First measure the Massy bodyes contentes, and so cast it in that forme, then measure the hollowe or concaue place, as though it were Timber. Then cast the contentes thereof, and pull that su [...]e away frō the whole contentes, & that which doth remaine, shalbe the true contētes of that peece of timber, or stone, & so forth.How to measure any thyng that is more then his forme. And now for superfluous bodies as Timber or stone, or any other thing, which is more thē their proper forme, as by these ensāples
[Page] it dooth appeare. Then shall you first measure the principall bodye by it selfe: that beyng doone, then measure the superfluous parte or partes, by themselues, then adde or put all those numbers together, and that wyll shewe vnto you the iuste contentes of that body.
How to measure mixed bodyes.And nowe furthermore for the measuring of mixed bodyes, as a mixed bodye is that which is hollowe in one place or places, and more then a body in another place or places, as these figures doth shewe.
And for the measuring of these bodyes as afore is declared, first measuring the principall bodye, and then nexte measuring the superfluous parte or partes, and put all those together, and then measure the hollowe parte or partes, as afore is declared, then cast the contentes of the hollowe Tymber or mettall by it selfe, then pull that summe out of the other summes, and then that which dooth remayne, shall bee the true measure of the bodye that you haue measured, and so foorth.
And nowe furthermore, for the measuring of all bodyes, as Cubes or Globes, as for ensample thus, for the measuring of Globes or Cubes, as a shotte or a Bullet beyng a perfyte Globe, that all bodyes as Cubes or Globes, or anye other forme eyther rounde or square, [Page 11]
if that it be as much more in measure euery way. As I doe knowe the opinion of some people,Erroure in the commō people as by ensample that wyll saye that is but as bygge agayne, where it must needes of force be 8. tymes so bigge, as for Ensample thus.
By a peece of Tymber or of Stone, beyng a foote square euery way lyke vnto a Dye. And there is an other cube of Tymber or Stone of two foote square euery way lyke a Dye in forme. Now that cube of one foote square, is but one foote of Tymber or Stone: and the other cube of two foote square euery way lyke vnto a Dye, is eight foote of Tymber or Stone, as these two fygures doo represent.
Now you doe see this to be true: and yf that the measure of any thinge being as much more in length, bredthe and thicknesse, that it is 8. times so bigge, whether that it bee cubes or Globes, longe Tymber or Raske, or what soeuer it be.
And furthermore, as it is afore rehearsed, if that you haue a peece of Tymber,Ensample of large Tymber. yf that it be in squarenesse as long more and as thyck or broade more, that it is 8. times as bigge, whether that it bee rounde or square all is one matter, as for ensample thus. By a peece of Tymber of 10. foote longe, and .12. ynches square, that peece of timber shal be 10. foote of tymber: & if that you haue an other peece of tymber, that is 24. ynches square and .20. foote longe, that peece of timber shalbe 80. foote of tymber, as by these 2. figures it is shewed.
And furthermore, if that you woulde haue an other peece of tymber iuste as bigge agayne, as that of 10. foote longe, and one foote square, beinge iuste 10. foote of Tymber, and to be of that proportion in length and in squarenesse, that is declared heereafter in the 7. chapter.
And furthermore whether that it be in Cubes or Globes, and if that you doe knowe the contentes of the one, and woulde know how much the one is bigger then the other: then shall you do it thus. You must tryple the proportiō of the sydes of the cubes or Globes, and then multiply them together,To know the proportion of Cubes or Globes, the one by the other. as you doe in fractions: then looke what that number commeth vnto. Then if that you do know the contents of the lesser, and would knowe the conte [...]tes of the bigger, then multyplye the contentes of the lesser cube or Globe, with the number of the bigger: and looke what that number commeth vnto: then deuide that sūme with the number of the lesser cube or Globe, and that number that standeth in the quantitye Lyne, shall bee the contentes of the bigger cube or Globe, as for Ensample thus [...] , by a Bullet of Iron of .5. ynches in height, or Diameter, and suppose it to weigh 16. pound. And you haue an other Globe or Bullet of that stuffe of 9. ynches in Diameter, how many pounde shall that way? you shall knowe it thus.
[Page]triple the proportion of them both, & set thē downe thus .555.999: Then multiply thus .5. times 5. is .25. and then .5. times .25. maketh 125.
An ensample of Globes.And now to the bigger Globe, 9. times 9. is 81. and then .9. times 81. maketh 729, and now the lesser Bullet wayinge .16. pounde therefore multyplye .729. by .16. and that will make .11664. and now deuide this number by 125. and then there wyll stande in the quantytie Lyne 93. then there remayneth ouer 39. so as you may conclude, that the bigger Bullet doth way 93. pounde, and .39.125. whiche is neare 5. ounces, the true wayght of the bygger Globe. And now contrarywyse, you knowing the contentes or waight of the bigger cube or Globe: then you must multyplye the contentes by the number of the lesser, and then deuide it agayne by the number of the bigger.
And for more playnnesse, by the Bullet before rehearsed of .5. ynches high,The seconde ensample. to way 16. pound. Now I haue a lesser that is but 4. ynches in his Diameter, what shall it way: you shall knowe it thus 444.555. fyrst multyply 4. times 4. and that is 16. and then 4. times 16. is 64. Then multiply 64. by the waight of the bigger Bullet, and that is 16. times 64. and that maketh 1024. and then deuide the number by 125. and then there wyll stande in the quantytie Lyne 8. & 24. wyl remayne ouer. So that yee may conclude, that the lesser Globe or Bullet doth weighe 8 pounde & 3. ounces. And so by this order you may know the proportion of all maner of other bodyes, what forme so euer that it hath: by multiplyinge the length, bredth and thicknesse, and then doyng as before is rehearsed, the contentes shall appeare.
The fyfth Chapter sheweth how for to measure Globes, and to know the contents in ynches or feete.
ANd furthermore, for the measuring of Globes by proportion, how much that the one is bigger then the other, it is no otherwyse then the proportion of any other body, as by ensāple of the measuring of cubes, as afore it is declared. For this is generall [Page 13] for euer in the measuringe of all solled bodyes, as Tymber and Stone, or Raske, or any other thinge what so euer that it be, if that the proportion of measure be as 1. vnto 2. the body contentes as 8. vnto one, that is to saye, that if a shotte or Globe of Iron of .2. ynches heyght doe weigh one pounde, then shall a shotte or Globe of Iron of 4. ynches height, weigh 8. pound, and so forthe as afore is rehearsed. And also this is a verye good way to know the contentes of a Bullet or Globe, a cube of .4. ynches, wyl goe very neare to make a Globe of .5. ynches in Diameter: and for Ensample of this matter beefore rehearsed, they doe vse for to measure Globes or Bullets in this sorte, to know their contentes. Fyrste thus.The measuring of Globes. The Circumference bringe knowne, as 7. vnto 22. the Diameter is founde.
Then multyply the halfe Circumference w [...]th the halfe Diameter, and that being done, looke what number that commeth vnto. Then multyply that by the Diameter agayne, and looke what that number ryseth vnto: then take ⅔. partes of that number, and that shall be the contentes of the Globe or Bullet, Ensample thus.
By a Globe of 12. ynches high in the Diameter. Now to knowe the Circumference: then multiplye 12. by 22. and that commeth vnto 264. and then deuide 264. by 7. and that shall shew vnto you the Circumference: so that commeth vnto .37. and .5.7. the true compasse of the Circle. Then take the halfe of both the Circumference, and the halfe Diameter, that is to say, halfe 37. and .5.7. and that maketh 18. and 6.7. pa [...]tes and halfe 12. and that is .6. Then multiply 18.6.7. times .6. and that commeth vnto .113. and then multiply that number by the whole Diameter agayne, and that cōmeth vnto 1356. & that is lyke vnto the end of a pyller: Then for that take ⅔. partes of the number, and that wyll be .905. the true contentes of the number of ynches in that Globe, and by this order you may measure the contentes of all Globes how big or small soeuer they be. But now if you would know the contents of the superficiall, that is to say, what number of ynches would couer the Globe or Bullet: then you must doe thus: multiply the Circumference with the Diameter, and that number shalbe the contentes [Page] of the [...]n [...]yden [...] the Globe or Bullet. &c.
And furthermore, [...]o know the true contentes of a Globe, how many ynches it doth contayne, this is the easyest maye that maye be deuised.
Take the true Diameter of the Globe, and multiplye it cubitly, and then multiply thathy 11. and then deuide that by .21. and tha [...] shall shew vnto you the true contentes of the number of ynches in that Globe, as for ensample thus: by the Globe before rehearsed of 12. ynches in Diameter or height, and 12. times 12 is .144. and then 12. times 144, maketh 1728. and then that multyplyed by 11.19008 and then it maketh 19991. and then that beinge deuided by .21. and then there wyll stande in the quantytye lyne 905. and 3. wyll remayne ouer: So that you maye conclude that the Globe of 12. ynches in height or Diameter, doth containe 905. ynches and 1. of .7. parte of an ynche.
To measure the playne of a Circle.And furthermore, to knowe the contentes of a playne Circle how many ynches or feete that it doth contayne: then multyplye it by the Diameter squarely, and then multiply it agayne by .11. & then deuide that nūber by 14. & that shal shew vnto you the true: contentes of the platforme of that Circle. Ensample by a playne Circle of 12. foote broade or ouer, and to knowe how many feete that it doth contayne: Then multyplye 12. times 12. and that maketh 144. and then multyply 144. by 11. and that maketh .1584. and then deuide 1584. by 14. and then there will stande in the quantytie lyne 113. and 2. wyll remayne ouer: so that you maye conclude, that the contentes of that Circle that is 12. foote broad, that the platforme of that Circle doth contayne 113. foote, and 1/7. parte of a foote.
The syxt Chapter sheweth howe for to builde Shyps by proportion, that is to say, if that you haue one Ship for an ensample, if you woulde haue an other as bigge agayne, more or lesse: this Chapter doth shew vnto you howe you may doe it, keepinge that moulde and proportion in all poyntes, that is to saye, by extractinge of the cubike roote.
AND furthermore, I doe thinke it conuenient, for that I doe know that many that are Naupegers or Ship carpenters, haue not the exact knowledge in these causes, that is to saye, that when they haue builded any Shyppe or Boat, and the tonnage then knowen vnto them,Of the bending of Sh [...]ps. yf that you woulde haue an other Ship or Boate of that mould and of that proportion in all poyntes, to be double that tonnage or burthen that the other is: I doe know that there is but few Naupegers or Ship carpenters that can do it: for that they d [...] look for the [...]st parte of them the extractions of C [...]thicke rootes for otherwise it is not possible for it to be done: for no man may keepe iust proportion in all poyntes without the extracting of Cubes, they may well keepe the tonnage or but then, but not the proportion and moulde in all poyntes. For according as it is afore declared, by the measuringe of Cubes or Globes or any massy bodyes, if that they should double the measure, then it were 8. times so bigge.
Therfore whensoeuer that you haue builded any ship or Boat, or any other crafte, whatsoeuer it be,How to alter the bignes of a ship and [...]e [...] to keepe the proportion mould, and fashion. then if that you would haue an other of that selfe some moulde in all poyntes, and woulde haue the other as bigge agayne, or twise or thrise so bigge agayne, or halfe so big agayne, or any other quantity more or lesse, then shall [Page] you doe thus.
First for the length of the Reele, you shal multiply it cubitely, and then in lyke manner euery beame: the mydshippe beame and all the rest of the Beames, to multiply them cubitelye, and also the rackinge of the Shyppe both the Stem and the Sterne post, to multiply thē cubitely, and also the principall tymbers that doth moulde the Shyp, to multiplye them cubitely, and also the depth that the Shippe is in holde, to multyplye it cubitely, and so consequentlye euery place or places with the Ship that doth leade any worke, to multyply it cubitely.
Then that being done, yf that you woulde haue the other Shyp or Boat as bigge agayne, then double that number that you haue before multiplyed: Then extractinge the Cubite roote thereof, then according vnto the number make your Reele, your timbers, your Beames, and so consequently all the rest of your thinges, according vnto the Cubite roote so extracted, and that beinge done, you shall make hir of that moulde and proportion, and of double burthen, without any fayle, otherwyse it is not to be done.
And furthermore, if that you woulde haue one thrise so bigge, then 3. foulde your number, and so foorth: then if that you woulde haue her but halfe so great, then take halfe the number so multyplyed, and the Cubite roote so extracted, shal make a Shippe or Boat, but halfe the burthen: and thus you may make a Shyppe or Boate of what proportion so euer you lyst [...], and also to be of that selfe same moulde that the other was.
Prouided also, for the squarenesse of your Beames, and your Tymbers, and also the thyckenesse of the Planke, that you doe obserue this order before mentioned, or els in otherwyse doynge, you ma [...] put more Tymber or lesse Tymber, then the proportion of the burthen doth come vnto, and so by that meanes you may commy [...]te errour. As for Ensample thus briefely.
By a shippe that was .44. foote long by the Reele, and .20. foote broade vppon the mydshippe beame, and dyd racke it wyth the [Page 15] stem forwardes 13. foote, and the Sterne poste dyd racke 7.An ensample of the altering of the burthen of a ship, and to keepe the moulde and proportion. foote offwardes, and the shippe was 9. foote deepe in holde. Now this shippe was .100. tonnes, my desire is to haue a shippe of that selfe same moulde, in all poyntes, to be of iust double burthen, that is .200. tūnes. Then first multiply the lēgth of the keele cubitely, and that is 44. foote: therefore multiplye .44 tymes .44. and that maketh 1936. and then againe by 44. that maketh .85184. so it is multiplyed cubietly. Nowe double the number, and that maketh 170368. and nowe extract the cubite roote, and that will bee 55. foote and .3993.9075. parte, which maketh in ynches .5. and .⅗. partes of an ynche, so that you maye conclude, that the shippe must be .55. foote, and .5. ynches, and neere .32. quarters in length by the keele. And nowe for the breadth of the beame, and that is 20. foote, and .20. tymes .20. is .400. and that multiplyed by .20. maketh .8000. and this double is .16000. then extract the cubite roote, and that is .25. and .375.1875. and that maketh in ynches 2. and .⅗. partes of an ynche, so that you may conclude that the ship must be .25. foote and .2. ynches, and neare a halfe ynche vpon the beame, for the bredth of the shippe. And nowe for the racking of the Stem, that is .13. times .13. and that commeth to .169. and nowe cubitely, and that maketh 2197. Now this number double, maketh .4394. Nowe extracting the cubite roote it will be .16. and .298.768. and that commeth vnto .4 ynches and 4/7. partes: so that you may conclude, that the shippe must racke forwardes with the Stem .16. foote, & .4. ynches & neare .¾ partes. And now for the sterne poste, and that is .7. foote, therefore .7. tymes .7. is .49. and that multiplyed againe by 7. and that maketh .343. then it beyng double .686. then extract the cubite roote, and that is .8. and 174.1.92. and that commeth vnto .10. ynches, and .7.8. parte, so that you may conclude that the shippe must racke wyth the sterne post 8. foote and .10. ynches, and .7.8. partes of an ynche. And now for the depth in the whole, that beyng 9. foote, 9. times .9. is .81. and that multiplyed cubitely, maketh 729. and that beyng doubled, then it is .1458. and then the cubite [...]oote beyng extracted, is .11. [Page] foote & 127. of 363. part, & that cōmeth vnto in ynches .4. & 4. of 5. partes, so that you may conclude that the shyppe muste bee in deepenesse in holde, 11. foote and 4. ynches, and 4. of 5. partes of an ynche iuste. And nowe the shippe of 100. tonnes, dyd drawe 12. foote, when that shee was Laden. Wherefore you must keepe a proportion, in all the partes of the worke, as is afore declared vnto you: then shall the shippe of 200. tonnes, drawe or goe into the water by this aforesayde meanes, 15. foote, and one ynche and a halfe: and by this meanes which is the extracting of the cubicke roote, you may make a shippe or boate or any other crafte, of what burthen soeuer you [...]yst [...] ▪ and to keepe that [...]ulde and proportion that the other was made of, in all poyntes. And by this meanes and order, you may know the quantity of any maner of Caske, and to make it by proportion howe bygge or little soeuer you wyl haue it.
The seuenth Chapter dooth shewe in lyke manner the making of shippes by proportion, sauing that the cubike roote is extracted already with an easye way howe to make them, of what tonnage or burthen, you liste, and of that moulde and proportion in al poyntes.
ANd nowe for that I doo knowe the most parte of men cannot extract the cubike roote, for that kinde of Arithmeticke is very harde, and not easye too bee learned, therefore I meane to make a litle easye note▪ for that they shall not altogeather leese theyr tyme, in readyng of this, but that they shall haue some helpe for the doubling of cubes, although it bee nothing in the respect of them that haue the vse of the seconde parte of Arithmeticks, as the extracting of rootes and cubes, and cubike numbers. &c.
[Page 16]F [...]rst thus: if so bee that you haue a cube or globe, and would haue an other as bygge agayne, or but one quarter more,Of Cubes. then put the syde of the cube, that you haue for ensample, into 4. equal partes, and if that you woulde haue that one quarter bygger, then make the bigger cube of 4. of those partes and 1. of 3.To make a cube a quarter bigger. parte, and then haue you your desyre. And if that you woulde haue it halfe so bygge more, still putting the syde of that Cube that you haue for ensample, into 4. equall partes, then make the syde of the other cube of 4. of those partes, and 2. 3. partes more, and that shal make an other cube as bygge, and halfe so bygge agayne, as the other.
And furthermore,To double a Cube or globe. if that you woulde haue a Cube to be two tymes the bignesse of the Cube that you haue for ensample, that is double measure, then put your Cube into 4. equall partes, and make the other Cube of 5. of those partes, and 1 of 25. partes more, and that shal make a Cubbes bigge agayne:To make a Cube 3. times so bigge. and to haue a Cube three tymes so bygge, then make the Cube of 5. of those partes, and 8. of 9. partes more, and that shal make a Cube .3. tymes so bigge.
And furthermore, for to haue a Cube 4. tymes so bygge, then make the Cube of 6. of those partes and 5. of 14. partes. And furthermore, to make a Cube 5. tymes so bygge, then make the Cube of 6. of those partes and 6. of 7. partes more:If a Cube or Globe be double measure, thē that is 8. times [...]o bigge. then to make a cube 6. times so bigge, then make the cube of 7. of those parts and 1. of 6. parte more, & if you would haue a cube 7. times so bygge, thē make that cube of 7. of those parts, 13. of 18. parts more: thē if you would haue a cube .8. times so bigge, then double the measure, and that is iust 8. times so bygge without any fayle, as afore it is declared, the one being 4. and the other being .8. then your measure is doubled. Nowe this short note or remembrance, you may accordyng vnto the Chapter going before, you hauing a shippe or boate that you woulde haue an other of that moulde and proportion in all poyntes, and woulde haue her as bygge agayne, more or lesse, you may do [...] it by this [...]o [...]e afore written: as thus: if you would haue her as byg againe, [Page] Then put the length of the Keele of the shippe that you woulde haue an other made by, and to keepe that moulde and proportion in all poyntes, into .4. equall partes, and then make the bygger of 5. of those partes, and .1.25. howe large or shorte soeuer that it be, and doo this also by euery beame and euery principall Tymber: and euery other thing that leadeth any worke, and you shall not fayle of the truth, for so muche as this dooth shewe, which is nothing in the comparison of them that can extract the cubite roote, it maketh not matter howe bygge or small soeuer the proportion is. And this note is but till the roote is encreased to .8. times hys bygnesse, and so muche as this dooth shewe, you shall fynde it reasonable exact ynough.
And yet furthermore, this is an easier way to builde any shippe or boate by proportion.An easy way to make ships by proportion. And first this: if you doe meane to bee one quarter bygger, that is to say, if that you woulde haue a shippe of 4. score tonnes, and [...] haue an other .100. tonnes: then for euery 12. foote or ynches, that the shippe that you haue for an ensample, is, in length, breadth, and deepenesse, and so consequently euery parte that leadeth any worke, make the bygger of 13. foote or ynches, and you shal haue your desire.
And f [...]rther, if that you woulde haue her halfe so bigge more, that is to say, your shippe that you haue for ensample, being .80. tonnes, and to haue the other 120. tonnes, then for euery 6. foote or ynches, make the other of 7. foote or ynches. And furthermore yf that you would haue her full as bygge agayne: then shal that be for euery 50. ynches, make the bygger 63. ynches, and then that Shippe shalbe of .160. tunnes, that is, double burthen. And then to bee three tymes so bygge, then for euery .36. ynches, make the bygger of .53. ynches. And then if that the lesser shippe be .80. tonnes, the bygger shalbee 240. tonnes: and if that you woulde be 4. tymes so bygge: then for euery 56. ynches, make the bygger of 89. ynches, and then haue you your desire, the one beyng 80. tonnes, the other shalbe 320. tonnes.
And further, if that you woulde haue bee 5. tymes so bigge, then for euery 7. foote or ynches make the bigger of 12. [Page 17] foote or ynches, and then the one being 80. tonnes, the other shal be 400. tonnes, and if that you woulde haue the bygger to be .6. tymes so bygge, then for euery .24. ynches make the bygger of .43. ynches, and then the one being .80. tunnes, the other shalbe 480. tunnes, and then to be .7. times so bigge, for euery .72. ynches, make the bigger .139. ynches: and then the bigger shippe shalbe, 7. times so bigge: the lesser beyng .80. tunnes, the bygger shalbe .560. tunnes: and then as afore is declared, if that the measure be double, then the bigger is .8. tymes so bygge: that is .640. tonnes.
The eight Chapter sheweth howe muche that one rope is bigger then an other: and if that you haue a rope of any syse, then you may knowe howe to haue another of what syse you lyste: and also if that you do knowe the waight of one rope: you may knowe the waight of anye rope by proportion.
YEt furthermore, I do thinke it conuenient for diuerse considerations, for that I do do knowe that there is but very few Sea men, that hath the vse of the extracting of the square roote: and without that they cannot knowe howe for to fit a shippe with ropes, but that they must of force, many times put too bygge or too smal a rope in diuerse places, not meete for that rome,How to a [...]e [...] the bignes of ropes & how to double the syse vntill they doo see it by common experience, and afterwardes amende it. Wherefore I wyll make a little briefe note, for the doublyng of ropes by proportion. And fyrst by a rope of .3. ynches compasse: and to haue another as bigge agayne, some wil holde an opinion, that it must be .6. ynches compas, but then it is 4. tymes so bigge: therefore to haue it as bigge agayne, it must be in compasse .4. ynches, and 1. of 4. partes, and then to haue a rope of .3. times so bigge as the rope of .3. ynches compasse, [Page] then that rope must be of 5. ynches, & .1. of 5. part, in cōpas: then to be 4. times so bigge, then that must bee double measure: that is 6. ynches compasse. Then too haue a rope .5. tymes so bygge: then that must be in compasse .6. ynches and .3. of .4. parte of an ynche: then to be 6. tymes so bigge, then it must be in compasse .7. ynches and .5. of 14. parte: and then .7. times so bigge to be in compasse .8. ynches, lacking 1. of .16. part▪ then to be 8. times so bigge, to be in compasse .8. ynches .1. of 2. part: then .9. times so bigge, to be in compasse, iust 9. ynches: then being 10. times so bigge: then it must be in compasse .9. ynches, and 9. of 20. parte: then 11. times so bygge, to be in copmasse .9. ynches, and 9. of 11. partes: and then to be 12. times so bigge, to be in compasse 10. ynches 2. of 5. partes: then .13. times so bigge, to be in compasse .10. ynches: and 17. of 20. part: then to be 14. times so bigge, as the rope of .3. ynches compas: therefore that must be 11. ynches, and 5. of 22. partes in compasse: then to be 15. times so bigge, then to be in compasse 11. ynches, and 7. of 11. partes: then 16. times so big, in compas iust 12. ynches. And then to be 17. times so big, thē to be in compas .12. ynches, & 3. of 8. parts: thē to be 18. times so big, then it wil be in compas 12. ynches, 9. of 12. part: & 19. times so big, then it wil be in compas 13. ynches, & 1. of 13. Then being .20. times so big, thē it wilbe in compas 13. ynches 11. of 26. parte: and then to be .21. times so bigge, it must be in compas .13. ynches 10. of 13. partes. Then to be 22. times so bigge: then it wilbe in compas 14. ynches and .1. of .14. partes: then to be .23. tymes so bigge, it wylbe in compas 14. ynches, and 11. of 28. parte: then too bee .24. tymes so bygge, it wilbe in compas 14. ynches, and .10. of 14. partes: then 25. tymes so bygge, too be in compasse iust 15. ynches: and then too bee 26. tymes so bygge: then it wyl be in compas 15. ynches, & 3. of 10. parts & then to be 27. tymes so bygge, it wyl be in compasse 15. ynches, 3. of 5. partes: and then too bee 28. tymes so bigge, that wylbee in compasse 15. ynches, and 9. of 10. partes: then 29. times so bygge too bee in compasse 16. ynches, and 5. of 32. partes. [Page 18] Then too bee 30. times so bygge to be in compasse 16. ynches, and 7. of 16. parte: and then to bee 31. times so bygge, to bee in compasse 16. ynches, and 23. of 32. parte: then to be 32. times so bygge, must be in compasse 17 ynches, lacking 1. of 34. part: and then to be 33. times so bigge, that wilbe in compasse 17. ynches, and 4. of 17. part: and then to be 34. times so bigge, it wilbe in compasse 17. ynches, and 1. of 2. part: and then to be 35 times so bigge, that wilbe in compas 17. ynches, and 13. of .17. part: and then to be 36. tymes so bygge, it wilbe in compas iust. 18. ynches. And then to be 37. times so bigge, then too bee in compas 18. ynches, and 1. of 4 part: then 38. times so bigge, to be in compas 18. ynches, and 1. of 2. parte, and then to be 39. times so bygge, it wylbe in compas 18. ynches, and 3. of 4. parte: then to be 40. times so bigge, it wilbe in compas 19. ynches, lacking 1. of 38. part. And nowe by this litle note, you may knowe howe bigge or smal that one rope is by another, so that the ropes bee all of one kinde of stuffe, and also of lyke hardenes in the woorekmanshippe, or laying.
And yet furthermore, I do thinke it conuenient, for to cōpare one rope by another, of the bigger sort:Of doubling of the bignesse of of ropes. for that which goeth before, they be all compared but vnto one rope of 3. ynches compas. And fyrst by a rope of 6. ynches compas: and to haue another as bigge agayne, that must be in compas 8. ynches, and 1. of 2. parte: and to haue a rope 3. times so bigge as that of .6. ynches compas, that must be in compas 10. ynches, & 2. of 5 parts: and then to be 4. times so bygge, as afore is declared, that must be double measure 12. ynches compas. And you haue another, of 7. ynches compas, and would haue another as bygge agayne, it must be in compas, 9 ynches, and 17. of 18 partes: and to haue another 3. tymes so bygge, must be in compas .12. ynches, and 1. of 8. part: and 4 times so bygge, is 14. ynches compas: then you hauing a rope or cable of 8. ynches cōpas, & would haue another, as bygge againe, then that must be in compas .11. ynches, and 7. of 22. partes: and to be 3. times so bigge, that must be in compas 13. ynches, and 23. of 26. partes: and 4. times so big, double measure, that is 16. ynches.
[Page]And then you hauing a rope or cable of 9. ynches compasse, and too haue an other cable as bygge agayne, must be in compas 12. ynches, 3. of 4. partes: and then to bee 3. tymes so bygge, must be in compasse .15. ynches, and 3. of 5. partes: and then to be .4. tymes so bigge, that is double measure .18. ynches. Nowe you hauing a cable of .10. ynches, and woulde haue another, as bygge agayne, that must be in compasse .14. ynches, and .1. of 7. parte: and to be .3. tymes so bygge, must be in compasse .17. ynches, and .11. of .34. partes: and to be .4. tymes so bygge, to bee .20. ynches. Nowe you hauing a cable of .11. ynches, and to haue another as bygge agayne, that must be .15. ynches, and .17. of 30. partes: and to be 3. times so bigge, must be in compasse .19. ynches, and 1. of .19. parte. Then to be 4. tymes so bygge, to bee double measure, that is, 22. ynches. Then you hauing a cable of .12. ynches compas. And to haue another as bygge agayne, that must be in compas 17. ynches, lacking .1. of 33. partes: and to be .3. tymes so bygge, must be .20. ynches, and .4. of 5. partes: and to be .4. tymes so bygge double measure, that is, 24 ynches in compas, and then furthermore, if that you haue a cable of .13. ynches, and woulde haue another as bygge agayne, then that must bee in compasse .18. ynches, and 7. of 18. partes, and to bee .3. tymes so bigge, must be in compasse 22. ynches, 23. of .44. partes: and then you hauing a cable of .14. ynches, and would haue another as bygge agayne, then shal that be in compasse .19. ynches, & 31. of .38. partes. Thē you hauing a cable of .15. ynches compasse, and to haue an other, as bigge agayne, then shal that cable be in compasse .21. ynches, and 3. of 14. partes. Nowe I do thinke this sufficient yenough, for to knowe the proportion of ropes, the one by the other, and also by thys little note they may fitte any shyppe wyth a maste, dooyng, euen as you doo by the proportion of ropes, in all poyntes: for if that you shoulde double the measure of any maste, that Mast shalbe .4. tymes the bignesse of the other, so that by the order of the proportion of ropes or cables, they may knowe the proportion of the mastes without any fayle.
[Page 19]And furthermore, I doe thinke it conuenient to shew vnto you, how to double any rope or Mast: and that you shall doe thus:Howe to double any rope or mast, by extractiō of the square roote. Take the Compasse of that rope that you haue for ensample, and that being knowne: then multiplye that number in it selfe: then that being doone, looke what quantitye you woulde haue the other bigger: then encrease that number vnto that bignesse, then extract the square roote therof, and that rope shalbe in compasse your desyred purpose. As for ensample thus, by a rope of 5 ynches compas, & I would haue an other rope as big againe, & you must do that in this manner. Fyrst multyplye that rope in it selfe number, that is to say, 5. times 5. and that maketh 25: then double that number, and then that is double 50. and then the square roote of .50. is 7. & 1. of 14. so that you may conclude that the rope of 7. ynches compasse, and 1. of 14. parte, is as bigge agayne as that rope of .5. ynches compasse: and by this order you may double anye rope as often as you lyst.
And now furthermore, in lyke manner,Ensample if that you doe knowe the waight of the fadome of one rope, you may easely knowe the wayght of a fadome of an other rope, how bigge or small soeuer that it be, as thus: double the proportion of the 2. ropes, and multiply them as you doe in fractions: suppose it as thus. I haue a cable of 13. ynches compasse, and that waigheth 16. pounde euerye fadome: Nowe what shal a fadome of that cable, waigh [...] both of one kynde of that stuffe, that is 16. ynches compasse? Fyrste multiplye .10. tymes 10. and that is 100. and then multyplye .16. times 16. and that maketh 256. and then multiplye the number of the bigger rope by the waight of the lesser, that is to say .256. times 16. and that maketh 4096. and now deuide this number by the number of the lesser rope, and that is 100. and then there will stande in the quantytie Lyne 40. and 96. wyll remayne ouer: so that you may see the cable of 16. ynches compasse, that a fadōe therof doth waigh neare 41. poūde, & by this order you may know the waight of any rope or cable, and if that you would know the waight of a lesser rope; you knowing the waight of his bigger, then multyply as afore is sayde, and then shall you multiplye the waight of the bigger with the number of the lesser, and then deuid [...] [Page] that sūme by the number of the bigger, and so shal you know how many pounde that a fadome of the lesser rope waieth. As for Ensample thus, by the cable afore mentioned, of 10. ynches compas, and a fadome dyd weigh .16. pounde, what shall a fadome of a rope of 8. ynches in compasse waigh: Nowe as before is declared .10. tymes .10. is .100. and .8. times .8. is 64. therefore multiplye 64. by 16. and that maketh 1024. and then deuide that by 100. and then there wyll stande in the quantitye Lyne 10. and 24. wyll remayne ouer: so that you may conclude that the rope of 8, ynches, that euery fadome doth way 10. pounde and neare a quarter, and this is true without any fayle, and by this order you may know the waight of all manner of ropes. &c.
The ninthe Chapter is as touching the mould of Shippes, to haue good qualities.
ANd furthermore, in as much as I haue shewed how for [...]o double or alter the tonnage or the burthen of Shippes too what bignesse you lyst at your discretion, and also to keepe that moulde and proportion in all poyntes: therfore I doe thinke it necessary and conuenient to say somewhat in this poynt, that is to say, what manner of forme or fashion that the mould of a Ship should be, that shoulde goe or fayle wel, and to haue good qualyties in the Sea. And although that it is possible that some wyll think that I doe meddle with those matters that I haue no skyl in for that I am neither Naupager or ship carpēter, neither vsuall Sea man: therfore it is posible tha [...] I maye be dislyked, for that I doe meddle in this matter or causes. Yet not with standing you that do reade this, vse not to condemne any thing before that you haue perused it well: and so wayinge it in a payre of indifferent ballances, that affection doth not leade you, it is possible that it is not altogether vntrue, but that there is some matter in it that is good to bee consydered of in the buildinge or the makyng of ships: and those matters that you doe knowe by experience to be vntrue, thē you neede not make any account thereof. &c.
[Page 20]And fyrst thus,Of Ships that sayle well with the wiend. as concerning the making of the moulde of any ships, this is to be noted, that those ships that are of easye draft, that is to say, not to goe to deepe in the Sea or water, and wyll beare a good sayle, and doth stere well, that is to say, that it wyll feele the Ruther as soone as the Helme or Tyller is put to or fro, and those ships doe goe or sayle well beeringe or afore the winde, that is to say, the winde to be large or to come right after them, all those ships doe sayle well and close by the winde, that is to say, the Bowline to be haled harde or close, and the ship to stande or come as neare the winde as may be: those Shippes must draw a reasonable draft of water: and also to be a reasonable good length, and these ships wyll goe well a head the sea,Of Ships that sayle wel by the Bowlyne to be harde pulled or also to sayle well a hed the Sea. that is to say, the Ship to stande close by the winde in such places as the grating of the tyde doth cause the sea to come agaynst the head or bowes of the Ship. Then those ships that haue a reasonable length and well brested or bowed, and not the buttockes or sterne of the ship to be to bigge or to full quartered behinde, but to bee reasonable lancke at the Sterne, those shippes do goe or sayle well a hed the Sea, so that they wyll beare a good sayle,Of ships that ryde well or yll at ancor. and not ouer helde, that is to say, not to goe to muche on the one syde, but if that any ship be too fat buttocked or brode behind at the sterne, & the bowes or brest of the ship before be to slender or narrowe, those Ships wyll neuer goe or sayle well a hedde the sea, but wyll fall or beate into the sea, that it wyll let or hynder the way or goyng of the Shippe. And also those Shippes wyll ryde very yll at rode or ancor in the Sea, for that the broadnesse of the buttockes of the Shippe dooth so thruste downe the head of the Shippe into the Sea, and especially if that the bowes of the Ship he to narrow or slender, that the Sea shall flye into the ship or quite ouer her, as well at an ancor or sayling, or goyng a hedde the sea: which is a very yll propertie in a ship in a number of causes. And all those ships that doth draw or go a good deepenes into the water; as before is saide, doe saile wel by the wind, & also wil ly a holde wel in the sea, that is to say, the ship hauing no sayle abrode, wyl not seele in rolle so much, neither in lyke maner it wil not go so much vnto lewards, that is to say, that the wind nor the [Page] sea shall not driue it so fast back agayne, as it wyll doe a Shyppe that doth draw or go but a litle way into the Water: and also those Shippes that doe drawe but a lytle water, bee very yll in two causes, if that they doe lye a holde in the sea, that is to saye, to haue no sayle abrode, for they wyll seel or rolle in such sorte that it wyll put al in daunger, besydes the driuinge to lewardes with the sea & winde. Therefore these Ships must haue alwayes sayles abroade, if they be loose at the sea, and also those kynde of Shyps wyl ryde yll at an ancker, at such time as the tyde doth goe vnto the wyndewardes, for lying thwart, it wyll seel or rolle so much. But the wynde and tyde to bee al one, that the Ships head to bee right vppon the Sea, and as before is sayde, the Ship wel bowed, and the Sterne not to full quartered, then it wyll ryde very well at an anker at that time. &c.
Of Ships that [...]ere well and doe heare a good Sayle.And now furthermore, as touching the building or makyng of Shippes for to stere well, and also to beare a good sayle, which is two of the best qualyties that is or may be in a Ship: and except that it be a very chance those Ships doo alwayes sayle very wel, if that the moulde of them be any thing well ordered in the forme thereof. &c. And although that the moulde of a Shippe be neuer so finely made, and if it doe not stere well, then it can neuer sayle wel. And also if the mould of the Ship be neuer so well made, and yf it wyll beare no saile but ouer heeld, that is to say, to lay downe the syde in the water, then it can neuer goe well, how fyne so euer the moulde is, for it is yll shapen to goe, when al the one syde is downe in the water, and the other syde all out of the water, and then it cannot abide the force of the wynde to driue it: whereas the Ship that is able to beare a good sayle, must needes goe wel, for that the force of the winde must needes draw it, for that it is able to beare sayle, and then the winde must needes force it to goe. &c. And fyrste thus, as touchinge the cause that any Ship doth stere wel, is this: that the quicke water of the way of the Shippe doth come vnto the Ruther being put eyther the one way or the other way, that must needes, cause the Ship to cast or turne accordingly and the faster that the shippe goeth, the nimbler or quicker the ship [Page 21] steereth or turne [...]h.
Therefore when soeuer that they doe builde or make anye Shyppes, then it is good for to lette them make the moulde of a Shyppe to haue a sufficient tucke or runne, whiche tucke or runne must bee in length the thyrde parte of the length of the Reele, and in height, by the stearne post, three quarters of that depth that the Shyppe goeth into the Water,A thing to bee noted. and so to growe narrower and narrower forwardes: for it is the sufficientnesse of the tucke or runne that maketh a Shyppe to stere well. For if that bee not well made, then it requireth to haue the broder Ruther, and that is euell in two respectes: the one is this: the Helme beynge putte ouer, and yf that the Shyppe wyll not feele the Ruther quicklye, then the Ruther lyeth crosse the Stearne of the Shyppe: and the Ruther beynge broade, then it must needes hynder or lette the goynge or way of the Shyppe verye muche: Whereas a Shyppe that hath but a narrowe Ruther, and yet is yare or quicke of sterrage, then the Ruther cannot hynder the goynge or way of the Ship: &c.
And also it is euill in an other respecte to haue a broade Ruther, and that is this: for a Shyppe beinge at Sea in foule weather, a broade Ruther the Sea doth beate it one waye and an other way, by the meanes of the labouring of the Shyp to and fro, that it is apte to breake the tyller or the head of the Ruther & Ruther Irons: and besydes that, it is vneasye for the Shyppe in lyke manner. &c.
And thus I doe omitte the rest of the proportion of the moulde of the Shippe vnto the discretion of the Naupeger or Shyppe Carpenter, as touchinge the fore waye and the flowringe of the Shyppe, and the leadyng of all the rest of the woorke &c.The cause that a Ship doth beare a good sayle. And furthermore, as touching this poynte to cause a Shyppe to haue a stiffe syde to beare a good sayle, then this must be consydered in the buildinge or makynge thereof: and fyrste thus: that commonly those Shippes that haue a sufficient breadth accordynge vnto their biggnesse and length, wil beare a resonable good saile, for that the breadth doth beare it vp.
[Page]But commonly those be not the best, and fynest Saylers, neyther are they of the best qualities, in diuers respects. Yet notwithstanding, in my opinion, this is the principallest poynt to obserue in the building of ships, to haue them to beare a good sayle, and that is this, for to lay the breadth of the Shippe aboue the water, a foote, or a foot and a halfe, more or lesse, according vnto the bignesse of the shippe, and to hange wel of, that is to say, to be 4. or 6. ynches on a syde broder then it is iuste at the edge of the water, and to be more or lesse, according vnto the bignesse of the Shippe: and then vpwardes the worke may be housed inwardes, that is too saye, narrower and narrower vpwardes, which wyll doo well, both for the ease of the Shyppe in the Sea, and lesse charge of Tymber bathe in wayght, and otherwyse: and in so dooing, the Shyppe wyll beare a good Sayle, what lengthe so euer it haue, howe fine so euer the mould is, so that it haue quarters proportionally vntoo it. &c.
And the cause thereof is this: the breadth of the Shyppe being aboue the water in such sorte, as if the Shyppe come vnto heelding, that the same broder place dooth come into the water: then the Nadry or Reele of the shippe, dooth growe the further of, by the meanes of the hanging ofwardes of the syde or worke of the Shyppe.
And for that the ballast or the lading of the Shippe, the waightiest part lyeth downewardes towardes the Reele, therfore it maketh the shippe the lother to helde a tosyde, for that the syde hangeth outwardes, and then the water doth supporte it vp, for that the bigger or broder parte is out of the water, as the reason thereof more playnelye shall appeare in the fourth Booke of the propertie of Water in waight, called Statick, wherein you shal see the reason thereof more manifestly &c. Whereas those Shyppes that haue an vpright syde, must needes helde much the sooner, for that the Water doth not supporte the syde, not vntyll it doe helde very much.
Wherefore thus much I haue sayde as touchinge the moulde [Page 22] of Shippes, as concerning theyr qualyties, as thus:Note a Shippe that hath Tucke or Runne ynough, wyl steare well: a Shippe that doth hange well of on the nayle aboue the water, wyll beare a good sayle: a Shippe that doth draw a reasonable good drafte of Water, and well wayed forwardes, wyll sayle well by the winde: and beinge well bowed and not to fatte buttocked, wyll goe well a head the sea, and also ryde well at rode, and also wyll hold well at the Sea loose. and floty Shippes that s [...]eere well and wyll beare a good sayle, wyll sayle well, the [...]ynde beyng large. &c. And thus I doe ende this thyrde Booke. &c.
❧ A Table of the Contentes of the Chapters of the thirde booke, called a rteasure for Trauailers.
The first Chapter of the thyrde Booke, sheweth you howe to caste the contentes of lande by Arithmeticke, and also by the husbande mans rule, which is by the accounte of money. &c.
The seconde Chapter sheweth how to measure board and Glasse, and too caste the contentes thereof, with other necessary thinges belonging therunto.
The thirde Chapter dooth shewe howe for too measure Tymber, and to bring it too a square, aswell without Artihmetike as otherwyse, and also howe for too knowe the true contentes of any peece of Tymber.
The fourth Chapter sheweth howe for to measure all manner of bodies, as Tymber, or stone, Cubes, or Globes: and too knowe what proportion of measure or waight the one hath vnto the other.
The fyfthe Chapter sheweth howe for to measure Globes, and to know their contents in ynches or feete.
The syxt Chapter sheweth howe for too builde Shyppes by proportion, that is to saye, if that you haue one Shippe for an ensample, if you woulde haue an other as bigge agayne, more or lesse this Chapter doth shewe vnto you howe you may doe it, keeping that moulde and proportion in all poyntes, that is too saye, by extractynge of the Cubicke roote.
The seuenth Chapter dooth shewe in lyke manner the making of shippes by proportion, sauing that the Cubike roote is extracted already: with an easye way howe to make them of what tonnage or burthen you liste. [Page] and of that moulde and proportion in al poyntes.
The eight Chapter sheweth howe much that one rope is bigger then another: and if that you haue a rope of anye syse, that you may know how for to haue another, of what syse that you liste, and also if that you doo knowe the waight of one rope, you may know the waight of any rope by proportion. &c.
The nynth Chapter is, as touching the moulde of Shippes, to haue good qualities.
❧The fourth Booke of the treasure for trauaylers.
Wherein is touched the arte of Staticke or waight, shewing vnto you howe you may knowe the waight of any Shyppe that swymmeth vppon the water, with al her ladyng, and al the rest of her furniture. And also howe you may know the waight of any mettal that is sunke in the water, to knowe what it wayeth in the water, and also how you may measure any strange forme, suche as Geometrie cannot geue you any order for the measuring thereof, and also howe for too lyfte or way any thing sin [...]e into the water, with other necessarie matters belonging therunto, very necessary for al land men, and seam [...]n. &c.
Written by William Bourne.
To the Reader of this fourth Booke.
GEntle Readers, it is possible that you wyll maruayle, that I shoulde take vppon mee too deale in these causes, that is to say, to teache any newe Art, and Science, that hath not been as hytheretoo, written in any language or tongue, the which Art or Science, called Staticke, dooth shewe the heauinesse or lightnesse of any thing.
Wherefore there is conteyned in this fourth Booke, howe too knowe the waight of any thing swymmyng in the water, as the waight of any shyppe, with all her lodyng, and all her furniture: as Ordinaunce, Ankers, Cabels, Mastes, Sailes, with al other Implementes in them, and also it doth shew the waight of any thing sunke into the water, what it wayeth, to be lifted from the bottome, tyl the appearing of it aboue the superficies of the water: with dyuers other necessarye matters that are conteyned in this fourth Booke, and not before this tyme mentioned by any other, but onely by that famous and learned man Mayster Iohn Dee, who hath made mention thereof in his Mathematicall preface, wherein I haue hadde my principall instructions, as touching that Arte or Science.
Wherefore Gentle Reader, beare with my rudenesse, that I being vtterly vnlearned, shoulde enterpryse too take vppon mee too bee so bolde, too geue the fyrst attempt, to imploye that Art or Science vnto any purpose: for I do knowe the nature of most people, is to dislyke al thinges that are not done by them selues, whether it be good or euyll: and as I haue knowen many tymes by experience, that those persons that haue learned anye thing at any mans hande, when he dooth vnderstande it, then he wyll not be knowen where [Page] he learned it, but that he knew that before or euer he shewed it vnto him, which is a manifest robbery of any man, to learn any thing at any mans hande, & then afterwards to deny it, & to say, that he knewe it before he tolde it hym: as I do knowe a number of persons, that when they are ignorant in matters, then they wyl vse diligence tyl they haue atteyned it, and then when they haue a little instructions to serue their turnes, then they wil seeme too bee verye cunnyng, and that they neuer learned anye thyng at any mannes hande, which is a great poynt of ingratitude, too offer that person that he hath learned of, such a greate iniury: but yet notwithstanding the earth is greatly infected, with such maner of persons.
The fourth booke, of the treasure for trauailers.
The fyrst Chapter of the fourth Booke, sheweth you by the proportion of a Shyp swimming in the water, for to knowe the true waight of any Shippe, with all hir tackle, ordinance, and lading. &c.
FOR that I haue sayde somewhat heretofore as touchinge the makyng of Ships by proportion and otherwise: Therefore I doe thinke it necessary and conuenient to treate partly of this, as touching the nature and qualytie of water, for the sinkinge or swimming of thinges in it, and accordyng vnto the simple opinion of the common people,Of things that doo swymme. who thinke that things in the water do swimme or syncke, for that it is Woode, Iron, or Stone: but the onely cause of thinges that doo swimme, is this, that it is lyghter then the proportion in quantitie, then the water is. For this is generall for euer: Looke how much of any Tymber or any other thinge that is hydde, or in lownes euen with the water, as iust of waight as of so much water, as the true quantity of that parte that is from the edge of the water downewardes into the water neyther heauier nor lighter, and then that parte that is aboue the water doth shew iustly what diuersytie of waight is betweene the water and the woode, or any other stuffe that is putte into the water. For any thing swimming in the water, the halfe being aboue the water, and the other halfe vnderneath the water, that thing that swimmeth in that forme, is iust halfe the waight of so much water: and if in the swimming .3. quarters be buryed in the water, that thinge is iuste 3. quarters of the waight of so [Page] much water, and so foorth, to any other proportion, and then adding so much in wait, to make it of the iust waight of the water: then that thinge being in the water, shall swimme euen with the edge of the water neither hygher nor lower. But if it bee any thing heauier then the proportion of so muche water, then it sinketh vnto the bottome: and then looke how much in waight it is heuier thē the proportiō of so much water: so much it waieth in the water the lighter,Of things that synke. as the waight of the water cōmeth vnto. For if ani thing in the water, be double the waight of the water, proportiō for proportiō, then shal that thing waigh iust half the quantytie of that waight, til it be lyfted from the bottome vnto the very edge of the water, and then if that the thinge doe waigh but halfe the waight more then the quantitie of so much water: then shall that thing in the water to be waighed, waigh but one thyrde part of his waight that it would waigh, if that it were out of the water, and so foorth to any other waight or waightes, hauing proportion in bignesse, according to the quantitie of the water, whether it bee Brasse, Stone, or Iron, or any other stuffe what soeuer it be. And also things that do swimme, as wood, or any other stuffe. Wherfore this is to be noted by the way, the perfect waight of any ship with all her ladyng, Ordinaunce, Mastes, Sayles, and Tackle, with all other implementes in her, may be easyly knowen by her onely swimming, as thus:
Looke what quantitie of the Ship is buryed in the water, that is to say, from the edge of the water downwards: then if there were a vessell or great thing made of the proportion of the moulde of a Shyppe, as much as is buried in the water, if that were filled with that water that the ship were in, the water shoulde be of iust equall waight, that the Ship were of, with all her tackle and implements in her. And now this being true, as it is most certayne, then the waight of the water being knowne, any vessel or body is to bee measured by Geometrycall meanes. &c.
And furthermore, here is one speciall thinge to be noted, and that is this,Al water is not of lyke waight. all waters are not of lyke waight, for the finest water is lightest: therfore if that any Ship be in the lightest water, then dooth shee swimme the deeper, according vnto the waight of the [Page 4] Shyp, and the waight of the water, quantitie for quantitie, and in lyke manner any Shyp being in the heauier water, then shal not the Shyp swimme so deepe, for that the water of his owne force, wyll lyft the Ship out of the water, vntill there be that iust quantitie and proportion, according vnto the iust wayght of the water and waight of the Shippe: for this is seene dayly by common experyence, amongst Sea men and maryners, that if you doo lade any Shippe in a fresh water or ryuer very deepe,Salt water is the heauiest water. then when shee is in the Sea, and specially in the Occient Sea, that the Shippe shal be lifted vp hygher by .3. or .4. ynches out of the water wards: And then when the Shippe is come agayne into a freshe water ryuer, then she shal be as low laden as she was before. Wherfore in the buildyng of Ships, the one of the principal poynt [...]s is this, the flowring and quarteryng of them: for there may .2. ships be made both of one length, and of one breadth, and of one deepenesse in the water, and yet the one may bee [...]eare as bigge agayne as the other, for if that the one bee full quartered, and a broade flat flowre, (as the Hulks bee commonly) it must needs be of a greater burthen, then a sharpe Shippe that hath neyther flowre nor quarters, as commonlye the Spanish building is: for the water cannot beare it before it be deepe yenough into the water: therfore these kinds of Shyps drawe very much water & bee but of small burthen, for a sharpe Shippe must haue very muche ballast, or els shee wyll beare no sayle: and especiallye if they bee verye highe builded or larged aboue the water. &c.
The seconde Chapter sheweth how for to measure the proportion of the mould of any Shyp, wherby is knowne the waight of any Shyppe with all hir ladynge and furniture.
FOR to knowe howe to measure the proportion of the moulde of a Shippe whereby may be knowne hir waight, with all hir ladinge, it is somewhat tedious, and asketh long woorke, and must be precisely handeled, for that it keepeth no forme long together: therfore it must bee measured in manye parts.
Howe to measure the mould of a Shippe.And for to measure the moulde of a Shyppe, the Shippe must bee brought a grounde, and then beginne at the broadest place of the Shippe in this manner: Fyrste measure the breadthe of the Shyppe from outsyde vnto outsyde, at that very place of the vpper edge that the Shippe dooth swimme in deepenesse into the water: then that beinge knowne, measure the true deepenesse that the Shippe dooth swimme into the water, at that place of the broadest parte of the Shyppe: then that beinge knowne, take the true contentes of halfe the breadth of the Shippe, and then with a rodde or pole lay the ende of the rod or pole that is iust the length of halfe the breadth of the Shippe, vnto iust the halfe Keele in breadth at that place before spoken of, and then with an other rod or pole of the iust length that the Shppe doth swimme in deepenesse into the water, laye the ende of that rodde or pole at that place that the vpper edge of the water dooth touche: and then let both the other endes of the two rods or poles touch iust together, and so wil they make a square Angle: and then measuring or trying betweene the Ship and the 2. roddes or poles as you doe in the measuringe of superficiall or plat formes, so shall you knowe the contentes of that parte that is within the insyde of the Shippe, by subtractynge or [Page 5] takinge away of that measure betweene the two roddes or poles with the outsyde of the Shyp, for that you must consyder that it is a square inclosed from the middle of the insyde of the Shyppe, vnto the deepenesse that the Shyp doth swimme in the water, and vnto the two roddes or poles, and hath foure square or righte Angles or corners: and then if that you doe multyply it according vnto the breadth of the shippe and the deepenesse that the Shyp doth goe into the water, as you woulde doe yf that it were a plat forme: then pulling away the contentes of that same being doubled that the measure is betweene the Shyppe syde, and the two roddes or poles, then that which doth remayne shall be the true contentes of that parte which is within the insyde of the Shyp as though it were a plat forme: and then looke how manye foote longe it runneth in that forme and proportion in breadth and roundenesse of the syde: then accordynge vnto the length multytiply the one by the other, [...]hat is to say, the contentes of the measure before taken of the insyde of the Shippe, and the length that the moulde doth keepe in one proportion, and then cast the contēts therof. And that being done, do as before is rehearsed, accordyng vnto the breadth of the Ship in an other place: then accordyng vnto the deepenes that the Ship dooth swimme in the water, and then doyng with the two roddes or poles as before is rehearsed, and so trying betweene the Shyps syde, and the two roddes or poles, and castynge the contentes in all poyntes as before is rehearsed: and thus you muste doe in as many places and as often times as the proportion of the moulde dooth alter: and then addyng them altogether, you must see howe many foote that the Shypp doth contayne, if it were all one whole peece of Timber, and not hollow within.
And now this being done exactly as it may be done with precise diligence, you knowing the true contentes howe many foote the soaled body of the moulde of the Shyppe doth contayne as much as is buryed into the water, you maye knowe iustlye the whole waight of that ship that you haue so mesured, with al her ladyng, ordinance, tackle, anker, and cables, with al other implementes [Page] in her, as thus: Take of that water that the ship swimmeth in, and make a cube of mettall or wood of iust .12. ynches square, and deepe: for that 12. ynches square euery way, maketh a foote, and then waigh the water iustly howe many poundes and parte of a pounde the water dooth contayne in waight, and that shal shewe you iustly how many pounde and partes of a pounde euery foote square of the moulde of the Ship dooth waigh iustly, and then if that you doo multiply the contentes of the number of feete, that the moulde is, and the waight that one foote of the water dooth waigh in poundes and partes, then accordyng vnto that number, the Shyp with all her ladyng, dooth waigh iustly without any fayle: so that you haue measured the moulde of the Shyp truely, and also waighed iustly the contentes of one foote of the water: and then by that number you may say iustly, it contayneth so many Tunnes in waight, as thus: by diuidyng the number of the waight of the Shippe by .2240. for that a Tunne conteyneth 20. hundreth waight, and euery .100. waight, to contayne 112. pounds.
And furthermore, you may measure the moulde of a Shyp in this maner, with such a thing as the Shyppe Carpenters doo take the moulde of a Ship, and that they doo call a moulde, or lynck ginne, and that is made of many peeces, of a foote long, or there about, and it is clenched togeather with roffe and clenche, that the ioyning wyll be put to and fro at your pleasure, and wyll stande stiffe as you doo leaue it.
And now with this instrument, you may woorke more easely then before is rehearsed: for to know the contentes or quantity of the moulde of any Shyp in this maner: Take at euery place the halfe of the true breadth of the shyp, and then in lyke manner the true deepenesse that the shyp dooth goe into the water, at euery place that you doo measure the Shyp at, for that all shyppes doo draw more water at the Sterne, then they doo at the head: and then you may put three pinnes of wood into the grounde, the one pinne to be at the midle of the ship, and the other to be for the outsyde of the ship, and the thyrde to be for the middle of the Keele of the Shyp, and to set them truely in distaunce, accordyng vnto the [Page 6] halfe breadth of the shippe, and the other vnto the true deepnesse that tht ship dooth goe into the water, and so shall that pinne for the middle of the Shyp, make a square Angle vnto the pinne, for the syde and the keele of the shyppe, and then with the instrument lay that vnto the syde of the shyp, and put it in and out as the ship dooth rounde from the place of the vpper edge of the water vnto the Keele, and then laying that moulde of the Shyppe vnto the two pinnes, that is to say, to that pinne for the side, and the pinne for the Keele of the Shyp: and then measuryng that in closer, as you doo a platforme, the trueth of the contents shall appeare, and then doublyng that nūber, it wil shew you the contēts of the whole breadth of the Shyp, and then to multiply so much in length, as dooth keepe one proportion: And thus doyng as often tymes as the proportion of the moulde dooth alter, and then addyng al your numbers together, and casting the contentes in all poynts, as before is rehearsed, the trueth of the solid body of the moulde of the Ship shall appeare, and so taking the true waight of one foote of that water, as before is expressed in all poyntes. And thus I doo make an ende of the measuryng of the moulde of Shyppes, for that there wanteth or lacketh nothing, but to shew how to measure plat formes, and as for those matters, there are diuers bookes extant, sufficient ynough for that purpose, as Maister Leonarde Digges in his booke called Tectonicon, and Maister Thomas Digges his booke called Pantometria, with other.
The thyrde Chapter sheweth you an easyer way then before rehearsed, by the Arte Saticall, to knowe the true waight of any Shyppe, with al hir lading, and all the rest of hir furniture.
AND furthermore, for that it is somewhat tedious and asketh longe woorke, beesydes diuers other incombraunces that must bee vsed to measure the true proportion of the moulde of a Shyppe, I wyll shewe vnto you a more pleasaunter and easyer waye (by the Arte Scaticall) both very true and exacte, for to know the true wayghte of any Shyp, with all her ladynge, Mastes, Sayles, Ancors, Cables, and Ordynaunce, with all other implementes in her.
And any Noble manne, or Gentleman may doe it at home in hys Chamber, that hath any knowledge in the Mathematicall Sciences, as thus:
An easyer waye to knowe the waight of a Shippe.Fyrste cause the Carpenter that dooth builde the Shyppe, or otherwyse, yf that you desyre to knowe it by any other Shyppe that is builded already, yf that Shyppe haue any occasion for to come a grounde: then get some cunninge Carpenter to take the true moulde of that Shyppe, as though that hee shoulde builde an other of that moulde and proportion in all poyntes, as muche as is buried into the water, when the Shippe is loade vnto her lode marke, & that being exactly done, then cause hym for to make the true moulde and proportion, then cause the Carpenter for to cut out of a peece of Tymber the true proportion of the moulde of the Shyppe in all poyntes, as thus.
[Page 7]For euery foote long, make the moulde in Tymber in length, an ynche: and for the breadth in lyke manner, for euery foote make the other an ynche, and also for euery foote in deepenesse, that the Shyp swymmeth into the water, make the moulde in Tymber one ynche, and so consequently euery parte and place bothe of the roune, and way, and floore, with the quarters of the Shyp, to cutte the moulde for euery foote, and part of a foote, an ynch, with those partes, euen as the woorke or moulde of the Shyppe dooth runne, in all poyntes: and that beeing exactly doone, then let there be made in some kinde of mettall, as Leade or Tynne, the true proportion of the moulde, hollowe, and thight, that it may holde water, as the moulde in woode will shewe or leade them howe to doo it verye truly: and then that beeyng doone, then cause an other square vessel too bee made of mettall in Cubicke wyse, suche a one as you may measure the hollowe thereof as easilye as you may measure a square peece of Tymber, and if that there were lynes or prickes at euery ynche in deepenesse, it were all the better.
And then this beeing doone, then fyll that vessell, that is made for the moulde of the Shyppe, with that water that the Shyppe doeth swymme in, and that beeyng exactly fylled, then put that water into the other vessel, and looke that there be none of the water shed, then you may knowe iustlye howe many ynches square that the water is, by measuring the water with an ynche rule: and that beyng knowne, then you doe knowe howe manye foote that the solled body of the moulde of the Shyppe doeth conteyne. And then waying instlye one foote square euery way of that water, and then you knowing howe manye poundes, and partes of a pounde, that one foote square of water doeth waye, then multiplye the number of feete of the Ship, with that you haue founde before, by powring the water into the square vessel: and then for euerye ynche, the Shyppe is a foote, and so by that number multiplyed by the number of the wayght of the pounds, and partes of poundes, the true wayght of the Shyp shal appeare: and if you doe committe any errour, the fault shalbee in not waying, and measuring of it trulye.
[Page] The ensample of the knowing the waight of a shyppe.And for your better vnderstanding hereof, you shall haue an ensample of that matter before rehearsed, by a ship of .100. tonnes, and the length of the moulde of the Shyppe, to be 50. foote long, and the broadest place of the moulde to be .20. foote broade, and the deepenesse that the Shyppe goeth into the water, to bee .12. foote: and I first caused the Carpenter to take the true moulde of the Shyppe, and also to catte the moulde in woode, according vnto the length, breadth, and deepenesse, that is to say, for the .50. foote long, to be 50. ynches, and for the 20. foote broade, to bee 20. ynches: and for the 12. foote deepe, to be 12. ynches, with al the other proportion of the moulde of the Shyp, to be one ynch for a foote: And that doone, there was caused too bee made a moulde in Lead, agreable in all poyntes, to the moulde of the shp, as Lead, wil marke easily yenough: and then there was made the other vessel in Leade of 12. ynches square, and .48. ynches deepe, and then the moulde for the Shyp was fylled with water, and that being iustly, and equally fylled, the water was put into the square vessell, and then the deepnes of the water was exactly measured, & was foūd to be 42. ynches in deepnes, & thē for that the vessel was 12. ynches square, 12. times 12. is 144. & so many ynches there is at 1. ynche deepe: and then for that it is .42. ynches in deepenesse, multiply .144. by .42. & that maketh .6048. so that you may conclude, that the moulde of the Shyp, as much as is vnder the water, if that it were not hollowe within, that it woulde conteyne .6048. foote of Tymber. And nowe suppose that the water was of our water, here at Grauesende, and that is not of the lightest sort, neyther of the heauiest sort, and a foote square of that water wayeth .55. pounde, most commonly, although that it may waygh sometime lesse, and sometymes more, it wayeth lesse, after much rayne, and neape Tydes: it wayeth more in spring Tydes at a ful Sea, vpon some cause of winds, but it altereth no great matter within a pounde vnder or ouer. Wherfore multiply 6048. by .55. and that maketh .332640. so then you maye conclude, that the shyp waigheth .332640. pounde: And then as is declared in the Chapter going before, for to knowe howe many tonnes that the shyp dooth waygh, deuide that by .2240. and then there wil stand [Page 8] in the quantitie line .148. and there wyl remayne ouer .11209. so that you may conclude, that the whole shyp with all her ladyng, and al other furniture, and implementes in her, dooth waygh .148. tonnes, and a halfe of a tonne. And by this order, you maye knowe the true wayght of any shyppe, howe graat or small soeuer that it bee, or Boate, or any other thyng that swymmeth.
And furthermore, you may knowe by thys Arte Statical,Another way to know the waight of a ship, with al her furniture. the true waight of any shippe, without puttyng of water into the square vessel, although that you doo not knowe the contentes, howe manye foote square that there is in the Shyppe, as thus: the moulde of the Shyppe beeing taken, as before is declared, and the proportion of the moulde, made in mettal hollowe, as before is rehearsed.
And furthermore, you may make the moulde lesser then before is rehearsed, that is to saye, you may make the proportion of the moulde, for euery foote that the Shyppe is in length, breadth, and deepenesse, you may make it but halfe an ynche, or but a quarter of an ynche, at your descretion: and then fylling that with water, and then wayghyng the water trulye, looke howe many tymes the length of that moulde that is fylled with water, is in the length of the Shyppe, multiply the wayght of the water with that number Cubickely, and that shall shewe vnto you the true wayght of the Shyppe, with al her ladyng. As for ensample by that shyppe, before rehearsed, that was .50. foote long, and, 20. foote broade, and .12. foote in deepenesse.
And nowe I caused the moulde too bee made for euery foote,A ensample. but a quarter of an ynche, so that for the .50. foote long, the mould was made .12. ynches, and a halfe: and for .20. foote broade, but 5. ynches: and for .12. foote deepe, but .3. ynches: & that beyng filled with water, the water being wayghed, did conteyne in wayght 3. pounde, & 2. of .73. partes of a pounde, and that is scante halfe an ounce, and the true contentes of the wayght of the water: and then for that you doo see that the proportion of the length of the moulde, is but twelue ynches, and one of 2. parte: that is, but the .48. parte of the length of the Shyppe: [Page] therfore multiply it in this maner 48. times 48. and that maketh 2304. and then to multiply it by 48. agayne, and then it maketh 110592. wherefore nowe multiply .110592. by the wayght of the water, that is too say 110592. tymes 3. and 2. of 73. parts: and that maketh 334620. so that you maye conclude, that the Shyp wayeth 334640. poundes.
And nowe to knowe howe manye tu [...]nes that the Shyp doeth way, as before is declared by deuyding that number by 2240. and so further, as before is rehearsed. And furthermore, you maye cause in the proportion of the mould of Leade or Tynne, to be certaine Parallel lynes, to be made but a quarter of an ynche asunder, as many as you lyste, and then you may knowe by those lynes what wayght that the Shyp is of, when that shee is not laden. And also if that you list, you may knowe howe manye tunnes more in waight, wil loade the Shyppe, as often tymes as you doe knowe howe many foote or ynches the Shyppe dooth lacke of her loade marke.
And yet furthermore, you may knowe, howe for too knowe the wayght of anye Shyppe with all her loadyng, although that you haue not made the hollowe moulde of the Shyppe, as thus: by that moulde that the Shyp Carpenter hath made,Another ensample howe to knowe the waight of any shippe. the woode beyng not so heauye as the water, then make certayne holes in the moulde metall, then at those holes, put in Leade, vntyl such tyme as the moulde is heauier then the water, and then stop the holes agayne, that no water may goe into them, and cutte of that parte that there is more then the moulde of the Shyppe: and that doone, then in some smal thyng or vessell put in water vnto some certayne marke, and then put into that water, the moulde for that Shyp whiche you doo desyre for too knowe the waight of, and bee sure that the water dooth couer al the moulde: and then take out all that water verye precyselye, that is fed by that meanes of the moulde for the Shyp, vntyll suche tyme that the water bee iuste in that heyght that it was before, that the moulde was put in: and then waying that water truly, you dooyng as before is rehearsed▪ to multiplye the length of the moulde of the Shyp accordyng as before is declared, Cubickely, and then [Page 9] the wayght of that water that is hyghed more then it was before that the moulde was put into the water, and the wayght of that water beyng perfectly knowen too bee multiplyed by that Cubicke number, shall shewe iustly the true wayght of the Shyppe, as afore is declared in all poyntes.
And by all these rules or order, you maye knowe the iuste wayght of anye thyng that sooymmeth in the water, sauing that you must haue consyderation, that any moulde made of woode, when it is drye, dooth receyue or drynke vp water, and when it is wette, it swelled the bigger with the water.
The fourth Chapter sheweth by the Arte Statical, the wayght of anye mettall or stone, howe much, or what wayght that it dooth wayghe in the water, to be lyfted or waighed from the bottome, vnto the brimme of the water.
NOwe for that I haue sayde somewhat for too knowe the wayght of thynges sooymmyng on the water, I thinke it conuenient too treate partly by the Arte Statical, to knowe the waight of any thing that synketh into the water: and to knowe truclye howe muche that it waygheth more then the wayght of the water, proportion for proportion, whereby you may knowe what it waygheth iustly, being sunke into the water: and also you maye knowe by this meanes, howe for to measure suche things, whose forme, whether that it be mettall or stone, that for the strangenesse of the for me is not to be measured, as braunches of mettall, or pillers that be inbowed or hollowe [Page] in one place, and boyleth out in another, or any such other straunge forme, which is to de doone by that meanes, that Archimedes founde the deceite of the Kinges crowne of gold. And first for to knowe the true wayght of any Mettall that is suncke in the water, whether that it be brasse, iron, or stone, you knowing the wayght therof before that it was suncke: then make a cube, or any other square, of that kynd of Mettal that you woulde knowe what it waygheth in the water, and waygh that Mettal truely, and that being knowen howe many poundes, and parts that it waygheth, then take of that water, that the Mettall is sunken into: and then if you doo make a Cube, or any other square hollowe, in forme like vnto the massy Cube or square, neither bigger nor lesser, then that you haue made in Mettall, and waighed. And then fyl that hollow cube with the water, and then waygh the water truely, and that doone, looke what that water waygheth, pull that summe truely away from the waight of the massie Cube or square, and that which dooth remayne, shalbee the true waight that the massie Cube dooth waygh in the water: and so by that Cube you may knowe the waight of the greater portion that is sunke, as thus: The wayght of the sunken mettall beyng knowen, looke howe many tymes the wayght of the smal Cube is in the greater quantitie, that is sunke, so many tymes multiplye the waight of the water in the hollowe Cube, and that doone, subtract or take away so much in wayght from the sunken Mettal, and that which dooth remayne, shalbe the true wayght of the sunken Mettall in the water to be wayghed, tyll that it dooth begyn to appeare aboue the water: Or otherwyse, you may doo it in this manner, by the smal Cube, before rehearsed, beyng iusty wayghed, and the wayght knowen vnto you, take of that sorte of water that the Mettall is sunke into, and put it into some vessell, fytte for your purpose: and that done, then marke the edge of the water iustly vppon both the sydes, then put your massie Cube into the water, that it be couered with water, and then take out, as much of the water as is rysen aboue the marked places, and then waygh that water truly.
[Page 10]And now the true waight of the water being knowen vnto you, then as before is rehearsed, subtract or take awaye the wayght of the water frō the waight of the cube in mettall, & then that which dooth remayne, shalbe the true wayght of the Cube in Mettal, when it is sunke to the bottome of the water, and then by the small is knowen, the wayght of the greater portion, as before is declared, by knowing howe many tymes, that the greater quantitye is more then the lesser, and then multiplying the wayght of the water so many tymes as the quantitye dooth shewe, and then subtracting or pullyng awaye that wayght, then that which doth remayne, shall be the true wayght of the Mettall in the water, as for ensample thus:
By a peece of ordinaunce of brasse, that is sunke, that is to be wayged out of the water, and the wayght is knowen to be .7000. waight, for that it is a double Cannon, that is sunke, and I doo desyre for to knowe the true wayght, what it dooth waygh in the water.
Wherefore I doo take another peece of that sorte of Mettal, that waygheth .100. wayght, it maketh no matter, what forme that it hath, so that it be of that sorte, or of that kinde of Mettal, for whereas I spake of a Cube before, that was to no other ende, but to make the thyng the more playner, as hereafter it shall more playnely appeare: and then take of that water, that the peece of ordinance was sunke into, for that al waters are not of one wayght, and then put that water intoo some conuenient vessel, meete for your purpose, and then marke the water very precisely, rounde about, euen at the very edge of the the water, & then put the peece of mettal into the water, & then hauing some conuenient vessel already wayghed, and then take out, without anye sheddyng of the water, all that water that is aboue the place marked before, neyther more, nor lesse, nor hygher, nor lower, and that being doone truly, then take the waight of the water, and by supposition, it is founde to be .14. pounde iust, and the brasse, that is put into the water, being one hundreth waight, that is .112. pounde.
[Page]Therefore I do conclude, that the wayght of the water, is but the .8. parte of the wayght of the Brasse or mettall, so that I doo conclude, that the peece of Brasse or mettal dooth waygh in the water .7. of .8. partes of his owne proper wayght, that is, but .98. pounde.
And nowe for to knowe the wayght of the sunken Rannon, doo thus: Looke howe many hundred wayght that you haue in .7000 wayght, and that is .70. hundred wayght. Wherefore multiply .14. by .70. and that commeth vnto .980. poundes, which maketh 800 wayght, and 3. of .4. part: And this summe being pulled away from 7000. waight, which is .7840. poundes, then there remayneth .6860. poundes, and that is .6100. and .28. pounds in waight: and euery .100. waight, to conteine .112. pounde.Al thing in the water, is lighter then his owne proper wa [...]ght by the quantity of the water in waight that it occupieth, and out of the water, it waigheth his owne proper waight. And nowe by this order you may knowe the true waight of any sunken mettal, what it waygheth in the water, to be waighed from the grounde, vnto the appearing of any parte thereof aboue the superficiall of the water: and then too bee wayghed aboue, out of the water, then it hath his owne natural wayght, what kinde of mettall soeuer it bee, as Syluer, and Gold, Copper, Leade Tinne, Iron, Steele, or Stone, or whatsoeuer it bee that synketh into the water, you may knowe the true wayght of it, in the water, by the order before rehearsed, by puttyng into that kynde of water, anye peece or lompe, what forme soeuer it hath, it maketh no matter, so that it bee of that sorte of Mettall or stone, being truely and exactlye wayghed, and then to take out so much of that water, as by the meanes of that mettall or stone is hyghed more then it was before the puttyng in of the mettall or stone: And that water truly waighed, and the wayght thereof knowen vnto you, then rebate that waight from the wayght of the mettall or stone truely, and then that which doth remaine, shalbe the true waight of the mettal or stone, being sanke into the water. And by that meanes you may knowe the true wayght of any great quantitye that is sunke [Page 11] into the water, by knowing how many times the great quantitye is more then the lesser, and then to multiply the waight of the water, so many times as the waight of the greater is more then the lesser, & then that which dooth remayne, shall be the true waight of the greater quantity of mettall, or stone, that is sonke into the water.
The fyfth Chapter sheweth how to knowe the true measure in the ynches or feete, of any straunge forme, such as Geometrie can giue no ordering for the measuring therof, as to measure a braunche in mettall, or a piller that is enbowed and ful of hollownes in diuers places, and boyles out in diuers places: and also how to know the diuersitie of the waight of mettall, or the diuersytie betweene the waight of Stone and mettall.
AND furthermore, by this meanes you know the true measure in ynches or feete, of any straunge forme, what shape soeuer it hath, such shapes that no Arte by any capacitie are not to be measured, whether it be in mettall, stone, wood, or in waxe, or gommes, or what soeuer it bee, or a Crowne, or Crownes, or a branche, or braunches, or a pyller, or pyllers, or thinges that be inbowed in one place, and boyles out in an other, or a Cuppe, or bowle, or a Potte or Pottes that keepe not in thicknesse one quantitie, but it is thicker in one place then in an other, as there be diuers other formes not beere spoken of, that no man by Arte is able to measure them, for that they keepe in no place one proportion.
Wherefore I doo thinke it conuenient, to treate partly hereof, and to know the true contentes of any forme what soeuer it bee, in ynches or feete, then doo thus: Cause to bee made some hollow Cube or Square, in such forme that you may measure it [Page] with an ynche rule with ease, and to know the true contents therof, or any part thereof at your pleasure, within the hollow part, and then you hauing of diuerse sortes of these hollow cubes or squares, some that doo conteine more, and some that doo conteyne lesse, as neere as shall require: and then take some conuenient vessel mete for your purpose, and put water into it, and that done, then take that thing which you doo require too knowe the true contentes of the number of ynches or feete, & thē before you doo put that into the water, marke the syde of that thing or vessell roūde about by the very edge of the water very precisely, that you doo not committe errour by that meanes: and that being trulye done, thē put that mettal or thing into the water, that it be couered: and that doone, take out as much of the water as is rysen by the meanes of the thing of mettall put into the water, vntil the water do stande iust at the marke that it was before: & then put that water into the hollow cube or square, without any of the water shedde or spylled by, for that may cause some errour: & then with an ynche rule measure the true deepenes of the water in the cube or square, and so shall you know iustly, how many ynches or feete of mettall there is, by the multiplying of the length, breadth, and deepenes of the water: As for ensample thus: by a branche, or cādlestick (to hang in a house) of Latine or Brasse, my desyre is to know, how many ynches of mettall there is contayned in it: and then I dyd fyrst put in water into a tub or vessell, that I had appoynted for that purpose, and then I marked the water in the tubbe or vessell rounde about at the very edge of the water: and then I put the brauach or candlesticke into the water, and that sunke vnto the bottome, and then I tooke out all that water that was dyd by the meanes of the braunche or candlestick of Latine, & then I did put that water into a litle cube of 6. ynches square euery way, like vnto a dee, & dyd it precisely & shed none of the water, neither tooke I out any more or lesse of the water, but in I vnto the marke vpon the tub or vessel syde, & then I measured the true deepenes of the water in the litle cube, & found it to be 5. ynches, & ⅝. partes of an ynche, that is to say, that it was 5. ynches & a half & half a quarter & thē I dyd multiply it in this maner, for that cube was 6. ynches [Page 12] square .6. tymes .6. and that was .36. and then that being multiplyed agayne, by .5. & ⅝. partes: & that maketh .202. and .½. part so that I did conclude, that the braunche or candlesticke in lattine or brasse, was .202. ynches and a halfe in mettall, and so by this meanes you may knowe the true contentes of any forme, whatsoeuer it be: It is also very good, to trye the partes of a globe, or globes, or you may double any cube what soeuer it be, you may doo it very exactly, by this order, hauing this consideration, that you doo marke the water truely, and shed or spil none of the water, and that you doo measure the water truely, the deepenesse, and that must be done with some fyne styffe wyer, for if that you do put in any bigge rule, then that wyll swell, or hygh the water somewhat, according vnto the bignes of the rule or thing. Wherfore it is very good for to haue the cube or square to be marked with ynches, and partes of ynches, within the insyde rounde about with parallel liens at euery ynche ende, and also it is not good to haue your square vessel too broade, for the narower that it is, the more certayne: and also you may not shifte your water into to many thinges, and especially if it be wood, for that same water wyll hang vpon it, and also wood wyll receiue, or drynk water. And al these may be causes that may hinder the exact truth: and also this order of measuring is very good, to know if any thing be made in golde, for that it is a very heauy mettall, and no other mettall so heauy as it is, if there were made any vessell in golde, and any deceipt in it, then putting that vessell into water, then marke how high the water dooth ryse, than take out of that water the vessell agayne, then take that waight of golde, and put it into the water, and yf the vessell dyd rayse the water higher then the golde, then there is deceipt in the vessel, but if the water be at both the times of one lyke height, then there is no deceipt in it, as this was the very way, that Archimedes found the deceipt of the Crowne of gold, & also this art or order of mesuring doth not altogether shew the contents of ynches or feete, but also you may know the diuersitie of waight of euery seueral sortes of mettal, how much the [...]ne sort is heauier then the other, as thus: you hauing of 2 sortes of mettal, the water being fyrst marked, & then waighing the mettal before you do put it into the water, thē mark the water how hie it [Page] ryseth, and then marke it there agayne, & then take that mettal out of the water, and then put in of the other mettall so much in quantitie, tyll that it rayse the water, vnto that iust height that it was before: and it maketh no matter, although it be of many peeces, so that it be al of one sorte of mettall, and then take out the mettal, and waigh it iustly, and so shal you see certaynly how much in waight it dooth differ quantitie for quantitie, or otherwyse: you may know the diuersitie of the waight of mettals, by wayghing two sortes of mettal, and let them be both of one waight iust, and then the water being marked, put in the one sort of mettall fyrst, and then take out that water, as much as is rysen by the meanes of the mettall vnto the fyrst marked place, and put that into the hollow Cube, as before is rehearsed, and then cast the contentes how many ynches it contayneth iustly: and that doone, then take that mettall out of the water, and put in the water that is in the hollow Cube or square, agayne, into the vessell, that the water may stande at the fyrst appoynted marke iustly agayne: and then put in the other sort of mettall, that is of the iust waight the other was before, and then take all that water out, and put it into the Cube, and if that the water in the Cube bee fewer number of ynches then it was before, then that mettall is heauier then the fyrst mettal, as the proportion of the number of ynches wil shew you iustly: and if there be more water at the later time then there was at the fyrst time, then that mettall is lighter then the fyrst mettall, and the number of ynches wyll shew you the true quantitie, by multiplying them, as before is rehearsed.
And if the water at both the times bee of one height, or measure in the litle cube, then both the mettals are of one waight. And by this meanes, or Art Statical, you may know the diuersitie betweene the waight of Stone and mettall, or the diuersitie of waight of one kinde of Stone and an other, for that all sortes of Stone, is not of one kynde of weight, as all sortes of mettals are not of one waight. And also by this Arte Staticall, you may know the diuersytie of the waight of woode and stone, or any other kynde of mettall, although the one sorte dooth swimme, and the other sort sinketh, and that you must doo in this manner.
[Page 13]All those kynde of woodes that doo swimme, and if theyr forme be such, that you may measure them, then the matter is of no oportunitie, to know the contents thereof, for that it requireth no other thing, but to measure the contents in ynches, & to waigh them how many pound they doo both contayne: and if the forme in woode be such, that you cannot easely measure it, by such order as afore is declared, you may know the contents of the woode, by putting it downe into the water by some slight, although it would swimme, to synke it, you waighing it before it commeth into the water, to know how many pounde it contayneth. And as touching all these matters before rehearsed, it is a very easye matter to know how many ynches, and partes of an ynche, wyll make a pounde waight of any kynde or sortes of mettall, or water, or woode, as thus:
You knowing how many ynches, that any stuffe doth containe, whether it be Golde, Siluer, Copper, Lead, Tinne, Iron, stone, wood, or water: the waight being known [...], then deuide the contentes of the number of ynches, by the number of poundes, and that wyll shew you the true contentes, how many ynches and partes of an ynch, wyll make a pounde waight,
The syxt Chapter sheweth by Arte Staticall to know the waight of any Shyppe, that is sunke into the Sea, or any other riuer, too know how many tunne wyll waigh her vp agayne.
AND furthermore, insomuch as I haue declared heretofore, how to know the true waight of any kinde of mettall, that is sunke into the Water▪ nowe I thinke it conuenient, too shew vnto you, how too geue a neare gesse, or an estimation, yf any Shyppe by any misfortune should be sunke, eyther in the Sea, or in a hauen, or ryuer, to know how many tunnes would waigh her vp agayne, that is to say, to know [Page] how many tunne in waight she dooth waigh in the water, being sunke, which is to be done in this maner: fyrst they must knowe what kynde of goodes the Ship is laden withal, that is sunke, and to set downe a remembrance or note of euery sorte, & how much of euery sort of the sayd goods, & also to set downe a remē brance or note of the contēts of the waight of her ordinance, & ankors: also if it be such goods as do require knitlege or ballast, you must know how many tuns there may be therof, & also what kind of ballast it is, whether it be sand, or stones, or earth: & al these being knowne, then according as the kinde of goodes is, then trye how many tunnes euery sort of that goods may weigh in the water, as thus: if it be Copper, Lead, Tinne, Iron, Steele, or stone, or such other lyke, that doo not penetrate, or doo not drynke, or suck in any lyquor, or water: and the waight therof knowne, then for al those matters, by the rules before rehersed, do shew vnto you the trueth of the matter. Then if the lading, or part of the lading, be Waxe, Pytche, or Tarre, or Hony, or such lyke, Gummes, or what soeuer it be that is heauier then the water, the consideration of the rule Staticall before rehearsed, wyll shewe vnto you the truth of the matter, accordingly as is bfore rehearsed in al points, and if the ladyng or any part thereof be such thinges as doo penetrate, or doo receiue or drynke in lyquor or water, vppon that matter there may grow some error. But to take away some part of that errour, you shal haue this remedye or helpe, and that is thys.
If it be Wool, or Woollen cloth, or Cotten, Sylke, Flaxe, Hempe, or Lynnen cloth, or any such other lyke, then shall you make your proofe in this manner, as before is rehearsed in the Chapters goyng before, and that is thus: Fyll some vessel with that kinde of water, that the Ship is sunck into, & then marke the edge of the water, and that being doone, if there bee any great quantitie of that kynde of goodes or marchaundize, then take of that sorte drye, as the goodes were before it was laden, whether it be Wooll, or woollen Cloth, or Cotten. &c. And then that being drye, waigh it, and then open it loosely, that the water may [Page 14] drynke into it, and that being soked, by imagination as the goods is or may bee, then take out so much of the water as is rysen by that meanes of the wooll or woollen cloth, or what soeuer it bee, and then the waight of the water being knowne, pull the waight of the water from the waight of such thinges as you haue made proofe thereof, and that waight which doth remayne, shal bee the waight that the sayde goodes dooth waygh in the Water. And furthermore, yf the ladyng of the Shyppe bee such,Some kynde of goods is of that nature that it wayeth no waight in the water. as dooth requrie kintlege or ballast, if it be wines, or oyles, and such other lyke, for that kind of goods is of no waight in the water, for it is rather lighter then the water: then you must make account of the Kintledge or Ballast, and if it be stones, then the order or Art Staticall dooth shew you what it may contayne in wayght very wel, by making your proofe as before is rehearsed.Some sort of goodes must haue kintledge or ballast. But if the Ballast bee earth or Sande, then put the Sande or earth into the water, & then let the earth or sande settle vnto the bottome: & that being done, you shal see the water wyll be cleare aloft: and then take out of the water, vntil the water be of that height that it was before, & thē waigh the water, & thē pulling the true waight of the water frō the waight of the earth or sand, then that waight which dooth remayne, shal be that waight that so much earth or sād shal waigh in the water. And thē doing as before is rehersed, by the waight of a litle, by the proportion of the waight of a greater, is knowne what it doth waigh in the water. And furthermore, there is some kynde of goods, although it be heauier then the water, yet in remaining long in the water, it will consume, & that is suger or salt. &c. But most kynd of goodes, the longer it remaineth in the water, the heuier it is, for that the water soketh into it throughly. And also any ship being long sunke, there groweth diuers, accidēts to make it the heuier, that is, by the means ther wil settle both sand & owes into her, & also the dry timber that is a loft in a ship, wyl becō heuier by the soking of the water: for this is to be noted, that a ship would not sinke vnto the bottome, but by the meanes of the ballast or such other like heauy goodes: & therefore for the very holde of the Shyppe, as much as is Tymber, a verie smal allowaunce wyll serue for the wayght of it in the water. [Page] For although it besoked, yet it is but lyttle more then the waight of the water, for the Tackle or ropes wyll waigh more in the water, then the holde of the Shyppe wyll, for they be much the heauier, for the pitch and tarre that is vpon them. Wherefore, you must take a note, what number of Cables, and other ropes may be in her, and their waight being known, then make your proofe, as before is rehearsed, by the Arte Staticall. But if that any part of the loding be oyle, or Wine, or Tallow, or such other like, it is not heauier then the water: all such kynde of goods is of no wayght in the water, but wyll rather helpe then hynder. And also if any parte of the ladyng be of Timber, as Mastes, or Sparres, Deales. or Waynscot, or such other lyke, all such kynde of goods wyll rather helpe it to swimme, then hynder any thing. And now this being done, and you knowing what kynde of goodes there is in the Shyp, and how much of euery sort, and your proofe beyng made by this Arte Staticall, and you knowing the waight of euery particuler thing, what it dooth contayne in the water, as well the waight of the Ordinaunce, Cables, Ankers, Ropes, and the Ballast. &c. And then addyng all your numbers together, then shall you see very neare what all the whole wayght of the Shyp with her ladyng dooth waygh in the water, and that being knowen, then you doo know what number of Tunnes wyll waygh the Shyp vp agayne, and that being knowne, then the matter is the more easyer to know how to make prouision for to waigh her vp agayne.
The seuenth Chapter sheweth howe to waygh a Shyppe that is sunke, where it dooth ebbe and flowe. &c.
NOwe you knowyng the wayght of any Shyppe that is sunke, if you woulde waygh her vp agayne, then when you doo make your prouision for to waygh her, take as many Shyppes, Hoyes, or Lyghters, as will beare that number of tunnes, that the sunke Shyppe dooth waigh in the water, and in euery .40. or 50. tunnes, take .10. tunnes more, for that it is better to haue too muche, then any thing too litle: And looke that you haue good Ropes that are able to beare so much in wayght, as the sunken Shyppe dooth waygh in the water, and thē when you haue made your Cables, hawseres, & ropes faste vppon the sunken Shyppe, you muste take suche order in the making fast of your Cables, or Ropes, that euery Shyp Hoye, or Lyter may waygh or lyft vp the wayght of her proper burthen, for els you may be deceyued, for that I haue seene by experience, that the Shyppe which hath beene sunke in the water, hath not wayghed .40. tunnes, and the Hoyes or Lyters woulde carrye more then .60. tunnes, and yet they were not able to waygh the sayd Shyp, but were dryuen to let go theyr fastes or Cables, and ropes agayne, or els they shoulde haue ben sunke, and that was but for lacke of knowledge in that matter, for the Shyppes, Hoyes, or Lyters wyll waygh or lifte moste from the bottome, when they haue no lading, and yet notwithstanding they wyll waygh or lift the lesser, if they doo vse that matter as I haue seene, for that they doo make fast theyr Cables & ropes some vnto the side of the Shyppes, Hoyes, or Lyters, and [Page] some vnto the head, and so foorth.
And nowe the Shyppes, Hoyes, or Lyters, are not able to waygh or lyft, not one quarter of theyr proper burthen, and they lift or waigh much the les, for that they haue no lading within: for if they doo make fast theyr Cables or Ropes vnto the syde, then it wil not lyft the .10. part of theyr proper burthen, for that the side wyl soone goe downe. And if they doo make fast theyr Cables and Ropes vnto the heade, (for there it wil waygh or lyft most) yet it wyll not waygh or lyft one thirde parte of theyr burthen, for hauyng no lodyng, the heade wyll soone goe downe into the water. Wherefore whensoeuer they doo meane for to waygh any Shyp that is sunke:How to vse the lighters to make them lift or waygh their owne proper burthen. then they must prepare long, strong, and great Timber, or strong Mastes, and let them be layde crosse the Shyppes, Hoyes, or Lyters, ouer both the sydes, and to match .2. and .2. togeather of equal burthen, as neare as you can, and let the long Tymber or Mastes lye crosse both the Shyps, Hoyes, or Lyghters, and ouer both the sides, and then bring your Cables or ropes that are fast vnto the sunke Ship, ouer the long Timber or masts, and then make the ropes fast within the Shyppes, or Lyghters: and this doone, then the shippes, Hoyes, or Lyghters wyl waigh or lyft, their owne proper burthen, otherwyse they wyl not. And then it standeth you in hande to gette such Timber that wil not breake for that burthen, for if the Tymber dooth breake, it wyll put al in hassard of synking agayne. Also it is very good to waigh a shyppe with kaske, and euery hogeshead, pype, or butte, wyll waygh or lyfte as much in waight, as it woulde waygh, if it were ful of that water, excepting the proper wayght of the vessell or kaske, so that the Kaske be made thight, that no water may come into it. And then when you doo meane for to waygh or lyfte vp anye Shyppe, that is sunke, your Ropes, or Cables being fast vnto the sunken Shyp, then you hauing al your things in a readinesse, your Shyppes, Hoyes, or Lyghters, and the great Tymber or Mastes layde crosse ouer both the sydes of them, and two and two of them, and also your kaske, then make fast your ropes and Cables vnto the Shippes or Lighters, [Page 16] at a lowe water, the flood beyng in hand. Prouided alwayes, that you bring the ropes or cables ouer the Tymber,you must make your ropes fast at a low water, the flood being in hand. that lyeth crosse the Hoyes or Lyghters, and also then to make fast the Kaske vnto your ropes or Cables. And then as the flood ryseth, so shall the sunken Shyppe ryse from the bottome: and then as the water dooth ryse or hygh, so goe towardes the lande, or shoare, tyll it be a ful Sea, and then the sunken Shyp wyll rest vppon the grounde agayne. And then at the next lowe water: they shortenyng or making fast their cables or ropes agayne, then the next full Sea, they may bring the sunken Shyppe, nearer vnto the lande or shoare. And thus they may bring the sunken Shyppe vnto the lande or shoare, vntyll such tyme as the sunken Shyppe shalbe layde vppon dry grounde at a lowe water. For you may knowe in howe many Tydes that you may waygh her, and lay her vppon drye grounde, at a lowe water, as thus: Sounde,How to knowe in how many Tides you may waigh a shyp. or looke howe many fadome, the sunken Shyppe lyeth in at a lowe water, and then looke how manye fadome the water hygheth, or floweth till it bee a full Sea, and then consider howe deepe that your Shyps, Hoyes, or Lyghters, wyll goe into the water, before they are able to lifte the sunken Shyppe from the bottome: and then consider howe much, or howe manye fadome or feete, the water wyll ryse afterwardes: and so shall you see in howe many Tydes that you shall bring her to bee drye at a lowe water. As for ensample thus: Suppose that any Shyppe or Hoye is sunke at eyght fadome at a lowe water, and the water dooth ryse or hygh two fadome and a halfe from the lowe water vnto a ful sea:An ensample of the w [...]ght of a Shyppe. and then the Hoyes or Lyters wyll not be able to lyfte or waygh the sunken Shyppe from the bottome, not vntyl they be laden downe two foote, and better. So that you may conclude, that the water wyll not ryse or high lytle more then two fadome, after that the sunken Shyppe is lyfted or wayghed from the bottome: and then goyng vntoo the Lande or Shoare, tyll that it was a ful Sea.
[Page]And then the sunken Shyppe dyd rest vppon the grounde againe at .6. fadome, at a lowe water, and then at the next lowe water the Cables and Ropes were made fast agayne, and when it was flowed two foote and better, the sunke Shyp was lyfted from the grounde agayne.
And then goyng vnto the lande or shoare, tyll it was a full Sea, then the sunken Shyppe dyd rest at .4. fadome at a lowe water: & then at the next lowe water, the Cables and ropes being made fast agayne, when it was flowed .2. foote, and better, the sunke Shyppe was lifted from the bottome, and so going in vnto the lande or shoare til it was a full Sea: then the sunke Shyppe dyd rest agayne, at .2. fadome at a lowe water: and then the Cables or ropes, being shortned, and made fast agayne, then going vnto the lande or shoare, vntyl that it was a ful Sea, and then restyng, the sunke Shyppe shalbe drye at a lowe water: so that you maye conclude, that the Shyppe that was sunke at .8. fadome at a lowe water: and the water ryse or dyd flowe .2. fadome and a halfe, from the lowe water vnto the ful Sea, and the Hoyes and Lyters woulde waygh or lyft the sunke Shyppe from the bottome, by that tyme they were title more then .2. foote buryed or setled into the water, and then in foure Tydes the sunke Shyppe wylbe layed vpon drye grounde, at a lowe water.
And by this order you may knowe in howe many Tydes that any Shyppemaye he wayghed, and layde on drye grounde at a lowe water, you knowing howe deepe that the Shyppe lyeth at a lowe water, and howe much it dooth flowe in anye place where it doth ebbe or flowe.
The eyght Chapter sheweth howe to waygh a Shyppe, where it dooth not ebbe and flowe.
ANd furthermore, if that any Shyp or anye other vessell be sunke in such places, where that it dooth neyther ebbe, nor flowe, that is too saye, where the water dooth not hygh and lowe, there is some matter, and asketh great charges, and labour for to waygh or lyfte anye great wayghte from the bottome: yet this way it is to bee doone, the wayght of the sunken Shyppe or vessell being knowne, what that it dooth waygh in the water, as before is rehearsed.
Then the number of tunnes beyng knowen,As touching the waighing of shyps, whereas it doth not ebbe and flowe. prepare so many Shyppes, Hoyes, or Lyghters, as wyll carrye syxe or eyght tymes the wayght, that it dooth waygh in the water, and then let them be neare halfe laden euery one of them, wyth some handsome ballast that is wayghty, and good to be remoued too and fro.
And then when you haue made your Ropes, and Cables fast vnto the sunken Shyppe or vessell, then bring your Hoyes, and Lyghters vnto the sunke Vessell, and let all that Ballast bee throwne into one ende of all the Hoyes and Lyghters, and then make fast your Ropes and Cables vntoo that ende that hath the ladyng or ballast: Then your ropes and Cables being made fast, throwe or carrye all the ballast or ladyng vnto the other ende, and then it will waygh or lyfte the sunken Shyppe from the bottome.
Wherefore you muste haue double so manye as is able too lyfte or waygh it:Not [...]th [...] poynt. for when that all the ladyng is throwne vnto [Page] the other ende: then whylest that the one hath lyfted or wayghed it, the other Hoyes or Lyghters must make faste theyr Ropes and Cables vnto the laden endes agayne. And thus they muste doo as often tymes as the lading is throwen vnto the further ende, they must haue as manye Lyghters as are able too lyfte or waygh it, whyllest that the other Lyghters doo hang or turne the laden ende, and to bee made fast vnto the Ropes, and Cables agayne.
And thus in tyme, they shall waygh or lyft the sunken thyp or vessell, vnto the drymme of the water, and then they maye carrye the sunken vessell vnto the lande or shoare. And by this order or meanes, they may waygh any Shyppe or vessell vp vnto the brymme of the water, in such places whereas it dooth neyther ebbe nor flowe.
The nyenth Chapter sheweth how to bring in any shyppe ouer a shulde or barre, and to make the Shyppe beare Sayle, when al the ballast is out: and also if neede requyre, how to lyft the Shyppe higher out of the waterwardes, to the intent to bring her in. &c.
ANd now, insomuch that I haue shewed how to waygh any Shyppe that is sunke, as wel in such places wheras it dooth not ebbe and flowe, and also ebbe and flowe. In lyke manner, I doo thinke it conuenient too shewe vnto you, how for to bryng a Shyppe in ouer a barre or Shulde, whereas there is not sufficientnesse of deepth of water to come into any hauen or Ryuer, and if that all the ballast is out, and if there is [Page 17] not sufficientnesse of deepth of water: Then howe to lyft her higher out of the waterwards, vntyl the shyppe is sufficiently out of the water, to bring her in ouer the shulde or barre. &c.
And fyrst thus, if that any Shyppe bee come intoo anye Hauen or harborowe, and by the meanes of a shulde or barre, that she hath not deepth of water yenough, and yet the Shyppe is but in her ballast: Then doo thus: Prepare two greate Hoyes or Lyghters, and also strong haulsers or Cables, and then bryng the one of the Hoyes or Lyghters, on the one side, and the other, on the other syde, and that doone, then make faste the head, and the sterne of both the Hoyes or Lyghters, with strong Ropes or Haulsers, and make them fast, as high in the Shyppe, as you can conuenientlye, and then heaue all the ballast out of the Shyppe into the two Hoyes, or Lighters: And that doone, the Ropes and Haulsers being fast vnto the heade and sterne of the Lyghters or Hoyes, and vnto the Shyppe, the Shyppe cannot ouerthrowe, although al the Takle, and Mastes are standing: for looke when the shyppe would shelde, then it cannot doo it, except that it shoulde lyft the furdest Lyghter or Hoye out of the water, which is not possible for to doe, as long as the Ropes, or Cables doo holde: and then if that it doo offer to holde the other way, then that lighter that is on the other syde, wyl not suffer it, as long as the ropes or fastes doo holde: Wherfore the shyppe may beare saile, although al the ballast were out, &c.
But if that there be not sufficientnesse of deepth of water vppon the shulde or barre, to bring the Shyppe in ouer it, when al the ballast is out: yet notwithstanding you maye make such prouision, that you may lift her hygher vp out of the water, vntyl such tyme as the Shyppe may be able to come in, as thus: you hauyng prouided two such Lyghters, meete for the purpose, as before is declared, then prepare long and strong great Timber or Mastes, that may be of such sufficient length, that wyll reach the breadth of the Shyp, and the breadth of both the Lyghters all at once.
[Page]And then the Lyghters being made fast, as before is rehearsed, and al the ballast heued or throwne out of the Shyppe into the two Lyghters, then the Lyghters beyng laden with the ballast, then make holles thorowe both the sydes of the Shyppe in sundrye places, and then put the long and strong great Tymber thorowe both the sydes of the Shyppe, that it may bee ouerthwarte crosse ouer both the sydes of the Lyghters, and in such sort, that the Shyppe maye rest or hang vppon the long and strong great Tymber or Mastes, and rest or lye vppon the two sydes of both the Lyghters. And then hauyng out all the ballast out of both the Lyghters, the two Lyghters wyll heaue vp out of the waterwardes, as muche in wayghte as theyr owne proper Tonnage or burthen commeth vntoo, &c. And by thys meanes you may lyft any Shyppe out of the water, vnto what proportion you lyst: and also you knowing the wayght of the Shyppe, as you maye knowe it, as it dooth appeare in the seconde and thyrde Chapters going before: Then accordyngly you maye make your prouision of the two Lyghters, to lyft such sufficient quantitye of the Shyppe that shalbee able to serue your turne, and also if that it shoulde happen, so that the Shyppe shoulde be a grounde vppon the shuld or barre, and yet the place that the Shyppe is a grounde on, dooth neyther ebbe nor flowe, yet notwithstanding you haue this remedye to helpe it, then lade both the Lyghters agayne, and let the Shyp rest vpon the grounde, and then you maye boulster [...]t vp by some prouision betweene the two Lyghters sydes, and the long Tymber or Mastes, vntyll that it be sufficient to serue your turne: and then discharging the Lyghters, they shall lyft vp the Shyppe hygher agayne: And by this meanes you may bryng in any ship, higher againe ouer any shuld or barre, so that the water be sufficient deepe, that the Lyghters beyng laden, may passe in ouer the barre or shuld. &c.
The tenth Chapter dooth shew vnto you, how for to come vnto the Keel of any Ship, without the grounding of her, wherby you may collect any shippe, and make her thight vnto the Keel, which is called carriyng of them. &c.
AND for that our Countrye of Englande, is inuironed rounde about with the Sea, so that no other Nation, or Countrye can come vnto vs, neither we vnto them, but only by sea, Scotlande only excepted: Therfore it standeth vs most principally in hande too bee moste skilfull in shipping, for that it is our most principall force, and for that it is a very necessary matter for to know how to cauke a Shyppe, or to stop a leake, and to make her thight downe vnto the Keel of the Shippe, in such places whereas it dooth not ebbe and flow water in, for to grounde any shyp, then they must vse such means as those doo that are in the leuāt sea, that is, the sea called Mare Mediterraneum, as the Genewayes & Vemsians & Rogosones, with a number of other, that haue shipping in that Sea, that I do omyt, & that haue great ships, and yet neuer doo grounde them, but only doo bring them ouer on the one syde, which is called carriyng of them, and many people that haue hearde therof, haue thought that they haue wound them ouer by force: and some haue iudged one way, and some an other way, but few or none of them haue iudged the truth of the matter, although that diuers Englishmen haue been there, and haue seene the thing done: yet as farre as euer I coulde perceaue at their handes, they coulde neuer vnderstande the trueth of the matter, and the cause thereof was, that they were neuer in the [Page] Shippe where she was a karrenyng, and yet for to karren a ship, it is a great deale more ease for the Ship, then it is to be grounded in diuers respectes, and also they shall haue more time and leasure both to searche the Shyppe, and caulke her, and to marke her thight, then they shall haue in the grounding of a Shyppe, and also they shall the better perceaue where any leake is in the karrenyng of them, then in the grounding of them.
And as touching the karrenyng of a Shyppe, this is too bee done, fyrst thus, Cauke the sydes of the Shippe thight aboue the water, and especially that syde that you doo meane to bryng her ouer on, and also caulke the decke and portes, and the sperkettes thight, and that done, then prepare labourers ynowe, and bryng the Shippe resonable light, that she may haue litle more ballast, then she may beare her selfe well. And that done, her ordinaunce, and euery loose thing taken out of the Shippe, then let the labourers heaue the ballast ouer, vnto that syde that you doo meane to bring her ouer vpon, and so heauing the ballast ouer, the Shyppe wyll goe ouer vnto what proportion you lyst, and by that meanes you may come vnto the Keel of any ship, and marke her thight at your pleasure, But diuers people haue made argument and saide, that the ship wyll not ryse vpright agayne, and some haue sayde, that lying a to [...]e syde, it woulde ouerthrow, and other would think that the ballast would slyp, but the trueth is this: as soone as euer the ballast is throwne or heaued backwards agayne, the ship wyll beginne to ryse, and so in the ende become to bee vpright agayne.
Wherfore it is a straunge matter, to see the straunge opinion of some people in the worlde that seemeth to be wyse, and for that generally the most part of men haue thought that in the karrening of Ships, that they haue beene wounde downe with caxslienes, and gearres, & tackles by great force, and therfore they haue made fast the ballast by some prouisiō, & also haue made raftes of masts, to the ende that they might lay the syde of the Shyp vpon them, to help to beare vp the shyppe. And see the simple opinion of them that should bee wyse, to thinke that the same should doo any good, [Page 19] for Mastes being massy, and not hollow, are but litle lighter then water, so that .20. tunnes waight of them, wyll not support vp two tunnes, therfore that can doo no great good at al. And what a vayne folly is it for them to make fast the ballast, that it should not slyppe, for .20. tunnes of ballast, being made fast at the bottome of the Shippe, must require the force of 20. tuns to wynde it downe ouer: and then the ballast, for that it is made fast, and the Shippe wounde downe by force, the Shyppe is forced downe with more then fortie Tunnes, for that the Ballast dooth hang ouer one waye towardes the Keelwardes, and the Shippe is wounde downe the contrarye waye on the one syde, whiche must of force be in such sort, as a thing that lyeth in a colepresse, and doth charge the Shippe with a double waight or burthen, to preasse it into the waterwardes: and then what can the quantitie of the supporting of any thing that cannot lift a tunne or two tunne waight therof, doo them any pleasure, besydes the great cumber that they shall haue in those causes, to get such a number of Mastes, and also to make them fast, or to frappe them together: and also in deede the ballast woulde slyppe, the Shyppe being wounde downe by force, for when that the shyppe hath her Ballast into the end, to make her to swym vpright, and then to bee wounde downe by force, then the ballast dooth hang towards the Keele, and the ship beyng wounde downe to the syde, then it must needes slyppe, as before is sayde, except that it bee made fast, for that the Ballast dooth hang ouer one way, and the Shyppe is wounde downe the other waye, and then it is not possible to come vnto the keele, so well as they shall doo, when the Ballast is but throwne or heaued ouer vnto the one syde, for that it hath then no more then hys owne proper wayght, where as otherwyse the Shippe is charged with double wayght, for yf shee shoulde haue but forte tunnes of Ballast, the Shyppe is charged with more then eyghtie tunnes in wayght, and also it is very hurtfull and vneasy for the shippe. &c.
[Page]And furthermore, as before is declared in this fourth booke, called Staticke, that no kynde of thyng doth enter no further into the water, then the quantitie or body or any thing that waigheth so much in waight, as the proportion in bygnesse of so much water. Therefore any thyng that is in the water, howe lyght soeuer it is, can enter no further into the water, then the proportion of suche a magnitude of water. For if the thyng be not the .xx. part of the waight of the water, then the one of twenty part of the body dooth enter into the water: and 19. of .20. partes shalbe aboue the superficies of the water, &c.
And furthermore, for that the water is an Element ponderous or heauye, and yet thynne: therefore it is the nature and qualitie of water, to support or beare vp a thyng that is lighter then it selfe: and yet it dooth geue any thyng place or leaue to turne it selfe in the water, so that it shall swymme with the heauyest part downewarde, as by experience is seene of any thyng that is put into the water, as thus: Take a Raske, as a Pype or Hogshead, or a Barrel, and put it into the water, the thyng beyng thyght, the tenth part of the bygnesse or magnitude dooth not goe into the water, for that it is so lyght. And yet notwithstandyng, if any one part of the kaske be heauyer then the other, that same part wil turne downewards. And if you doo turne it vpwardes, as soone as euer you doo let it goe, it presently turneth of it selfe downewardes agayne. So that experience dooth shewe this to be true, that the heauyest part of any thyng that is in the water, dooth alwayes turne, and seeketh downewardes. Therfore we may perfectly conclude thus of any shyp, if the ballast be cast or heaued ouer vnto the syde of any shyp, that the shyp dooth turne ouer accordyngly, alwayes to haue the heauyest part downewardes.
Wherfore, contrary vnto the vayne opinions of a number of persons that shoulde be wyse, that if the ballast be throwen ouer vnto the syde, that the shyp shal swymme vpon the side, and yet the ballast shal neuer slyppe, for that alwayes the shyp dooth turne of itselfe, to bryng it vnto the leuel, except it be let by some cause, whiche is, eyther by makyng it fast, or els by some other accidental matter, or els it wyl followe accordyngly. &c. And some people [Page 21] haue bene of that opinion, that no Shyp dooth swimme vpright, but that there is as much waight or more belowe in the water, as is aboue the water: but that is vntrue, as before it dooth appeare, by the ensample of a Raske or Barrel. For you doo see that it wyll swymme, and the hea [...]yest part wyll turne downwards: & if that it be not one quarter of a pound heauier on the one syde, then it is on the other, that part wyll turne downewardes: and yet for all that, that part that is in the water, wyll not waygh the .10. part of that which is aboue the water.
Therefore you may conclude, that if the ballast doo lye all vppon the one syde of the Shippe, the Ship shal swimme vpon that syde, and the Keel shall come out of the water. And if that the ship syde be [...]hight, there is no more daunger in her swimming on the one syde, than if she were vpright in the water. And also the Ship dooth not swim so deepe into the water, lying on the one syde, as she dooth swim when shee is vpright, for that the Shippe is more lancker, or slenderer, or sharper: that is to saye, not so full and rounde, by the means of her Tuck and Runne, and the Foreway, as the syde is rounde and full. Therfore it cannot go so deepe into the water, for as before is sayde, that nothing can goe no further into the water then the proportion of so much water in waight. Wherfore the syde being rounde and full, it is the more boyenter a great deale, &c. And also it is very good to bring a Shippe in ouer a barre or shulde, for lying vpon the syde, it dooth draw much lesse water, then when it dooth swimme vpright &c. But notwithstandyng it is not so good for to Karrene the Queenes maiesties Shippes, as it is the Marchants Shippes, for two speciall caues, and the fyrst is this: the Queenes highnesse Shippes haue alwayes as muche ballast in them, as they doo vsually goe to the Sea withall, to be fast to beare a sayle, which is no small quantitie in her bigger sorte of Shippes: and then what a charge is it to take the greatest part of the ballast out of them, and too take it in agayne, for they must take more then .3. quarters of the Ballast out, when they doo Karren them: whereas the Marchauntes Shippes doo delyuer all the ballast out when they do lade their ships: therfore the Marchants shal not occupy the 20. part of the [Page] charges that the Queenes Shippes must. And the seconde cause is this, that in the Queenes Shippes, the ballast is alwayes fyrme and harde, by the meanes that it is seeldome or neuer styrred, and also the Cooke roome is made vp with bricke vppon the ballast, and also there is set vp in the Cooke roome with Brycke worke the furnases, to boyle theyr beefe, and other prouision, that is made for the dressing of mens vittailes, as Quens and hatches &c. which were no smal charge to remoue and make vp agayne, whereas in the grounding of them all, these two great charges are saued, that Marchauntes shyps in theyr karrening shall not neede to bee at. &c. And thus I ende the fourth Booke.
❧A Table of the Contentes of the Chapters of the fourth booke called a Treasure for Trauailers.
The fyrst Chapter of the fourth Booke, sheweth you by the proportion of a Shyppe swimming in the water, for to knowe the true waight of any Shippe, with al her tackle, ordinaunce, furniture, and lading, &c.
The seconde Chapter sheweth how for to measure the proportion of the mould of any Shyp, wherby is knowen the waight of any Shyppe, with all her ladynge and furniture.
The thyrde Chapter sheweth you an easyer waye, then before rehearsed, by the Arte Statical, to knowe the true waight of any Shyppe, with al her lading, and all the reste of her furniture.
The fourth Chapter sheweth by the Arte Statical, the wayght of anye mettall or stone, howe much, or what wayght that it dooth waygh in the water, to bee lyfted or waighed from the bottome, vnto the brimme of the water.
The fyfth Chapter sheweth howe too knowe the true measure in ynches or feete, of any straunge forme, such as Geometrie can giue no order for the measuring thereof, as to measure a braunche in mettal, or a piller that is enbowed and ful of hollownesse in diuers places, and boyles out in some places: and also how to know the diuersitie of the waight of mettall, or the diuersity between the waight of Stone, and mettall.
The syxt Chapter sheweth by the Art Statical, to knowe the waight of any ship, that is sunke into the Sea, or anye riuer, too knowe howe many tunne wyll waigh her vp agayne.
The seuenth Chapter sheweth how to waigh a Shyp that is sunke, where it dooth ebbe and flowe, &c.
[Page]The eyght Chapter sheweth howe to waigh a Shyppe, where it dooth not ebbe and flowe, &c.
The nynth Chapter sheweth howe to bring in any ship ouer a shulde or barre, and to make the Shyp beare Saile, when al the ballast is out: and also if neede shoulde requyre, how to lyft the shyppe higher out of the waterwards to the intent to bring her in, &c.
The tenth Chapter dooth shewe vnto you, howe for to come vnto the Keele of anye Shyppe, without the groundyng of her, wherby you may collect any Shyppe, and make her thight vnto the Keele, which is called carenning of them. &c.
❧The fyfth Booke of the treasure for Trauaylers.
Wherein is shewed the cause of dyuers thynges that are to be seene on the Sea, and the Sea Coastes, and the cause of Rockes and sandes in the Sea, and the cause of the ebbyng and flowyng of the water, and the cause of currantes in the Sea, with such other like matters. &c.
Being very necessary for al sortes of Trauaylers, either by Sea, or by lande, to knowe. &c.
Wrytten by William Bourne.
To the Reader.
GEntle Reader, it is possible that some wyll thinke that I haue taken vpon mee to meddle with those causes, that are past my capacity, for that this fyfth and last boke is as concerning the naturall causes of Sands in the Sea and riuers, and the cause of marish ground, and Cliffes by the sea Coasts, and rockes in the Sea, and also the cause that the sea dooth ebbe and flow, and the cause that the water in the Sea is salt, and the cause of Earth quakes, with other matters. And for that my opinion dooth differ from some of the auncient writers in naturall Phylosophy, it is possible that it may be vtterly dislyked of and condemned to be no trueth. But yet notwithstanding they may geue such credit vnto it, as the sequell of the reasons shall support vnto them, for that they bee but my simple opinions: wherfore they may beleeue them as they lift. Therfore gentle Readers, I desyre you to beare with me, for that I am so bolde to shew my simple opinion vnto the world, for it is possible, that some people may mallice me, for that I am so bolde to deale in these causes, consydering what a great number of so excellent learned menne there are in Englande, bothe in the Vniuersyties, and in diuers other places in this Lande.
The fifth Booke of the treasure for trauailers.
The fyrst Chapter of the fyfth Booke sheweth the naturall causes, how Sandes and Bankes are ingendered or made, both in the Sea and Riuers.
NOw beginneth the fifth Booke which is concerning the naturall causes of sundry things that are to bee seene in traueilyng vppon the face of the earth. And although there bee nothing that happeneth, but the prouidence of almightye God, dooth bring it to passe: yet notwithstanding it hath a naturall cause why it is so, although it seemeth supernaturall or vnpossible for that God dooth woorke all thinges by a meanes, and yet doth come to passe by some naturall cause.
And fyrst of the naturall cause of Sandes and Bankes in the Sea and ryuers, my opinion is this: that whereas a great number of Sandes and Banks are many times seene at the mouthes and entraunce of many great riuers both into the Sea, and also vp into the riuer, that it happneth by this meanes, by the shalownesse of those seas, and the great indraft of the Ryuer. And then by the meanes of the soyle of the Countrye in the riuers, beyng a good distaunce from the sea, and especially after any great raine, dooth bring downe the soyle, for all the lande water dooth alwaies runne downe towardes the sea, where as it dooth ebbe and flow, and sometime the water ouerfloweth the banks, and then the swiftnes of the running of the water dooth fret away the bankes, and sometime it happeneth in the winter after a great frost. [Page 5] And such other lyke causes, sometyme from sandye grounde, & sometime from clay grounde, & sometime stony grounde: & other good moulde dooth fall into the Ryuer, and so is myxed and tumbled too and fro with the water, and is alwayes caried towardes the sea by the violence of the streame, for that alwaies, where it doth not ebbe & flow, the streame runneth towards the sea: & wheras it doth ebbe & flow, there the ebbe doth runne both swifter & longer then the floods doo, & so by that meanes, it is alwayes caried towardes the sea, & also any thyng is apter to rolle, or runne down the hyll, rather then agaynst the hyll. And thus the soyle of the countrey beyng tumbled too & fro in the water, is washed and soked in such sorte, that the water is made thycke therewith, and the fat or clammye substance, become owes, but the greety or sandy, or grauelly substāce doth alwaies keepe towards the bottome, for that it is more pōderous or heauier then the fatty or clammy substance, and then this grauelly or sandye substance, beyng dryuen downe towardes the sea, by the violence of the streame, goyng by the bottome, then where it dooth find any place to staye at by the way, there it resteth, and so groweth more and more, and so becommeth a sande, and then the Tyde, by the meanes of ebbing and flowyng, dooth make or scoure out a chanel, or pasadge betweene one sande or bancke, and another. And alwayes thys happeneth, whereas the Sea is but shalowe, and the Ryuer or hauen hath a great indraught, that is to say, to run a great distāce into the lande, whereby there is much soyle brought downe by the meanes afore rehearsed. And then the Sea beyng but shallowe, it hath no great descent to runne downe the hyll. And then by the meanes of the floods, & the bellowes of the Sea, dooth cause it to be stayed, although that sometyme it happeneth, that one sande or bancke doth decrease, and weare away, and another dooth increase and waxe bigger, and many tymes the chanels doo alter, sometymes deeper, and sometymes shallower: and sometymes whereas a chanel was, becommeth a sande, & sometyme whereas a sande was, is become a chanel, as experience hath many tymes shewed, which happeneth manye tymes by some stormes or great wyndes, sometymes from one quarter of the [Page] world, and sometyme from another quarter. And by that meanes the greatnesse of the bellowes of the Sea, dooth beat, or washe awaye the sande from one place, and so dooth rest vppon another place: and then the Tyde or streame doth scoure or frette a newe Chanell, betweene one sande and another. &c. As we maye see by experience in dyuers places, as the mould of the Ryuer of Thames, and Humber, and the Ryuer of Roane, and suche other lyke places, whiche I doo omitte at this tyme.
The seconde Chapter sheweth the natural cause of Marish ground, and other plaine meadowes or ground by the sydes of Ryuers. &c.
AND furthermore, as touching the naturall cause of Maryshes or Marish grounde, and other playne and leuell grounde, that is by the sydes of great Ryuers. &c. and in such other lyke places: mine opinion is this, as in the Chapter before is expressed, by the bringing downe of the soyle of the countrey, which is ground or earth, of al kinde of sorts, whiche is fallen into the water, and brought downe by the streame.
And as before is rehearsed, the grauelly or sandye substance dooth dryue with the streame,Of the soyle of the Countrey. by the bottome, but the fatty or clammy substance is mingled with the water: for although you shoulde take any earth or substance, and washe it and tumble it in water neuer so much: yet notwithstanding it cannot be consumed all away, but if you doo let it stande styll, then it wyl settle it selfe vnto the bottome, and you shall fynde the substance agayne. [Page 6] So although the earth is mingled with water, by the meanes of the fretting of the streame and the Tide, and also the soussyngs of the bellows in great winds, tossyng it to & fro in stormy weather, yet notwithstanding in fayre and calme weather, in such places, whersas there dooth not runne a great Tyde or streame, then that earthye substance doth settle it selfe agayne on such places as are defended by some Naase or poynt, and in some Bay or place, that the grating of the Tyde or streame dooth not greatly trouble it, & is then called Owes, or as the common people that be not neare dwellers vnto such Ryuers, doo call it Durt, Myre, or Mud. And then in such places where it dooth ebbe or stowe, being setled, nowe a litle and then a litle, the winde and the Sunne doo somethyng harden it, vntyll at the last,How Marish groude is ingendred. through the setling nowe some and then some, and styll dryed with the wynde and the Sunne, that it is as high as the common foule Seas: and then it will beginne to beare some greene thyng, and so it wyl become Marishe ground in tyme, and so is ouerflowed in the spring tides, but in the Neape Tydes, it is bare at a full Sea. And then many tymes it happeneth, that those that are the dwellers there aboutes, or els the Lordes of those soyles, doo Inne that same grounde, and make the walles for the defence thereof. And in processe of tyme, it becommeth maine lande, and by this meanes commeth all your playne and leuelled groundes neare vnto Riuers sides: And this kinde of grounde must needes be verye fertyle and riche, so that it be not ouerflowed with salt water, for that all the stonye and sandy substance is washt out thereof, and it must needes bee playne and leuell, for that it is braught to be leuell with the water at a ful Sea. &c.
And furthermore, it happeneth diuers times,Marish groūd is fertyle, if the salt water come not at it, as in the Chapter before is rehearsed, by great wyndes and stormes in sundrie ages of the worlde, that the Channel [...] doo alter by the washyng or fretting away of some poynt or firme lande or Naase, and then that which hath been many yeeres before, mayne grounde, may be fretted awaye, and be ouerflowen agayne.
[Page]And the substance of the grounde maye be landed in some other place, as by experience in manye places hath beene seene, so that, that place that hath beene before meayne grounde, hath become Sea and water,How land hath been sea, and sea hath been land. and that place that hath beene before sea and water, hath become drye lande. And these things haue happened in pracesse of tyme, by the meanes of the chaunging of the chanels, which doo alter the setting of the Tydes in Ryuers and Hauens, whose principal cause hath happened, as before is rehearsed, by frettyng awaye some Naase or poynt, and then some Naase or poynt hath turned the Tyde some other waye, and so worne or fretted a newe chanell: so that whereas the Tyde or streame hath runne most swiftest, hath become an eady, and so in processe of tyme, grounde in lyke manner. &c.
The thyrde Chapter sheweth the naturall causes of the hyghe clyffes by the Sea coastes. &c.
AND furthermore, as touchyng the naturall causes of clyffes that are by the Sea coastes, as wee maye see some of harde stone, and some of Chaulke, and of a monstrous height, and some of Claye, and other of earth. &c.
My opinion is thys, as the age of the worlde is of no small tyme, so in processe of tyme the often sufferynges of the bellowes of the Seas haue beaten away the feete of those hilles, that are by the sea coastes.
[Page 7]And so vndermyning it, although it were of harde stone, yet the wayght of that which was vndermined hanging ouer, in rayny wether, or after great frost, must needes fall downe into the Sea.Of Cliffes by Sea Coast. And then that sayle or substaunce that fell downe, in processe of time was beaten or washed away agayne, by the often soussing of the bellowes of the sea, in the time of great wyndes and stormes. And then the stuffe so fallen down, being washed and consumed away, the sea doth begin to vndermine it agayne, by litle and lytle, tyll at the length by the meanes before rehearsed, there falleth downe an other portion of the sayde substaunce, or stuffe from the hyll, so that in the ende, they become such monsterous Cliffes, as wee may see by experience, are on the sea coastes in a number of places: And thus they do were away by litle and lytle, vntil that an other place is become aforelande, without that lande, that is to say, an other Naase or head land to stande further out into the sea, then that dooth, and then that Clyffe wyl stay without fallyng downe any more, of the substaunce or stuffe of long time, by the meanes of some beache, or shingle, or sande, or stones that shall be brought thither, by the cossing to and fro of the bellowes of the sea, and that shall lye there, and defende the foote of the sande cliffe, as by experiēce we may see in a nūber of places by the sea coasts, and then doth we are away an other Cliffe, in some other place of the sea coastes: for it happeneth many times, in sundrye ages, that at one time, one place dooth were awaye, and an other dooth increase agayne: and in an other age agayne, that whiche dyd increase, shal weare away, and the other shal stay, or perhaps increase agayne, by the meanes there is some head land, or Naase without that, which dooth breake away the fretting or gratyng of the tyde: For many times it happeneth vpon the sea Coastes, through some great and huge storme, that maketh a breache by the monstrousnesse of the great bellowes, that teareth away some great quantitie of ground, from some one place in short time, and the bellowes of the sea shall dryue or bring it, or lande it in some other place, yea euen in a short space, as experyence hath many tymes shewed it, and as it many tymes hapneth, that in one age [Page] of the world, that the great huge windes or stormed doo happen sometime in one quarter of the Worlde, and at an other time, in an other quarter.
In foure yeres the great stormes are in one quarter of the world, and an other yeare in an other quarter.For as we may see, that in some yeares, the most great winds and stormes doo blow in the East quarter of the worlde, and in other yeares, in the West quarter of the world, and in other yeres, in the South quarter of the worlde, and in other yeares, in the North quarter of the worlde. &c. By which meanes it fretteth at one time away the substaunce or stuffe from one place, and then the bellowes of the sea doo driue or force it to lande in an other place: and so it continueth for a certayne time, vntill such tyme that the great windes or stormes doo blowe in a contrary quarter of the world: and then the stuffe or subtaunce is beaten by the bellowes of the Sea, and dryuen and forced from that place, and so is landed in an other place: And it is possible to bee forced or landed at the place that it fyrst came from, although it may be 20. or 40. myles distance asunder. And thus those that are neare dwellers vnto the sea coastes, doo see the great and mighty workes of God, wrought by his greatnesse and almighty power, the great or huge bellowes or waues or knots of the sea, in great winds and stormes or tempestes, For euen those things that shew or seeme vnpossible, he bringeth to passe, as by experience hath beene seene at sundrye times. &c.
The fourth Chapter sheweth the naturall cause, why that the beache, and the great bolder stones, on the sea coastes, are become rounde and smooth, without any edges or corners.
NOw furthermore, as touching the natural causes, why that the Beache, and the great bolder stones in the sea, and the other small shingle are all smooth and rounde, without corners or sharpe edges, and yet they be of all kindes and luites of stones,The shingle beach or the bolder stone is of the substance of the nature of the Cliffes nere vnto them as Marble stone, and Flynt, and other hard stone. &c. For they bee of those substance & natures, as the Cliffes that are neare vnto those partes, as in the Chapter goyng before is declared, by vnderminyng of the hilles or bankes, with the bellowes of the Sea, the substaunce falleth downe into the Sea, what soeuer manner of stuffe it bee, according vnto the mineralles of those groundes or hylles that falleth into the Sea, whether it be hard stone, or Marble stone, or Flynt, or what stuffe els soeuer it bee, accordyng vnto the vaines of the mineralles in the grounde, that so by that meanes before rehearsed, do fall into the sea. Then when it is forced or brought to lande vpon any place of the Sea coast, it is all smooth, without any corners or sharpe edges. The cause therof commeth to passe by this meanes, for when it doth fyrst fall out of the Cliffe into the sea, then it hath the fashion and forme as those haue that are digged forth of the grounde:The cause or reason that the beach and the great bolder stone is rounde without any sharp edges. but after it is fallen into the sea, & hath had any continuance there, & so tossed to & fro by the waues and bellowes of the sea, a great number of them together, the one doth so fret and rubbe or grinde against the other, that it must needs rubbe or fret away al the sharpe edges of those stones, how hard soeuer the stone is, for the soussing of the bellows of the sea doth neuer forget it self to stand styl, neyther is euer wery, nor desyreth rest, but is alwayes labouring and tossing that is in it to and fro, according vnto the bignesse of the winde. &c. as by experience vpon the sea coast may be seene, the great and mighty force of the bellowes, in the soussings and forcing of the Beach a shore in the time of any great windes or stormes, amongst the Beache & shingle:The force of the Sea. for you shal heare the soussing of the bellowes of the sea amongest the Beache, as though it weee the powring downe of a thousande Carte loade at once:
[Page]So that you may heare it two or three miles from the place wher as it is, yea and sometimes after a Storme, you may see Stones that waygh a pounde wayght, throwne from the full sea marke, into the landewardes two or three rods, by the very meanes of the soussing of the bellowes or waues of the sea, as those that doo occupy the sea coastes, doo see by experience. &c.
The fyfth Chapter sheweth the naturall cause of the Rockes in the Sea. &c.
AND yet furthermore, as concernyng the naturall causes of Rockes and pinacles that doo stande in the sea very strangelye vnto suche as doo beholde and see the same in sundry places in the sea, and some on the sea Coastes, and some in Hauens, & harborows that are adioyning vnto the sea. And this is generall for euer, that looke whereas there is any great store of rockes, it is a token of a deepe sea, it is a token of a shallow Sea, that hath many sands. And the cause of rocks in the sea, in mine opinion is this, as it is knowne vnto all persons, that the age of the world is of no small time: so that I am of that opinion, that the Rockes that are now standyng in the sea, haue beene parcell of the maynelande, or at the least, some Ilandes standyng in the sea of long time agoe, although there bee no mention made of any suche Ilandes standyng in the seas, in those dayes. The cause thereof might be this: for that they that were of long time agoe, made no accoumpt of any small Ilandes, that were towardes our West Occian. For [Page 9] these west partes, in those dayes were scant peopled, as Ireland, and Englande, and Scotlande, and Brytayne, the west part of Fraunce. For it is no long time agoe, that Irelande hath beene throughly well peopled, although it bee a long time agoe, since the fyrst entraunce of Brute, yet it was long since the Incarnation of Christ, before that this Countrye became throughly peopled, as it dooth appeare both by the Chronicles, and other ancient hystories.
And also in those dayes,Nauigation not much vsed in the West Occian. Nauigation was not so much vsed in these our West Occian Seas, for the Sea was litle vsed in these our partes, except it were by small Botes, to goe a fishing, and to transport people from place to place, as wee doo see by experience. Yet in these dayes, those that doo inhabit, and dwell vppon the Coast of Afryca, to the West Occian, doo occupye no shypping vnto the Sea, except small Cannoses, to goe on fishing, and such other lyke, as al Barbary and Ginny, which were countryes well people before these Northwest parts were peopled as it dooth appeare by Histories.
And furthermore, in the olde time, those people that were the dwellers in these Northwest partes, were very simple and ignoraunt, as touchyng the drawing of Plats and Cardes, whether they were Cardes Geography, or Hidrographie. &c. Although that Pitholomias made Tables, as touching the description of the Countries, yet hee dyd not manyfestly or plainly shew the Ilandes in the sea, not to this west Occian, as they bee now well knowne. And furthermore, it is but a very short time agoe since that Englishe menne did muche occupie the sea, to trauaile on long voiages, neyther dyd fewe or none know or vnderstande the vse of their Sea plats, called Cardes Hydrography, for within these three score or foure score yeares, it hath been thought a great long voiage, for to goe into Spayre, and then when they dyd go into Spayne,Now Englishmen are as suff [...]tient to trauaile a long voyage, as any other nation. they went al alongst by the coast of France, and so to the coast of Byskey. &c.
But thankes be vnto God, now in these dayes, Englishmen are as sufficient to trauaile in long voiages, as any other nations [Page] be. But now to returne to our former matter, as concerning the causes of Rocks in the sea, and as I haue sayde before, that the Rocks haue beene parcell of the mayne lande, or els some Ilande long agone, & by the often soussing of the bellowes or waues of the Sea, that neuer standeth styll, the other substaunce or stuffe is beaten and consumed away, through the great deepenesse of the sea: the other substaunce or stuffe is tumbled to the bottome, and is no more seene. And as the mynerals in the ground be of diuers kinds of substaunces, as some earth, and some sande, and some stones: to conclude, of a hundred seuerall sortes, so that all those loose substaunces, that woulde be mollysted with the water, are beaten and washed away, so that there dooth remayne nothing but the harde myne of stone: and so he dooth stande in the sea, as a pynacle or Rock,The cause of Rocks in the Sea. as by experience is seene in a number of places to the west Occian, as the West part of Englande, and the West part of Brittayne on the Coast of Fraunce, and such other lyke places, whereas there be innumerable companyes of Rocks, some being of a gret height aboue the water, other some do shew thēselues iust with the water, and other some are sunken Rockes being rounded with the water, some deeper then other some, which would not bee knowne, but onely by the breaking of the sea ouer them. &c.
And this is my opinion as concerning Rocks in the sea, that haue beene of long time agone parcell of the mayne lande, though they be now Rockes in the sea. Then it may be sayde, that the lande is much lesser then it hath beene before time, and so it is. And yet it is but a trifle in respect of any great quantytie or bignes, as it may be compared vnto the ragged edges of a peece of cloth, and yet the ragged edges thereof being pared away, the thing hath not much chaunged his fashion or forme, neither in respect is become litle the worse. &c.
The syxt Chapter sheweth the naturall cause of the ebbing and flowing of the Sea, and the ebbyng and the flowing of the Hauens and Ryuers.
AND furthermore, as concerning the ebbing and flowing of the sea and other riuers, we do see by common experience, that the Moone dooth alwayes gouerne the same. Wherefore it may bee supposed, that the waters doo seeke and repaire,The waters are drawne by the power of the Moone. or most speciallye are drawne by the power of the Moone, that when the Moone is in the midst of the skie, that is to say, vpon the Meridian, then the waters are deepest or thickest, and also in lyke manner, in the opposite part, or els it would ebbe and flow but once in .24. houres and 4/ [...]. partes, accordyng vnto the dayly motion of the Moone, which we do se by experiēce, that it doth ebbe & flow but once in 12. houres & ⅖. part of an houre, and then by this reason it shoulde flow or be a full sea in all places at a South Moone, and a North Moone: & so as the Moone passeth vnto the Westwardes to be a ful sea in those partes, and so to goe with the diurnall or dayly motion of the heauens, which we see by experience is contrary, for we doo see by dayly experyence, that vpon the Coast of Spayne, and all those partes that are vpon the West Occian Seas, that the Moone in the Southwest dooth make a full sea, which is 3. houres after the Moone is vppon the Meridian: and yet notwithstanding it woulde bee a full sea alwayes where as the Moone is vpon their Meridian, and so to folow the daily motiō of the moone, as the moone is caried with primū Mobile: so that it were not let by this gret accidēce that this [Page] West Occian Sea, is shot in betweene the firme lande of Ameryca, on the West part, and the mayne lande of Afryca, and Europe, on the East side, by which meanes the waters cannot folow to bee a full Sea, accordyng vnto the Moones course, as she doth goe in her dayly motion, accordyng vnto the Moones commyng vnto the Meridian.
Wherefore it is to bee supposed, that yf there were no suche accidence in the Sea, to be let by the lande, that then it would follow orderly, that the waters in the Sea woulde goe rounde, accordyng vnto the Moones course in .24. houres, and so the streme or currant, to goe from the East into the West, and so rounde about. &c.
But nowe wee see that the waters, in the ebbing and flowyng, are let by this great impediment: for Ameryca dooth inclose the West part,The Moone doth gouerne the ebbing and flowing of the water, in two great and notable causes. and Europe and Afryca the East part, and yet we doo see by experience, that the Moone dooth gouerne the ebbyng & the flowyng of the waters of the Sea in two great and notable respectes. The one is this, as it is daylye seene in euery place, wheras it dooth ebbe and flow, that the Moone in one quarter of the Skye dooth make a full sea for euer, in that place, or hauen, or harborow. And the other great effect of the Moone is this: as it is alwayes seene, that at the full of the Moone, and also at the chaunge of the Moone, how that the waters are quickened, and doo rayse or lyft them selues muche higher then they doo at any other times, and also dooth descend much lower, where by it maketh the tyde or streme to runne much the swifter, as it is seene by dayly experience, in such places whereas it dooth ebbe & flow, at which times it is called in the time of the full Moone, and the chaunge of the Moone, spring tydes, or spring stremes: & in the quarters of the Moone, it is called Nepe tydes, or Nepe stremes, for that the waters doo not lyft them selues, or flowe so high as they doo at any other time, neyther doo they descende, or ebbe so low, as they doo at any other times of the Moone, and by that meanes the streme doth not runne so swift as it doth at other times, for as in spring tydes it dooth flowe or lift it selfe higher, and descende or ebbe lower, then of custome.
[Page 11]So in neape Tides it doth lift or flow lesse in height, & also ebbe or descende lesse in deepenesse, then it dooth of custome, as it is seene dayly by common experience. &c.
But yet furthermore,The var [...]etie of being a full sea in one Ryuer. as touching the ebbyng and flowing of the water, both in the Sea, and also in Hauens and Ryuers, and although that it dooth keepe an order or methode in anye one assigned place, yet is there great varietye in places harde by: yea in one Ryuer, it shalbe a full Sea in one parte of the Ryuer, and in that Ryuer, and at that instant, a lowe water, as the proofe thereof maye be manyfestly seene here in the Ryuer of Thames, as it is not vnknowen, that the Moone in the South dooth make a full Sea on the landes end, at the entraunce of the Ryuer of Thames, and the Moone in the Southwest, dooth make a full Sea at London, and then it is halfe ebbed on the landes ende: But in Rychmonde aboue London, there the Moone in the West, dooth make a ful Sea, and then on the landes end, there it is a lowe water, as it is manifestly to be seene. &c.
And furthermore, as touching the ebbyng and flowyng vpppon the Coast of the Occient Sea, for that it floweth generally a Southwest Moone, so mine opinion is this,A ful sea and a lowe water act at one instant in the Ryuer of Thames. by the meanes of the shuttyng or inclosyng of the Sea betweene America, and Europe, and Africa, that it commeth to passe thus, for the water cannot followe the course of the Moone, for after that the Moone is past the Meridian in the Bay of America, commonly called the Bay of Mexico, that then the waters can no longer followe the course of the Moone, for that it is letten by the mayne lande. And then when the Moone dooth come rounde about, vnto the Southeast, then the powers of the Moone doo tracte or draw the waters vnto the Eastwardes, by whiche meanes the waters hauing a great course or swaye vnto the Eastwardes, are drawen so vehementlye by the powers of the Moone, vntyll suche tyme, as the Moone dooth come vnto the Meridian, that it cannot sodaynely reuerse, although the Moone bee paste the Meridian to the Westwarde, as we maye see manye tymes by common experience, that any thing forced to moue violentlye, is [Page] not presently stayed, but that it must haue a tyme in the staying, as the force of the dryfte dooth decay, which must be by litle and litle. &c. And so by that meanes the Mone is in the Southwest before the waters wylbe descended: and for proofe thereof, if that you doo put water in any broade or long vessell, and sturre the water in such sort,The cause of the ebbing & flowing in Hauens, and Riuers. that it may swaye from one ende vnto the other, and after that it hath begunne to sway from ende vnto end, it wyll be a long tyme before it wyll stande styll: for you cannot make it to staye vppon the sodayne, but it wyll sway too and fro, vntil that it dooth stay it selfe by litle and litle. &c.
And furthermore, as touching the ebbyng and flowyng in the other inferior Seas, and Hauens, and Ryuers, that happeneth by this meanes, as it is a full Sea in all the places vppon the West parte towardes the Occian Sea, so that when it door finde the water of our inferior Sea, lower then that which dooth come out of the Occian Sea, then it runneth in vntil that it commeth to be leuel. For the propertie of water is alwayes to runne vnto the lower partes, and so by that meanes, and also the sway that it hath, it runneth and floweth into al Hauens, and Harbours, and Riuers, as long as it fyndeth any place lower or inferior in hight vnto it selfe. And then as soone as it fyndeth the water behynde it, lower then it is before it, then it stayeth, and beginneth to runne backe agayne, for as is sayde before, the propertie of waters is alwayes to runne to the lower partes: and by this meanes it floweth into al ryuers, Hauens, and Crickes vppon the Sea coast, and in some place it dooth hygher flowe more water vpryght,The c [...] that the water doth rise and flowe higher in one place then it doth in another and dooth ebbe more water in lyke manner downe right, then that it dooth in some other places, and that happeneth by this meanes, and if any place haue a wyde enterance, and then afterwardes is shut vp into a narow roume, hauing some distance to reuerse backe agayne, then the water dooth ryse and flowe very hygh, for that th [...] water commeth in with a great sway, and will not vppon the sodayne reuerse backe agayne, as by ensample it may be seen in Seuern, that commeth vp to Bristow and as before is sayde by the Ryuer of Thames, that it is not a ful Sea in all [Page 12] places at one instant. For when that it is entred in at the mouth, and hath taken his sway withal, then it runneth in by the meanes that the water is lower within, then it is with out at the Sea, for that it is a quarter flood, and more at the Sea, before that the flood entreth into the Ryuer, and so floweth vpwardes, for it must haue a tyme, before that it can hygh so much water at the mouth or enterance to be hygher then it is within vp into the Ryuer: for it is three parts flood vpon the landes end, before that it be anye flood at London, for that the distance is a great way in, & the Ryuer very crooked and narrow, and many poynts, and Naases that doo let and stay the Tyde, but afterwardes, when it is in, and hath taken his sway, then it cannot so soone reuerse backe, vntyll that the water is well descended or ebbed behynde it too the Seawardes, as it dooth manifestly appeare by experience. And by this order it floweth into all Hauens and Ryuers, accordyng vnto the indraught.
The seuenth Chapter sheweth the cause of Currantes or streames, that runneth in the Sea, in such places, where it dooth not ebbe, and flowe, and of Currantes or streames in the Sea, there are three seuerall sortes, as in the Chapter it dooth appeare. &c.
AND furthermore, as touchyng the Currantes, or the streame in many places in the Sea, whereas it dooth not ebbe and flowe, as that is perceyued in manye places, as by experience is seene and knowen in the Sea. And to let you vnderstande what those Currantes or Strames bee, that it is a continuall runnyng of the water in the Sea alwayes [Page] one way, and not reuersyng or commyng backe wardes to and fro, as it dooth in such places where it doth ebbe and flow, but that the water alwayes in those Seas or partes doth [...]unne continually one waye,3. sortes of Currātes. or els at the least a long tyme, according vnto the naturall cause of that currant. And of these currantes I doo fynde three seuerall sortes, that doo come of three seuerall causes, and the cause of euery one of them is contrary vnto the nature of the other.
And fyrst concerning the naturall cause of the principallest Currantes, as by experience of them is seene in diuers places, by those that haue trauayled into those partes by the Sea, as thus: The currant rūneth forceably, and continually from the East vnto the West,The principall and chiefe Currant of the sea. at the Cappe bone speraunce, the Southermost Cappe of Africa, or Ethiopia, and so reboundeth vpon the Coast of America, which is drawen by the powers of the Moone by ber dayly motion, as in the Chapter next before is rehearsed, as it dooth appeare by the ensample of ebbyng and flowing, and so rebounding vppon the Coast of America, by that impediment, that it cannot get passage that way, accordyng vnto the dayly motion, then it is forced to seeke other passages, so that parte thereof dooth seeke, and dooth goe thorowe the strayghtes of Magelen [...]s into the South Sea, and there the currant dooth go continually from the East, into the West. But that strayght or passage beyng vnsufficient, for that it is so narrowe, the currant is forced to seeke some other waye. Wherefore partly it dooth deuide it selfe, and so dooth runne vp vnto the Coaste of Brasyll, towardes the Equinoctiall by Cappe Crucis, and Saint D [...] myngs,The reuersing backe of the currant. and so into the great Bay of Amerrica or Bay of Mexico, and so reuerseth backe agayne, and so thorowe the Cannel or Chanell of Bayhaina, between the Cappe of Terra Florriday, & the great Ilande of Coba, goyng from the West into the East, which is the cause that those that doo go into the West Indies, doo fyrst goe to the Cannaries, and so to the Westwardes, to the intent to haue the currant to the Westwardes, into the Bay of Mexico, and then when they doo returne home, then they doo [Page 13] go by the North part of the Bay of Mexico through the chanel of Baphamea, for that the currant dooth reuerse backe from the West into the East, so that they haue the currant or streame to help them backe home agayne. &c. And thē in lyke maner, partlye the currant that commeth about Cape bone sperance, being beaten by the mayne lande of America, as is sayde before, part runneth or goeth thorowe the strayght of Magalenus, and partly thorowe the great Golfe or Bay of Mexico, as before is rehearsed, and part dooth reuerse or goe backe alongest the coast of the South land that lyeth on the South side of the straightes of Magalenus, where the South pole or pole Anterticke is raysed more thē .50. degrees, and so goeth backe from the West into the East, alongest the South Coast, vntyl it dooth come into the East Occian sea agayne. &c.
And this is the principallest currant,The seconde sort of currants or streames. as those that doo occupie those partes by sea, doo knowe, and these currantes are wel knowen to runne continually alwayes one way. &c. The seconde sort of currantes or streames, is this, as it is seene in dyuers places, that they shall haue a currant or streame, where it dooth not ebbe & flow, that alwayes doth goe vnto the windewards. But that neuer happeneth but in the tyme of great wind, and the cause thereof is this, that the sea beyng wrought or troubled with great stormes of wynd, dooth rayse great bellowes or waues, or great knottes in the sea, and that runneth rollyng with the wynde, and dooth cause the water too bee vnleuell or vneuen, as it is the nature of water to seeke to the lower partes tyll that it doth come vnto his leuel:The cause that it doth not ebbe and flowe in some seas. so by that meanes as the wind beareth the water in the sea, with great waues or bellowes, so the currant in the water dooth goe agaynst the wynd, to come vnto his leuel againe: as the experience thereof is seene in dyuers places, where it dooth not ebbe and flowe, as in the myddle earth sea, or leuant seas, and within the Soūd, that is to say, within Elson Nore that hath narrowe enterances, and yet is great seas within, which dooth take away the effect of ebbing and flowing, for that the straight is not sufficient to let in water ye [...]ugh, for to cause it too ebbe and [Page] flowe. And this effecte in lyke manner is many tymes seene, sometyme on the coast of Barbary, and in such other lyke places, where it dooth not ebbe and flowe. &c.The thirde sort of streames or currantes. The thirde sort of currants or streames that runneth in the Sea, where it dooth not ebbe and flowe, as by experience is seene in diuers places, is caused by the sailyng into the Sea of some great and myghty Ryuer, that the lande water commyng forceably downe the Ryuer, and so emptyeth or runneth into the Sea, dooth cause a currant to goe in the sea, agaynst the mouth of the Ryuer, as it is seene in the middle earth Sea, agaynst the mouth of Nilus, and also it is many tymes seene in the North partes, at the spryng of the yeare, when the Snowe and the Ise is melted or consumed into water. And then agaynst the mouthes of such Ryuers, as doo emptye them into those seas, dooth cause a great currant to runne a great distance from the lande, in such places as this effect happeneth in those seas. &c.
The eyght Chapter sheweth the cause that the waters of the Sea are salt, &c.
AND furthermore, as touchyng the naturall cause that the water of the Sea is salt, whereas the opinion of some Authors is, as Aristotle, & other, that it is made salte by the powers of the Sunne, by the drawing of the fyne substance of the water, vp into the ayre, the Sea is made salt by that meanes. Then if that were the whole cause, thē the water of the Sea shoulde be most saltest vnder, or neare the Equinoctiall. For that the Sunne hath a greater force by the meanes of the direction of the shadow of the Sunne, whereby the [Page 14] Sunne shoulde drawe or distil it more faster, then it dooth in any of the other Clymates.
Yet notwithstandyng, it is seene by experience, that the water of the Sea is as salte in the Latitude of .60. degrees,The sea is salt very farre to ye Fro [...]th partes. in the Occian Sea, as it is vnder the Equinoctiall. And as some haue sayde, it is as salte in Iselande, and at the North Cappe, which is within the Polle or Cyrcle, neare fyue degrees. And there the Sunne cannot haue any great power, for that the Sunne hath but a very glaunsyng shadowe in Iune. And in the Wynter part of the yeare, the Sunne wyll not appeare or ryse vnto them, in the space of tenne Weekes.
And furthermore, if the water of the sea were made salte onely by the powers of the Sunne, then those seas must needes become freshe, by another great cause, and that is this: For in the Spring of the yeare, in the meltyng of the Snowe and the Ise, there falleth such abundance of freshe water, that it would make it freshe, and yet the water is verye salt, insomuch that in dyuers places in the North parte, they doo make salt of the sea water, although that it is not made by the heate or powers of the Sunne, as it is made in Spayne and in Fraunce, for that they doo make it in Scotlande with the heate of the fyre,Salt is made of the sea water in Scotland & in Rosey. & so as some haue sayde, it is made in Rosey, not farre from Sainct Nicolas. And furthermore, as it may be prooued, the water is not made salt by the power of the Sunne, for that the heade of the great Ryuer Nylus that commeth from the Mountaynes of the Moone, & hath Latitude beyond the Equinoctial twelue degrees: And so in sundry places, standeth in sundry great pooles,Fresh water in seas or pooles vnder the Equinoctiall. not farre from the Equinoctial, and so passeth from vnder the Equinoctiall, vnto the Northwards, and dooth empty it selfe in the middle earth sea: and yet that water is fresh, and not salt. So that it is manifest that the powers of the Sun, are not altogether the cause that the water of the sea is salt. Wherfore in mine opinion, the water of the sea is become salt by the Minerals or substance of the nature of the ground, which is salt properly of it self, and so mollified or soked, that it turneth vnto water, hauing anye moysture or lyquor to come vnto it.
[Page]As for an ensample, that in sundrie places, it is knowen that there is Salt found and dygged out of the ground, and is perfect Salt, and occupied for Salt, after they haue made it cleane, and beate it smal. And as it hath been credybly reported vnto me, there is a hyll or Mountayne in Barbary in Africa,Salt mines. that Salt is digged out thereof, and is a great distance from the sea. And the like is reported to be in the kingdōe of Hungary, here in Europ, that there is salt digged out thereof, and is solde and bought into dyuers places, as into Polonia, and into some places of Germanye.
The sea made salt, by the substance of the grounde.Then it is a playne case, that there be such wynes or mineralles in the grounde, which maketh the thyng to be most manifest, that the Sea is made Salt by the mineralles or substance of salt in the grounde.
And yet for further proofe therof, here in England, at the Wyches in Chesseshyre, there is in sundrye places, a water or Bryne that they doo make Salt of, and is a good distance from any Sea. And some haue made argument, that it may come from the Sea, thorowe the Vaynes or Coues in the grounde, which is moste contrarye, by thys meanes: for if that it come from the Sea, thorowe the grounde, then it coulde not be salter then the water of the Sea, for that at the Wyches, is much salter then the Sea water. For if that it come from the Sea, then it must be somewhat fresher then the Sea water, by the meanes of the scouring it selfe thorowe the earth, and by meeting of some fresh waters, as the earth is not without fresh water. &c.
And furthermore, as concernyng the saying of the Philosopher Plato, in his Dialogues of Tymeus, and Crecia, and also is written by Marcellius Ficius, that in the olde time, there was an Ilande in the Sea, ouer agaynst Africa, bygger then Africa and Asia, which Ilande was called Atlantyda, and that the Kynges of this Ilande did gouerne a great parte of Africa and Europa, and as Marcellius Ficius, and Plato say, by the meanes of a great earthqake, and a great rayne, thys Ilande sunke, and the people thereof were drowned: and after the sinkyng of thys [Page 15] great Ilande, the Sea Atlanticus was so full of mudde by the meanes of the sinckng therof, that the sea Atlanticus could not be sayled with shippes in a great time after. Now if this be true,Of the great Ilande called Atlantica that sunke. that there was any such Ilande, that dyd so sincke, & that the Sea was so full of mudde, then after that the mudde is setled vnto the bottome, as it wyll doo in processe of time, then the sea must needs be a very shallow sea, for such a great masse of earthy substance being sunck with water, must needes make a very shallow Sea: and yet it is seene and knowen almost generallye vnto all mē, that it is a depe sea, yea no man can tel of what depth, for that they cannot finde any grounde: for that sea is greatlye occupied with Shippes, and that Ilande lay [...]ast from Spayne and Barbary, which is most occupyed with Ships, of any sea: for all the great trade of shipping is now in these daies vsed out of Europe. And then what place can be greater occupied, then into our west Occian sea, called in olde time, the sea Atlanticus, as it is the whole trade from Englande, Fraunce, and the lowe Countrey, and Denmarke, and such lyke places of Europe, into Spayne, and Portugall, and Barbary, and into the myddle earth Sea, and into Ginny, and into the Carnarie Ilandes, the Madera Ilandes, and the Ilandes called the Syrtes, and to the West Indyes: so that it is the greatest occupyed sea with shipping in the whole world: so that the same sea is not vnknowne, but that it is a great deepe sea: therefore it is to bee supposed, that the fundamentall nature or stubstaunce, or ground therof was of Salt, and so soked or moyllfied with the water, that the superficies thereof might be sunck vnder the water, and so in processe of time to soke the minerall of the Salt, that the stony and earthye substaunce is nowe setled downe so low, that it seemeth vnto the simple people, that it hath no bottome: for otherwise such a huge masse of earthy substaunce coulde not be so lost, as it dooth appeare by that great Iland called Atlantida, that Maccellius Ficius, Plato, and Proclus, with other Authors, doth make mention of. &c.
The nienth Chapter is as touching the cause of Earthquakes.
AND furthermore, as touchyng Earthquakes, and the synking both of the mayne Lande, and also of Ilandes in the Sea, and also of the drying vp of Waters, as great Pooles & Riuers, and also of the casting vp of Grounde both in the sea, as well as vppon the mayne Lande, although it bee the prouidence of almyghtye God, to bryng it so to passe, for the punishment of the people,Whē god doth plague the earth, he dooth punish both good & bad. that are vppon the face of the Earthe: and as well the godlye doo perishe, as the wicked, when these thinges happen, whiche are the scourge of the wrathe of God, for that hee wyll haue his diuine glory knowne: yet hee dooth nothing but that it is done by a meane, & hath a naturall cause of the commyng of it so to passe, although the thing it selfe bee supernaturall.
And furthermore, although I am symple and vtterly vnlearned, neyther to the iudgement of the people to haue any great experyence in these causes, yet notwithstandyng being as one more bolde then wyse, to shewe myne opynion vnto the Worlde, and also it is possible that in some poyntes my opynion dooth not agree with some of the ancient Writers, that haue written of sundry thinges in their Bookes of naturall Philosophye. Yet notwithstandyng I am so bolde to shewe my opinion, although it be possible that it may dyffer from the trueth. Wherefore they may vse such credit vnto the matter, as the reasons in these matters shall support vnto them, for yf that by reason my opinyon be not to bee lyked, then they may the lesse regarde it. &c.
[Page 16]And this first, as concerning the sincking of grounde as experience hath shewed, that it hath happened in sundry places, and in sundrye ages of the worlde, my opinion is this, as in the Chapter before is shewed, that in those places that it hath happened, that the substaunce of the grounde in that place is Salte vnderneath,The cause of the sinking [...] the grounde. and so beyng soked or mollyfyed with water, in processe of tyme, it is turned vnto water, and then the earthy substance that is a loofe vppon it beyng ponderous and heauie, and not supported or borne vp wyth any harde thing, then it must needes settell it selfe downe and sincke into the water: and so by that meanes the water standeth aboue the superfycies thereof, as it is shewed in the Chapter goyng before, by the sincking of the great Iland called Atlantyda, &c.
And furthermore, as concerning some kinde of earthquakes, that happeneth in such sort that it renteth and lyfteth and shaketh the grounde, and possible lyfteth the grounde hygher then that it was before, and so remayneth and standeth styll afterwardes, wyth out any setling afterwardes. &c.
My opinion is this, by the meanes before rehearsed,Of Earthquakes. that there may be some vaynes in the grounde that may be of the substance of salt, as before is rehearsed, and yet may be inclosed with other mynes rounde about it, as we may see by experience, howe often that the vaines of the ground may alter, and in a smal circuite, as in some place may be hard stone, and in another place chalke, and in another place, claye, or sande, or the oure of diuers kyndes of mettalles, with a number of sundry sortes of substances that I doo emyt. &c. Now this myne or substance of salt being inclosed round aboute with other substances or stuffe, as before is sayde,Water cannot d [...]part from any place, vntil the ayre, or some other substance doth occupy the rounde and the springes of water in the grounde comming vnto it, both soke it & molifyeth it, that it is turned vnto water: & then being water it is apt to runne in the vaynes of the ground, & yet it can not depart to go from that place, vntyl that it doth draw ayre thither. And looke as the aire doth fynd [...]ent thorow the powers in the ground, & doth repaire vnto that place, so the water doth decrease & rūneth in the vaines of the groūd vnto other places: & thus in proces of tyme the substāce of salt being turned vnto water, shalbe diminished or gon [Page] and the roome thereof fylled full of ayre, and yet the grounde aloft shall stande fyrme and fast, for that it is borne vp or supported by rocky or stony substaunce. &c.
Now it is possible, that some will make argument, and say, how shoulde ayre come thither, for that it is so low in the ground, and that there is no place open vnto the ayre, wherby it may come thyther? But they doo not consyder this, that no place can bee vacant, but that it is furnished with somwhat, either with earthy substance, or water, or ayre, or Fyre, & euery one of thē is finer in substaunce then the other, as the earthy substance is grosse and harde, so the watry substaunce is thinner, and yet ponderous and heauy: so that there can be no place hollow or concaue in the earth, but it is filled with water or ayre. For the water by his ponderousnes dooth descend and seeke to the lower parts. And then looke where as the water is not sufficient to fyll the hollow place, then ayre dooth repayre thyther to fulfyll the rest, takyng his place next aboue hym, as we may see by experyence, that if wee doo dygge in the grounde, wee shall meete with Sprynges of water: as by the ensample of the digging of Wels in the grounde, that when they haue dygged so low, and haue founde but a small spryng, then letting it stande a certayne time, thither wyl repayre a great quā titie of Water afterwardes. And then this being true, that the water dooth fynde passage through the vaynes in the grounde, then it is a playne case, that ayre must the rather fynde passage, for that it is an Element more thinner and subtyller then water, and wyll soke through any small thing sooner. For the nature of ayre is to descende very deepe into the earth, if it bee not fylled with other substaunces. So in lyke manner water, although it be ponderous and heauy, wyll ascende vpwardes, yf the ayre cannot come thyther by the meanes of the closenesse or thightnesse of the thing that the water is inclosed aloft or ouer it, and also the water wyll not descende or fall downe sodaynlye, although the ayre be vnder it being inclosed in it, that the water by his [...]underousnesse or waight, dooth cause the ayre to seeke through the water, which wyll be a long time, except the water and the ayre bee [Page] be styred by some accidentall cause.
And now to returne to the cause of Earthquakes,The cause of Earthquakes. my simple opinion is this. The ayre being inclosed in the bowels of the earth, which hath happened by the meanes before rehearsed, or by diuers other meanes, which I am not able to rehearse, that the ayre may bee inclosed in the grounde or earth, and then when it shal please almighty God to bring it so to passe, for God is the worker of all thinges, either by one meane or another, that the waters may arise and encrease in the grounde, and especially after any great and continuall rayne, and the water being ponderous and heauy, dooth seeke into the earth, expelling or thrusting out the ayre that is neare the superficiall part of the earth, and so by his ponderousnesse setleth it selfe lower and lower, and then the great and continuall rayne dooth lode the superficiall face of the earth with water, and dooth cause the earth to swel and shutte it selfe close aloft on the vpper part of the earth, and that water in the earth, by setlyng it selfe lower and lower, and the earth by his closenesse wyll not suffer the ayre to depart out of the earth, so that there is no roome in the earth to holde or contayne both the Ayre and the water, but that the ayre in the earth is forced to rent the earth to haue roome sufficient. And also at that time the earth is more apter to seperate it selfe, then it is at any other time, for that the earth is soked and made soft by the great moysture that is in it.
And by this meanes, in such places whereas this cause dooth happen that the grounde dooth quake and tremble,Of the shaking of the earth. and the buildings that are neare thereabout, vntill such time as the ayre doth fynde passage to get out of the ground, and if that it cannot fynde passage, then it dooth split and rent the grounde, casting al things that are ouer it, or in the way of the ayre, that breaketh so out of the ground ouer it, and possible to turne the buildings vnderneath the earth or grounde to the great and maruaylous destruction both of the people and buildinges where this happeneth. &c.
And by this meanes those places, that haue beene Lande, may become Water, being neare vnto the Sea or any great Ryuer.
[Page]And in lyke manner whereas there haue bene any Pooles or Ryuers may be dryed vp, as cleane as though there had neuer beene any Poole, or Ryuer, or water there, by this meanes: for after that the ayre in the earth hath rent the earth to seeke passage out, then this thing happening there or neare vnto the water, may run or descende into that place wheras the ayre was before, and also in the turning vp or splitting of the grounde, there may bee some hilles or cliffes standyng vp much higher then the grounde was before. And so by this meanes the places that haue bene dry land, may become sea and water, and in lyke manner that place that hath beene water, may become dry lande. &c.
And furthermore, in lyke manner there may by this meanes before rehearsed, be Ilandes cast vp in the sea, by the meanes of the ayre breaking out of the earth. &c. for that is the propertie of ayre, to runne and to seeke into all places, that is not occupied or furnished with some of the elementall substances, so that rather then any hollow or concaue place in the earth shall bee vacant, ayre wyll seeke thither, if it were in the very Center of the earth. For as is sayde before, if water bee able to seeke passage through the vaines in the earth, then much rather the ayre shall doo it, for that it is much thinner, & subtiller then water, although that ayre wyll geue place vnto water, by his ponderousnes or waight. &c.
The tenth Chapter sheweth the reason, howe America, and all the Ilandes and newe found Countries, and Lands, became peopled, and of what posteritie they be come of. &c.
AND furthermore, as touchinge the vaine argumentes and opinions of some people, as touching the discouering of a number of Landes and Ilandes, that haue not beene founde nor knowne but within litle more then .100. yeares, as all America, and a number of Countries, and great and small Ilandes more, & none of them of any quantitie or bignesse, for that they are peopled: and for that they are peopled, I haue harde some vayne and foolish arguments therof, why there shoulde be people there, for that these Countries or places were neuer knowen before, except there were any more Adams then one, or any more [...]oyes thē one. So we may see by experience, how apt a nūber of people are to fal into errours, vsyng most vayne and contentious argumentes in those matters that are past their capacitie, whiche is a great offence before God, and also to the eui [...]l Ensample vnto the world, vnto such as doo heare of the same. For it is no smal errour for vs to fal into, for to think that there was an [...]more Adams in the world then one, for that it is vtterly against all the Canonycall Scriptures: and also it is as great an errour to say that there were saued any more people after the deluge or flood, more then N [...]y and his famyly, that was in the Arke with him, as it is manyfestly declared in Genesis. &c. Wherefore I thinke it not hurtfull to shewe my opinion as concerning how all America became peopled, with all the other new founde landes and Ilandes, lying in the sea, wheresoeuer they be. &c.
Fyrste thus my opinyon is, that America is parte of [Page] the great Ilande called Atlantida, as it is further declared in the eight Chapter goyng before,How all the new founde Countries became peopled, as all America, and all other Ilandes. that the Kinges of the Ilande dyd gouerne a great part of Europe and Africa, and accordyng vnto some Authors, that the Kings of that Ilande were the sonnes of Neptunus, then that dooth sygnifye that there was a trade or occupying of Shipping betweene these knowne partes and that great Ilande, and then when that great Ilande dyd synke, as before is declared, the Sea Atlanticus was so full of mudde,All the great Iland called Atlant [...]da, dyd not synk, but part remained. that it coulde not bee sayled in longe time afterwardes. And by the Ensample of America, that all the Ilande dyd not synke, but the Westermost parte dyd remayne still. Although this happened long beefore the commyng of Christ, and as before is declared, the great store of mud and fylth that dyd remayne in the Sea, was the onely cause that dyd let the Trafficke and passage betweene vs in these knowne partes, and them that were vnknowne vnto vs in all this long time of this mud remayning in the Sea: so long time, that those men that were the Sea men in those dayes, were of long time dead before the Sea was cleare of the mudde. And also those sea men,Olde sea men being gone, the other did neuer attempt to seeke any thing as it is to be gathered, that were in the Ilande, dyd perishe by the meanes of the sinking of the East syde of that great Ilande. Wherfore it is to be gathered, that those that were in these partes, dyd neuer attempt to seeke any Lande that wayes to the Westwardes, neither those that were remayning vpon that part of the Ilande that dyd not synke, dyd neuer attempt to seeke any Lande vnto the Eastwardes.
And in lyke manner, they could not so conueniently doo it, for that they had no Shipping to goe vnto the Sea, but small Boats called Cannouses, which be occupyed to no other purpose or vse, but onely to goe on fyshing, or els to transport themselues from Ilande vnto Ilande, neare vnto the mayne. &c. And yet it is possible that some people might passe out of these partes by shipping although they neuer made any returne agayne, but might tarry there, and inhabite in those parts.
And now insomuch that it is knowen, that they had boates, and dyd transport them selues from place vnto place, and from Iland [Page] vnto Iland, before the fynding of the mayne land of America. So it is not to be meruayled at, why al the Ilands in the sea, that are of any quantitie, haue people in them, considering that they had in al those partes, the vse of Boates from the beginning after Noy,The Indians had Boates asoone as we here in these partes. or what time we had Boates. &c. And nowe furthermore, as touching the great & fyrme land that lyeth to the Southe [...]wards beyond the Equinoctiall about .50. degrees, & is extended vnto the South partes, no man in these partes dooth knowe, and it is peopled too, and the people thereof may come out of America, for there is nothing to let them, but a narrowe [...]a, called the straight of Magalenus, and they hauing the vse of Boates, howe easily is it to be passed? So that there can be no I [...]and, lying in the sea, neare vnto America, that is of any bygnesse, but that it is peopled, whether it be to the Eastwardes towards vs, or to the West partes in the South Sea, or the East Ocean Sea. &c.
And furthermore, as it dooth appeare in the Scriptures, that Noy had three sonnes, that is to say, Sem, Ham, and Iaphet, and that Sem, the eldest sonne of Noye, dyd inhabite the partes of Africa, and Cham or Ham, the seconde sonne of Noy, dyd inhabite the partes of Asia: and Iaphet the youngest sonne of Noy, dyd inhabite Europe, and the Ilandes in the sea, as the great. Ilande Atlantida, nowe called America, and that the Kinges of that greate Ilande, were the sonnes of Neptunus, and the people, the posteritie of Iaphet, the youngest sonne of Noy. &c.
❧A Table of the Contentes of the Chapters of the fyfth and last booke called a Treasure for Trauaylers.
To the reader of the fifth and last booke.
The first Chapter of the fifth booke, sheweth the natural causes how sandes & bankes bee ingendred or made, hoth in the se [...] and riuers. &c.
The second Chapter sheweth the naturall causes of Marish ground, and other plaine meddows or ground by the sydes of ryuers, &c.
The third Chapter sheweth the natural cause of the high cliffes by the sea coasts. &c.
The fourth Chapter sheweth the natural cause, why the Beach, & the great bolder stones on the sea coasts is become roūd & smooth, without any edges or corners. &c.
The fyfth chapter sheweth the naturall causes of the rockes in the sea, &c.
The sixth Chapter sheweth the natural cause of the ebbing and flowing of the sea, and the ebbyng and flowing of hauens and riuers. &c.
The seuenth chapter sheweth the cause of currantes and streames that runne in the sea, in such places where it dooth not ebbe and flowe: & of currantes or streames in the sea, there are three seueral sortes, in the chapter it doth appeare &c.
The eight chapter sheweth the natural cause that the water in the Sea is salt. &c.
The ninth chapter is as touching the cause of earthquakes.
The tenth chapter sheweth the reason howe America, and all the Ilandes, and newe founde landes and countries, became peopled, and of what posteriritie that they be come of. &c.
Faultes escaped in printing.
| fol. | pa | ly [...]e. | faultes. | Correction. |
| 3 | 1 | 20 | set the | situate |
| 3 | 2 | 8 | marking | making |
| 3 | 2 | 24 | make | marke |
| 4 | 1 | 9 | of that, or | that are |
| 5 | 1 | 11 | for lyne | for the line |
| 5 | 1 | 12 | other side | [...]thelida. |
| 5 | 1 | 13 | ridge | ring |
| 5 | 1 | last | the heigth | 0 |
| 5 | 1 | last | measure of the | that measure |
| 7 | 1 | 12 | and the | and at the |
| 8 | 2 | 13 | standinges | places |
| 9 | 1 | 20 | as | is |
| 10 | 2 | 8 | lye | by |
| 12 | 1 | 11 | there | then |
| 12 | 1 | 20 | the line should | the line ye shoulde |
| 13 | 1 | 1 | there | though |
| 14 | 2 | 3 | thence | there |
| 14 | 2 | 23 | 12 | into 12. |
| 15 | 2 | 12 | 28 | 24 |
| 15 | 2 | 19 | 5 | 15 |
| 16 | 1 | 23 | lacke | looke |
| 17 | 1 | 1 | doo | mays |
| 17 | 2 | 4 | staffe | transuastorie |
| 18 | 2 | many | transytorie | transuastorie |
| 18 | 2 | many | ringes | wynges |
| 19 | 1 | many | transytorie | transuastorie |
| 20 | 1 | 32 | that | their |
| 22 | 2 | 16 | part | put |
| 27 | 2 | 22 | by | too |
| 28 | 1 | 7 | 52 | 32 |
| 29 | 2 | 10 | and halfe | of |
| 29 | 2 | 22 | the chapter | the .8. Chapter |
| fo. | pa. | line. | faultes. | Correction. |
| 1 | 1 | 22 | vnto | and vnto |
| 3 | 1 | 8 | 90 | 60 |
| 7 | 1 | 13 | Southwest | South Southwest |
| 9 | 1 | 10 | 32. put | put |
| 10 | 1 | 11 | 30. degr. 49. | 50. degrees .12. |
| 9 | 2 | 20 | [...]ondon | land |
| 11 | 1 | 2 | 54 | 16 |
| 12 | 1 | 13 | 36 | 360 |
| 13 | 1 | 30 | Eison More | [...]on Nore |
| 15 | 1 | 7 | Cappe hyll | Ape hyll |
| 15 | 1 | 13 | 18 | 25 |
| 15 | 1 | 15 | London | London .10. mi. |
| 15 | 1 | the longest day | the day .14. hours .35. mi. | |
| 15 | ||||
| 15 | 1 | minuts southeast | minuts, [...]nd is Southeast | |
| 24 | vnder the tropick of Cancer | |||
| 16 | 1 | 25 | 0 | |
| 19 | 1 | 11 | East and South | East & by south |
| 19 | 1 | 30 | 7 | 98 |
| 19 | 2 | 30 | Maria | in Aria |
| 21 | 2 | 11 | 25 | 52 |
| 22 | 1 | 33 | 20 | 4 |
| 22 | 2 | 2 | 12 | 4 |
| fo. | pa | line | faultes | Correction. |
| 3 | 1 | 28.29 | that that | that |
| 3 | 2 | 12 | of a boord | of boord |
| 5 | 1 | 2 | be corner | be from corner |
| 5 | 1 | 3 | 22 | 32 |
| 7 | 1 | 4 | leuel | beuel |
| 7 | 1 | 11 | leuel | beuel |
| 14 | 2 | 9 | with the | within the |
| 15 | 1 | 12 | 30 | 3. quarters |
| 15 | 1 | 19 | racking | raking |
| 15 | 1 | 32 | whole | holde |
| 16 | 2 | 15 | would haue | haue |
| 19 | 1 | 22 | 13. ynches | 10. ynches |
| fol. | pa. | lin. | faultes | Correction |
| 3 | 24 | as | is | |
| 4 | 1 | last | targed | karged |
| 5 | 1 | 27 | ma [...] | may |
| 7 | 1 | 30 | with | which |
| 7 | 1 | 53 | multiply by | multiply that by |
| 8 | 2 | 23 | in the mould of mettall | in the mould of wood. |
| 2 | 31 | |||
| 8 | 2 | 5 | led | raysed or highed |
| 11 | 1 | 1 | neare as | needes |
| 12 | 2 | 18 | 30. | 36. |
| 12 | 2 | 32 | waight the | waight that the |
| 12 | 1 | 23 | one kind | of one kynde |
| 14 | 2 | 6 | by the proportiō o [...] the | by proportiō, the |
| 17 | 1 | 19 | hang | chaunge |
| 18 | 1 | 22 | h [...]e [...] | hee [...]d |
| 18 | 1 | 3 | to hold | to heeld |
| 19 | 1 | 18 | collect | calke |
| 19 | 1 | [...] | in, | yenough |
| 19 | 1 | 24 | carying | carenyng |
| 19 | 2 | 30 | cartienes | Cap [...]tynes |
| fol. | pa. | lin. | faultes. | Correction |
| 5 | 2 | 6 | mould | mouth |
| 6 | 1 | 2 | so assynges | suff [...]ng [...]s |
| 8 | 1 | 8 | suites | sortes |
| 8 | 2 | 5 | su [...]f [...]nges | suff [...]nges |
| 8 | 2 | 22 | sea, it | sea, as it |
| 9 | 1 | 3 | Ireland | England |
| 9 | 2 | 4 | sou [...]inges | suffinges |
| 9 | 2 | 19 | rounded | couered |
| 11 | 1 | 15 | in | at |
| 13 | 1 | 6 | beaten | le [...]ten |
| 15 | 1 | 12 | wast | West |
| 6 | 2 | 3 | meayne | mayne |
| 11 | 1 | 30 | tra [...]t | attract |
| 11 | 26 | hygher | hygh or |
¶Imprinted at London for Thomas Woodcocke, dwelling in Paules Churchyarde, at the sygne of the blacke Beare. 1578.