A perfect and easie Trea­tise of the vse of the coelestiall Globe: written as well for an Intro­duction of such as bee yet vnskilfull in the studie of Astronomie: as the practise of our Countriemen, which bee exercised in the Art of Nauiga­tion. Compiled by Charles Turnbull: And set out with as much plain­nes as the Author could: to the end it might of e­uery man be vn­derstood.

Psalm. xix.
The heauens declare the glorie of God, and the fir­mament sheweth the worke of his handes. Day vnto day vttereth the same, and night vnto night teacheth knowledge.

Imprinted at London for Sy­mon Waterson.

INSIGNISSIMO VIRO, AC OMNI VIR­tutum genere clarissimo Magistro Henrico Nocllo, Carolus Turn­bullus salutem ac foelicita­tem perpetuam com­precatur.

CVM antiquissimorum scripto­rum singularem industriam in studijs Mathematicis iam an­te seriùs, accuratiúsque cogno­uerim: & recentium quorun­dam deprauatam lectionem summa cura, summáque diligentia viderim & obseruaue­rim: ne infestus error damnum inferret gra­uius: curaui (vir insignissime) ea faciliùs ex­plicare, quae si fideliter discantur, omnis er­roris tollent difficultatem. Eorum verò te pa­tronum esse volui, vt meo exemplo ad eadem vota multos inuitem, tanquam indicem te, in florentissimo hoc regno non solùm tanti nego­tij virum celeberrimum: sed omnium regia­rum virtutum laudúmque patronum. Ita­que [Page] minusculam opus hoc A [...], qualecunque sit, (quod scio quam sit indi­gnum) tibi dedico: vt qui imposterum non solum obseruationes astronomicas elaboratas magis, minúsque vsitatas: (siue sint theorica siue horalogica) sed opticas quoque & qua sunt geometriae communis praecepta, (vt tem­pus postulat) sis receptarus. Quibus vt es spi­ritus nobilissimi: ita mirificè quoque delecta­ris. Vnum hoc interim precibus etiam at­que etiam obsecrans: vt qua huma­nitate erga me semper vsus es. (cum maxime possis:) eadem iam indies confirmata magis (libertissime quoque velis patroci­nari.


To the Reader.

MEn which are more desirous of pu­blique Fame and Re­now ne, then studious of cōmon profit: with great curiositie set a glasse vpō such things, as being discoue­red, would shew dismēbred & mishapen. (As for my selfe I seeke no higher digni­tie, then to be reported to set forth a trueth: and therefore without any wre­sted cloquence, I make bold to offer the vse of the Globe, to the exquisite vewe of your curious eyes: (though farre in­feriour as I suspect to some mens expec­tation) to the end such grosse enormi­ties might bee amended, as often times in diuers haue bene discouered. Who for want of right conceat of things by them attempted: haue in the ayer built such fortresses, as haue without assalts woun­ded their louing enemies. But happely [Page] such men wil now retire, and arme them selues better against the next assault, lest they be like to the dogs in the capitall of Rome: which were placed to the end, that if by night spoylers should ariue, they might sound a warning. For, true it is, that by night these barke out false Allaromes at their enimies: but if by day, they barke likewise at friends: I hope ye wil iudge them worthy to haue their legs broken. which things I leaue to your gentle interpretation. Nothing misdoubting, but if in this tract either anything bee escaped contrarie to my will: or omitted not satisfying your ex­pectation: ye wil aequally suffer the same. For if ye receaue the fruites of my labor and care of your commoditie, I require no more. Wherefore my trauaile I bequeath to your discreet consideration, and your selues to the protection of almigh­tie God.


DEFINITIONS to be praemised neces­sarie for the vnderstan­ding of the Globe.

THe Sphaere or Globe, is a perfect round & sollide bodie, contai­ned vnder one su­perficies or face; in whose middle is a point, from which point all lines that are drawne to the superficies and face of the same: are aequall the one to the other.

The Center of the Sphaere, is the middle point of the same.

The Axe of the Sphaere, is a [Page] right line passing from one side of the same, (by his Center) to the contrary side, about which line the Sphaere is caried: but the line it self standeth still.

The Poles of the Sphere, be the endes of his Axe.

The Pole of any Circle, is a point without the compasse of the same: (and yet is aequally distant from all points, of the circuit or borders of the Circle whose Pole it is:) & from which the same Circle is drawne.

OF THE NAME of the Sphaere, and his di­uers and sundrie kindes of di­uisions: together with the motion of ech one in his kinde.

THE NAME OF the Sphaere, is taken either generally or particularly. Generally, and so it is said to con­taine all perfect round bodies, whether they be sollide or not: whether contained vnder one onely Superficies or moe. And so may euery Orbe be called a Sphaere. But if wee take the worde Sphaera, in his particular and proper signification: then nothing is a Sphaere: but a perfect round bodie being sollide, contained vnder one, &c. as the for­mer definition declared. This Sphaere is [Page] diuided either according to his substaunce: or according to certaine properties and af­fections which he is capable of.

According to his substance he is diui­ded into two parts: the one Elementall, the other Aethercall. The Elementall, con­taineth the fower Elements, Fire, Ayre, Water and Earth: and is subiect to altera­tions, by reason of their effectual working. The Aethercall, compasseth in round, the Elementall part, in his hollownesse, and is lightsome by nature, and vnchaungeable: and containeth ten Sphaeres. The first and highest from the earth, being called the first moueable, containeth in his hollownesse al the other: and by his natural motion is mo­ued directly from the East to the West, and so to East againe, in the space of 24. ho­wers continually, and carieth about with him by violence, al the other Sphaeres. The next vnder this is the ninth Sphaere, called the Christall heauen, and by his naturall motion is caried from West toward East, but very slowly, in many yeares passing but one degree: and this motion hath caused the Starres to alter their Lōgitudes. The third Sphaere is the Firmament or Sphaere [Page] of the fixed Starres: whose motion by na­ture is vpon two little Circles: the one be­ing described about the head of Aries, and the other of Libra: which motion is called the motion of Trepidation. The other sea­uen Sphaeres be of the seauen Planets: the highest of Saturne, which moueth by na­ture from West toward East, and that in 30. yeares one perfect reuolution. The next of Iupiter, moouing frō West to East by nature, and that in twelue yeares. The other of Mars, making his reuolutiō from West toward East in two yeares. Vnder Mars is the Sunne, moouing by nature from West toward East, making one per­fect reuolution in 365. daies and 6. howers almost. Vnder the Sunne is Venus, and then Mercurie, moouing from West to East about the same time as the Sunne. The last is the Moone, making one perfect reuolution from West toward East in 27. daies. 7. howers. 43′. 7″. yet all these are ca­ried by violence of the first moueable from East to West, as is before saide.

▪OF THE CIR­cles of the Sphaere of Heauen, and of their na­mes, and how they be made.

AStronomers to the end they might shewe the motions of Heauen, and the straūge and wonderful conclusions of the Coelestiall bodies: haue ima­gined certaine Circles in the bodie of the first Sphaere or first mooueable, and princi­pally ten: whereof some be greater Circles of the Sphaere, so called because the Center of these Circles is also the Center of Hea­uen: & euery such Circle diuideth the whole Sphaere into two aequall parts. Of this sort be sixe: the Aequinoctiall, Zodiack, Hori­zon, Meridian, and two Colures. Some bee lesser Circles of the Sphaere so called, because they haue not the Center of the world for their Center, neither diuide the whole Sphaere aequally. Of this kinde be fower, the Tropicke of Cancer, the Tro­picke of Capricorne, the Articke and An­tarticke.

The Aequinoctiall, called the aequator or girdle of Heauen, is a great Circle of the Sphaere, diuiding the Sphaere into two ae­qual parts, and is aequally distant from ech Pole of the worlde. And tooke his name of the aequator, either because it is aequally in the middle of Heauen, as Euclide saith in his Opticks: or for that the Sunne, com­ming to this Circle, maketh the day and night aequall. & it is diuided in 360. aequall parts, which parts are called degrees. His Axe is the Axe of the world, and Poles, the Poles of the world.

The Zodiack is a great Circle of the Sphaere, which crosseth the Aequinoctiall in two points, the one being the head of A­ries, the other of Libra, and swarneth from him in all other points, leaning toward ech Pole of the world in ye point of his greatest swarning, 23. degrees, 30. minutes. This Zodiack is of breadth 12. degrees, and of length, that is to say, in compas 360. de­grees, and according to his length, is di­uided into 12. aequal parts, which are called the 12. signes. Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sa­gittarius, Capricornus, Aquarius and [Page] Pisces. And ech signe contayneth of length 30. degrees. in the midle bredth of the Zo­diack, we imagine a Circle to passe, which we call the Ecliptick Circle or line: For that that when the Sunne and Moone bee both vnder this line in a Diameter: then the Moone is Eclipsed. Vnder this Circle the Sunne mooueth dayly (without decli­ning any waies) the quantity of one degree very neere in ech day. the rest of the Pla­nets are found some times on one side the Ecliptick, & some time on the other. This Zodiack taketh his name of a greeke word signifying a liuing creature: or as the La­tens will, is called Signifer, for that that it beareth the 12. Signes. the Axe of the Zo­diack and the Ecliptick, is all one, being a line diuers from the axe of the world, and the Poles bee two points alwayes so much distant from the Poles of the world: as the greatest declination of the Ecliptick com­meth vnto.

A Colure doth generally signifie any Circle passing by the Poles of the worlde, and hath his name of his vnperfect shewing himselfe in the motion of heauen. But now by the name of Colures, we vnderstād two [Page] great Circles, the one going frō the Poles of the worlde by the points where the Ae­quinoctiall and Zodiack cut them selues (which be called the Aequinoctiall points) and is called the Aequinoctiall Colure. The other passeth from the Poles of the worlde, by those points of the Ecliptick which swarue most of all others from the Aequinoctiall line (which points are called the Solsticiall points) and this is called the Solsticial Colure. And here be you to know that these foure greater Circles which we haue defined: be still the same through the whole worlde, and are sayd to be moueable Circles: for so much as in the motion of heauen, they be also mooued. of which, some are moueable perfectly: as the Aequinocti­all and Zodiack, (for they in the going a­bout of heauen, doe ascend by little and lit­tle, till the whole Circle haue gone oure the Horison) some vnperfectly moueable, as the two Colures, which neuer shewe the whole Circle in any crooked Sphaere. the other two greater Circles which followe, be called fixed, for that they neuer mooue by the motion of heauen. But they be change­able in euery Region.

The Horizon is a greater Circle diui­ding the halfe of the Heauen which we see, from the halfe which we see not, and is cal­led in Latine Finitor, because it endeth our sight. The Horizon maketh fower princi­pal points, East, West, North, and South. His Axe is a line imagined to fall from the point of heauen, which is directly ouer our head where we be, downe to the groūd like a plumme line, and his Poles be the endes of that line, called the Verticall point, and point opposite to the Verticall.

The Meridian is also a great Circle, passing from the Poles of the world by our Verticall point, cutting the Horizon in the North and South points his Axe is a line going from the East point of the Horizon to the West, and his Poles be the same points, and these two Circles doe alwayes chaunge, & are diuers in euery Region: for so much as the Verticall point of euery Re­gion is diuers, by the which the Meridian of necessitie must passe, and is the Pole al­so of the Horizon.

OF THE LESSER Circles of the Sphaere, and their names, and of their making.

THe lesse Circles of the Sphaere in number be fower. The Tro­picke of Cancer, the Tropicke of Capricorne, and the two Ar­tickes. The Tropicke of Cancer, is a lesse Circle of the Sphaere, which is aequally di­stant from the Aequinoctial, lying betwixt the Aequinoctiall and the North Pole, and touching the Ecliptick in the beginning of Cancer. This Circle is described by the bodie of the Sunne in the longest day of Summer, at which time the Sunne is en­tred the solstitiall point, or beginning of Cācer. & is called the Tropick, of a Greeke word, which signifieth a returning: because the Sunne being brought to this point, fal­leth in his noone height, and returneth a­gaine.

The Tropicke of Capricorne, is a like Circle betwixt the Aequator & the South pole, and is described by the Sunne in the shortest day of Winter, at which time the [Page] Sunne is in ye beginning of Capricorne, whereof it is called the Tropick of Capri­corne.

The Articke Circle is a lesse Circle of the Sphaere, described by the Northerne Pole of the Ecliptick. Proclus saith it is described by the formost foote of the great beare, and thereof taketh his name.

The Antarticke is a like Circle descri­bed by the South Pole of the Ecliptick, & is called Antartick of the Greeke worde, which signifieth Opposition, because it is opposite to the other.

Of the vse of the Circles of the Sphaere or Globle.

THE most principall cause why Arti­ficers inuented the Aequinoctiall, was first, because it is the measure of the first Heauen, by a conuenient, perpetu­al and aequal swiftnesse. Secondly, it mea­sureth and limitteth the time of rising of the Signes, as also the length of the Arti­ficial daies, and times of the Aequinoctials, with declinations and right ascentions of Starres, together with Longitudes of Re­gions. [Page] Lastly, for the exection of the twelue howsen of Heauen. In like maner, the Zo­diack serueth for Latitudes & Longitudes of Starres: for distinction of the times of the yeare: for the motions of all the Pla­ners and effects of the same. Not vnlike be the vses of the Colures and Meridian, ech shewing the greatest declination of the E­cliptick: but especially the Meridiā, which giueth as well al declinations of Starres, their noone height, and distinguisheth the daies and nights into two; aequal parts, and serueth for the Horizon of the right Sphaere. It beginneth likewise and endeth all Longitudes of Regions, and sheweth Latitudes and Eleuations of the Pole: It helpeth to diuide the 12. howsen. In like maner sundrie and diuers be the vses of the Horizon: As in seperating the hidden part of Heauen, from that which is seene, and sheweth the place of rising and setting of a­ny Starre: how farre from East or West, with his height. All which points are re­spected of Astronomers, as the Sphaere is secondarily diuided: that is to say, as he is a right, or a crooked Sphaere, which bee his properties and affections ment in the diui­sion [Page] afore specified. By a right Sphaere is ment such a kinde of position of Heauen: as that neither Pole bee r [...]ised aboue ground, but that ech lye in the face of the earth. And such a kinde of position haue they which dwell in Bersera, and the Islands of Mo­lucca, or such like. Contrariwise, it is sayd to bee a crooked Sphaere, when any one of the Poles is raised aboue ground. Such a Sphaere haue we at Oxford, and London: and generally all, which dwell not vnder the line. All which thinges for our better conceate, are shewed to the eye in the mate­riall Globe, whose names and diuisions ap­peare at the first vewe: two things only be­ing waied. First, that the mechanicall or materiall Globe which representeth the first mooueable: beareth in him the fixed Starres, (not because the Starres bee in the first mooueable) but because their mo­tion is so litle in their own Sphaeres in ma­ny yeares, that they may seeme not to haue mooued at all in a mans his age from their places vnder which they be of ye first moue­able: therefore they may bee supposed to stand in it. Secondly, the Globe represen­teth the Starres to vs in his connexitie, [Page] which appeare in Heauen in the concaui­tie. For that our eye is not in the Globe but without. Furthermore in the Globe, besides the aforenamed Circles, bee found three others of brasse: the one being a per­fect Circle of a litle quantitie, placed about the Pole which is eleuated: & is called the hower Circle, whose stile is called the In­dex. An other is a thinne rule of brasse, re­presenting one quarter of a whole Circle, called the quadrant of Altitude, and is al­waie to be fixed (when ye vse the Globe) on the middle of the halfe of your Meridian, which is aboue the Horizon: that is to say, 90. degrees aboue the Horizon. The third and last is a great halfe Circle lying at the Horizon, seruing aswell for the erection of the scheme of Heauen, as any Circle of position. All which things being aduisedly considered of, ye may proceede in the vse of the Globe: As followeth.

HOW THE Globe is to be placed, readie for his vse and practise.

THe placing of the Globe ought to be such, that the Horizon of the Globe may stand parallele or leuied to the true Horizon: and the Meridian of the Globe stand in the Superficies of the true Meridian of Heauen, and the Poles of the Globe and his Axe, answere exactly to the Poles and Axe of Heauen. Now to the le­uying of the Horizon: there ought to bee at your Globe a hanging plummet. and for the Meridian, a Needle touched of the lode stone, and touching the rectifying of the Poles and Axe of the Globe, the eleuation of the Pole of heauen is first to be knowen. the meanes to performe and accomplish the same, being such as followe.

Propositio. 1. To finde a Meridian line in any place appoynted.

SEt vp on your Horizon or some plaine leuied boarde, a Gnomon of any reaso­nable [Page] length then, (at such time as the same shineth, describe from the top of your Gno­mon a Circle by the tippe of his shadowe. and make a marke in the Circle where the shadowe ended, at your obseruation (which must be before noone.) Then marke in the afternoone at what time the ende of the shadowe returneth into the same Circle a­gaine, and make a marke at his point of fal­ling, so shall ye haue a portion of the sayde Circle inclosed betwixt the two points: If then ye diuide this portion into two aequal parts, and drawe a line from this middle point, by the point in which the Gnomon standeth, it shalbe a Meridian line.

Propositio. 2. To take the height of any Starre.

FRrom the point of Heauen, which is di­rectly ouer our heads (being called the Verticall point, or Zenith:) are imagined diuers Circles to fall by euery degree and minute of the Horizon: all which Circles are called Verticals, & serue for the height of Starres, for so much as the altitude of [Page] Sunne or starre is the portion of the V [...] ticall Circle, inclosed betwixt the Cen­ter of the Sunne or Starre (in the time of his obseruation) and the Horizon, which height is thus found.

Take your Astrolabe, and let him hang freely by his ring, then turne vp his Dio­ptral so long, that ye see the Starre (whose height yee seeke) thorowe his sights: for then, howe many degrees and minutes are inclosed betwixt the Dioptrall and the line of your Astrolabe, which is parallele to the Horizon: so many hath that Starrs of height. as the seauenth day of Ianuarie. Anno. 1585. vnder the Meridian of Ox­ford, at 9. of the clocke I sought the height of the Sunne. taking then my Astrolabe, and hanging him towarde the Sunne, and raising his Dioptrall till I espyed the Sunne. I found betwixt the Dioptral and the line representing the Horizon seauen degrees, and 16. minutes, so much was the height of the Sunne at that time.

Propositio. 3. To take the altitude of the Pole in in any place or countrey.

THe altitude of the pole is the portion of ye Meridiā Circle inclosed betwixt the Pole and the Horizon. and is thus found. Find a Meridian line, and drawe him in the Horizon by the first proposition: then take the height of any fixed Starre which setteth not (and that at the fore part of the night) at such time as he is pointed vppon your Meridian line, by the second proposi­tion. Again the next morning, or any other morning take the height of the same starre at such time as hee is pointed with your Meridian line: then subduct the lesse alti­tude from the greater, and diuide the diffe­rence into two aequall partes. Lastly, adde halfe the difference to the lesse altitude, so the whole number made giueth the altitude of ye Pole. As at Oxford I tooke ye height of a starre in the fore part of a night in win­ter, being the tenth of December. 1584. at what time he was pointed with my Me­ridian, and found his height. 55. degrees. 59. minutes. Againe the next morning I [Page] tooke his height, and found it 47. degrees 41. minutes. This lesse altitude I subourted from the greater 55. degrees. 59. mi­nutes, and the difference was 8. degrees. 18. minutes, which being parted, had 4. for his halfe, and 9. minutes. This halfe added to 47. degrees. 41. min. (the lesse altitude) giueth 51. degrees. 50. minut. for the true eleuation of the Pole at Oxford.

Propositio. 4. To rectifie the Globe perfectly for to be vsed.

KNow first the eleuation of the Pole of Heauen, for the place where yee vse the Globe, by the third proposition, then erect the Pole of the Globe so many degrees a­boue his Horizon, as the Pole of heauen is eleuated. Againe leuell the Horizon of your Globe by his hanging plummet, last­ly turne his Meridian to the South by helpe of his Needle, and put his Quadrant of altitude vppon the 90. degree from his Horizon: for then the Meridian answe­reth to the Meridian of heauen. Axe to axe, and Pole to Pole as is required. But this [Page] way of setting him South, albeit it be of antiquitie: yet hath it imperfection by rea­son of the variatiō of the needle. but of that ye shall heare more hereafter.

Propositio. 5. To finde the place of the Sunne at any tyme.

BY this place, is vnderstoode the degree of the Ecliptick line, in which he is, and this place is thus found. In the Horizon of your Globe be set, the windes, the signes, and moneths with their daies. find therfore the day of your moneth in which ye would haue the place of the Sunne in the Hori­zon of the globe. For looke what signe and degree of signe is right against the day, the same is the place of the Sunne. As on the twelfth day of December: Anno. 1584. I sought the place of the Sunne. this day being had in the Horizon, I found the first degree of Capricorne, 32. minutes to an­sware against it, and therefore that was then the place of the Sunne.

Propositio. 6. To finde the declination of any point of the Ecliptick or of the Sunne, at any tyme.

THe declination of any point of the E­cliptick, Sunne, or any Starre, is the portion of the Meridian Circle, inclo­sed betwixt the Aequinoctiall and the say [...] point, Sunne, or starre, and is found thus. Turne the poynt whose Declination yet seeke, to the Meridian of the Globe, and there see how many degrees and minutes there be of your Meridian inclosed betwixt the sayd poynt and the Aequinoctiall. For so much is the Declination. so hath the Sunne in the 5. of Aries 2. degrees decli­nation. And the 7. of Taurus 13. degrees. 52. minutes. and this declination is called Northren, when the point is of the North side the Aequinoctiall, and Southerne if of the South side. Here must ye also know, that two points of the Ecliptick want de­clination, and are the two Aequinoctials. Two haue greater declination then any­other, and be the two Solstitials. of the rest foure haue like declination.

Propositio. 7. To finde the right ascention of the Sunne, or any point of the Ecliptick line.

THE right ascention of any Starre, Sunne, or any point of the Ecliptick, is the portion of the Aequinoctiall Circle from the head of Aries, (where the Aequi­noctiall taketh his beginning) and that point or degree of the same, which meeteth with the said Starre, Sunne, or Ecliptick point, vnder the Meridian Circle in a croo­ked Sphaere: being numbred orderly in the Aequinoctiall, and is thus found. turne the Starre, Sunne, or any point whose ascen­tion ye looke, vnder the Meridian of the Globe, and see then what portion of the ae­quator is from the head of Aries to that point of the aequator which standeth then vnder the Meridian: for the same portion, is the right ascention of the Starre, Sun, or point looked for. So do I finde the right ascention of Bootes a Starre, to be 209. degrees. 1. minut. And the right ascention of the Sunne whē he is in the first of Tau­rus, to be 27. degrees. 54. minuts. And the [Page] right ascention of the first of Sagitarie, to be 237. degrees. 48. minuts.

Propositio. 8. To finde the crooked ascention of the Sunne, Starre, or any point of the Ecliptick.

THE crooked ascention of the Sunne, is that Ark of the aequator which is in­closed betwixt the beginning of the aequa­tor, and the point of the same which com­meth vp with the Sunne in a crooked Sphaere, & is found thus. Take the Sunne Starre, or point, whose crooked ascention ye desire: and put him to the East side of the Horizon till it touch: Then marke what part of the aequator is inclosed betwixt the beginning of it, and the point now in the Horizon, for so much is the crooked ascen­tion of the Sunne, Starre, or point. Th [...] doe I finde the crooked ascention of the Sunne in the first of Taurus, to be the 12. degrees. 48. minuts. All this being in the Eleuation 52. degree. 0. minut.

Propositio. 9. To find the difference of ascention, or increase of the day.

THE Sunne being in one and the selfe same point of the Ecliptick (except in the Aequinoctiall intersections) hath one degree of the aequator that commeth vp with him aboue the Horizon in any croo­ked Sphaere, and an other, (not the same) that cōmeth vp with him in a right Sphaere. And therefore the portion of the aequator, betwixt the point of the said, that commeth vp with the Sunne in the right Sphaere: and the point rising with the same in the crooked Sphaere, is called the difference of ascention. As in a right Sphaere the Sunne beeing in the first of Taurus, there riseth with him, the 27. degree. 54. minut of the Aequinoctiall. (Which point also meeteth him vnder ye Meridiā in a crooked Sphaere: for that ye Meridiā of any crooked Sphaere, sheweth the same that the Horizon doth in the right Sphaere.) but in the crooked Sphaere, where the Pole is eleuated 52. degrees, there riseth with the Sunne the same daye, the 12. degree. 48. minut of the [Page] aequator. Subducting now the lesse from the greater, the difference is 15. degrees. 6. minuts, and is called the difference of as­cention. And because the Artificiall day of the crooked Sphaere, is longer or shorter then the Aequinoctiall day by twise this dif­ference: therefore the difference of ascen­tion is called also the increase of the day. And this difference is thus found. Find the right ascention of the Sunne by the 7. pro­position: and againe finde his crooked as­cention by the 9. proposition: then subduce the lesse from the greater, for the remaines is the difference of ascention.

Propositio. 10. To finde the length of the Artifi­ciall day in any Region or Countrie.

FInde out the difference of ascention of the place of the Sunne by the 9. propo­sition, and dubble the same then conuert is all into howers and parts of howers, allo­wing for one hower 15. degrees, and for a halfe 7. degrees. 30. minuts, &c. This time which commeth of the difference of ascen­tion [Page] adde to 12. howers (if the place of the Sunne bee any degree betwixt Aries and Libra: or subduct it frō 12. if he be betwixt Libra and Aries,) for the number made or left, is the length of the day. As the Sunne being in the first of Tanrus, his difference of ascention is 15. degrees. 6. minuts: this dubble and conuerted into time, maketh 2. howers and 12. Aequinoctial minuts. And because Tanrus is a Northerne Signe, ye must ad this difference to 12. howers, so do ye make 14. howers and 12. Aequinoctiall minuts, for the length of that whole day.

Propositio. 11. To finde the hower of the Sunne rising, or of his setting.

KNowe the length of the Artificiall day by the 10. proposition: and take halfe of the same day, for that sheweth the hower of Sunne setting. But if ye recken so much from noone forward, it giueth Sunne rise. As the Sunne being in the first of Taurus, the day is 14. howers and 12. minuts. The halfe is 7. howers and 6. minuts. I say then the Sunne setteth after 7. of the clocke, 6. [Page] minuts. Againe, thus much taken from noone forward, sheweth the Sunne to rise before 5. of the clocke, 6. minuts.

Propositio. 12. An other way to finde the same more mechanically.

FInde the place of the Sunne by the 5. proposition, and turne the saide place di­rectly vnder the Meridian: thē put the In­dex of the hower Circle precisely on 12. of the clocke. Lastly, turne the saide place of the Sunne to the East side of the Horizō: for when he is there, then shall the Index shewe the time of the Sunne rising. And contrariwise, putting the place of the Sun to the West, it sheweth his setting.

Propositio. 13. To finde how farre the Sunne riseth or setteth from the true East or West point any day.

FIrst finde the place of the Sunne by the 5. proposition: then turne the same place to the East side of the Horizon til he touch [Page] the same, for then the number of degrees in the Horizon, (inclosed betwixt ye true East point and the place of the Sunne,) shewe how farr he riseth and setteth from the true East: And this portion of the Horizon is called his bredth of rising: and is called Northern bredth if the Sunne rise beyond ye East point toward ye North, & Southern if contrary. Likewise are ye to knowe, that of the Ecliptick two points Aries and Li­bra haue no bredth of rising. Two points also as Cancer and Capricorn haue grea­ter then any other: and of the rest fower points haue the like.

Propositio. 14. To rectifie the Index of the hower Circle euery day as he ought.

FInde the place of the Sunne euery day in which ye vse the Index, by the 5. pro­position, and put the said place vnder the Meridian: this being done, thē put the In­dex on 12. of the clocke, for afterward in the motion of the Globe he will goe true as he ought.

Propositio. 15. To finde the noone height of the Sunne for any day to come, or gone in any place whose eleuation is knowen.

THe height of the Sunne, is the portion of the verticall Circle inclosed betwixt the Center of the Sunne and the Hori­zon. But for as much as at noone the Me­ridian, and the Verticall of the Sunne bee all one Circle: therefore his noone height is the portion of the Meridian betwixt the Center of the Sunne and the Horizon. this height is thus to be knowen. Find the place of the Sunne for the day proposed, and turne the same place vnder the Meri­dian, for then the portion of the Meridian betwixt the sayd place and the Horizon is his noone height. Thus found I the height of the Sunne at noone in Oxford, whose Pole is raysed 51. degrees. 50. min. on the 2. day of May to be 59. degrees. 47. mi. and on the twelfth of Iune, to be 61. degrees. 41. minuts.

Propositio. 16. To find the depression of the Sunne at midnight.

AS the Meridian altitude is the portion of the Meridian from the Center of him, to the Horizon when hee is aboue the earth: so is his depression the part of the Meridian betwixt the Center and the Ho­rizon when he is vnder ground, and may thus bee knowen. Finde the place of the Sunne, and put it to the Meridian vnder the Horizon: for then the portion of the Meridian betwixt it & the Horizon, shew­eth his depression. So find I the depression of the Sūne, at Oxford (his place being the first of Taurus) to be 27. degrees. 40. min. but his place being the first of Scorpius, to be 50. degrees. 0. min.

Propositio. 17. To find what height the Sunne shall haue at any certaine hower of any artificiall day.

TAke the place of the sunne by the 5. pro­position: & rectifie the Index by the 14. pro. then turne the Globe, till the Index of [Page] the hower circle be on the hower, for whom ye desire the height of the Sunne, and scop­ping the Globe there, put the quadrant of altitude to the place of the Sunne, for his portion betwixt the place of th [...] Sunne & the Horizon, geueth his height. So find I the height of the Sunne at Oxford, at 9. of the clocke the 7. day of March. to be 24. de­drees. 25. min. and at one of the clocke the same day, to be 34. degrees. 51. min.

Propositio. 18. By any height of the Sunne geuen and his place: to find the hower of the day.

LEt it bee, that either ye take the height of the Sunne at some time of the day by the second proposition: or that yee haue some height of him giuen by supposition, and ye would knowe by it what it is of the clocke that day at that time. Finde there­fore the place of the Sunne for that day▪ by the 5. proposition & rectifie the Index by the 14. proposition. Lastly put the place of the Sunne to the Quadrant of Altitude, and mooue them both vp and downe, till ye [Page] allowe him the same height in your Qua­drant, as ye found or supposed him in trueth to haue. For then the Index of the hower Circle sheweth what was or is of the clock, as finding the height of the Sunne before Noone on the seauenth of March, at Ox­ford, to be twentie fower degrees. 25. min. I founde it to haue beene then nine of the clocke.

Propositio. 19. By the hower knowen, and the height of the Sunne at that hower: together with the Index, rectified as he ought: to find the place of the Sunne at that tyme.

MOoue your Globe till his Index stand on the hower which was knowen be­fore. Then fixe the Globe for remoouing: Lastly turne your Quadrant of altitude to the Ecliptick line, and looke what degree of the Ecliptick agreeth in your Qua­drant with the height that was before kno­wen, and that is the place of the Sunne on that day.

Propositio. 20. The hower and place of the Sunne be­ing giuen: to find howe farre the Sunne is gone from the true East poynt.

THe place of the Sunne being giuen by supposition: rectifie the Index by the 14. proposition: then turne the Globe till the Index shew the hower giuen. This be­ing done, fixe the Globe that he mooue not away, and set the edge of the Quadrant of altitude to the place of the Sunne: and withall marke howe many degrees of the Horizō are inclosed betwixt the true East point, and the edge of the Quadrant, at such time as he stādeth on the place of the sunne: for so much is hee distaunt in the Horizon from true East.

Propositio. 21. The distance of the Sunne being geuen, from true East, together with his height at the same time, and the height of the Pole for the same region: to finde the true place of the Sunne, at any time.

TO the ende wee make not vnnecessarie repetitions of the first principles: know [Page] this, that in all the propositions following, we alwayes suppose before the working, the Globe rightly rectifyed as is specified in the beginning. For the performance therefore of this practise: first consider dili­gently in what quarter of the yere ye be in▪ that is, whether it be betwixt the aequino­ctiall of March, and height of Summer: or betwixt height of Summer, and aequino­ctial of September. Likewise whether be­twixt aequinoctial of September and dept of Winter: or betwixt dept of winter and aequinoctiall of March. For then set the edge of the quadrant of altitude at the true distance of the Sunne from the East: and turne the Globe till that quarter of the E­cliptick come vnder him, which serueth for the quarter of the yeere in which ye be: and see what degree of that part of the Eclip­tick agreeth with the height proposed: For that is the place of the Sunne at that time.

Note therefore here, that to the Spring (which is from the aequinoctiall of March till the height of Summer) answereth the part of the Zodiack from Aries to Cācer. To summer which is from the height till the aequinoctiall of September: answe­reth [Page] the part from Cancer to Libra. The Autume is guided by the quarter from Li­bra to Capricorne: and Winter by the si­gnes from Capricorne to Aries.

Propositio. 22. The distance of the Sunne being geuen from true East, and the place of the same: to find the height of the Sunne which he hath at the same time.

PLace the quadrant of altitude at the true distance from East, so shall hee cut the place of the Sunne by the 21. proposition: and therefore the portion of the Quadrant betwixt the place of the Sunne, and the Horizon, is his height.

Propositio. 23. The distance of the Sunne from true East being geuen, and his place: to find the hower of the day.

FIrst hauing his place: rectifie your In­dex by the 14. proposition: again setting the Quadrant of altitude in the distance [Page] from true East, reduce the place of ye sunne, till he fall in the edge of the Quadrant, for then the Index doth shewe the hower.

Propositio. 24. The distance of the Sunne being geuen from true East, and his height, to find the time of his rising.

THe distance being giuen, find his place by the 21 proposition: and then rectifie the Index by the 14 proposition: Lastly put the place of the Sunne to the East side of the Horizon: for then the Index will shew the Sunne rising.

Propositio. 25. The distaunce of the Sunne being giuen from true East, and his height, to finde his Declination.

THE distaunce being giuen, his place is foūd by the 21. proposition: & his place being knowne, giueth his Declination by the 6. proposition: So may wee likewise by the said distaunce (finding his place) finde his right or crooked ascention, or difference [Page] of ascentions, and length of Artificiall daies.

Propositio. 26. The declination of the Sunne being knowne: to finde the place of the Sunne.

COnsider first diligently in what quar­ter of the yeare ye be in, as was expres­sed before: then take that quarter of the E­cliptick which answereth to your quarter of the yeare: and mooue it still vnder the Meridian of your Globe, till ye finde no more of the Meridian inclosed betwixt the aequator and Ecliptick, then the declina­tion that is giuen commeth vnto: for then looke what degree of ye Ecliptick is vnder the Meridian, that is the place of the Sun. As the declination of the Sunne in ye quar­ter of the yeare betwixt the Aequinoctiall of March, and height of Summer was gi­uen to bee 11. degrees. 50. minuts. And to this quarter of the yeere, aunswereth the quarter of the Ecliptick frō Aries to Can­cer. Therefore moouing the said quarter vnder the Meridian, I found the first of [Page] Taurus to aunswere to this declination: and therefore that was the place of the Sunne.

Propositio. 27. The declination of the Sunne be­ing knowne: to finde the day of the Moneth.

BY the declination giuen, finde the place of the Sunne by the 26. proposition: thē take the said place in the Horizon of your Globe: for looke what day aunswereth a­gainst it, that is the day of the Moneth.

Propositio. 28. The day of the Moneth being knowne, to finde the length of the Plane­tarie hower.

THE Artificiall day is from Sunne rise to Sunne set: and the 12. part of this day, whether it be longer or shorter then an hower by the clocke, is the Planetarie ho­wer: and may thus be knowne. The day be­ing gi [...]en, finde the length of that day by the 10. proposition: and diuide all by 12. [Page] The Quotient is the length of a Pla­netarie or Artificiall hower of that day. As the day being 15. howers by the clocke, I diuide it by 12. the Quotient is one ho­wer and a quarter, and so much is a Plane­tarie hower of that day.

Propositio. 29. The day of the Moneth being giuen: to finde the dawning of the day.

BY the day knowne, finde the place of the Sunne by the 5. proposition: and then rectifie your Index by the 14. proposition. Againe, take the degree of the Ecliptick which is opposite in a Diameter to ye place of the Sunne: and mooue him toward the West together with the Quadrant of Alti­tude, till ye haue 18. degrees of height: for then the Index sheweth the beginning of the dawning or spring of the day.

Propositio. 30. To finde the length of the whole dawning.

FInde the beginning of the dawning by the 29. proposition, and then the Sunne [Page] rise by the 11. or 12. proposition: for the dif­ference of those times is the whole daw­ning. And thus farre haue I followed such conclusions, as haue a more orderly cohae­rence: it remaineth now to shewe some o­thers, whose cohaerence is not so naturall.

Propositio. 31. An other way to finde the length of the Artificiall day or night.

FInde the time of the Sunne rising for your day proposed by the 12. propositiō: then dubble all those howers and partes of time which be from Sunne rise till noone, for it giueth the Artificiall day. Or if ye nū ­ber all the howers and parts from Sunne rise to his setting, it giueth the same.

Propositio. 32. To finde the hower of the day.

PLace the Globe in the Sunne shine, and rectifie him to his vse by the 4. proposi­tion, then finde the place of the Sunne by the 5. proposition. Againe, rectifie his In­dex [Page] by the 14. proposition. Lastly, [...] the needle or pinne directly vp in the place of the Sunne: then turne the Globe vp till the pinne cast no shadowe, for then the In­dex sheweth what is then of the clocke.

Propositio. 33. To finde the eleuation of the Pole, in any place.

DRawe in the open ayre vpon some table that is leuell, a Meridian line by the 1. proposition, and place the Globe so on it, that his Meridian Circle hang directly [...] ­uer it: then hauing the place of the Sunne, set a pinne right vp in it, and put the said place and pinne close to the Meridian cir­cle. Lastly, lift vp the Pole and Meridian Circle, till the pinne cast no shadowe: for then the degrees betwixt the Pole and the Horizō, be the true eleuatiō of that place. But this practise is to bee performed at noone onely or height of the day.

Propositio 34. An other way to doe the same.

TAke the height of any fixed Starre (whom ye know) by the 2. proposition, [Page] at such time as he pointeth with the Meri­dian line: then take the same Starre on the Globe, and by helpe of your Quadrant or Meridian Circle, cause him to haue the same Altitude in the Globe, and withall to be vnder the Meridian of the Globe: for thē is the Pole at his true Eleuation. So did I finde the Pole Starre (making my ob­seruation at Oxford, the 11. of December 1584.) by the plaine Sphaere, to haue 55. degrees▪ 59. minuts in Altitude, being thē in the Meridian of Heauen: and when I set him at the same in my Globe, I found the Pole eleuated there 51. degrees. 50. mi­nuts. And here ye are to knowe, that when soeuer ye haue by any way, the eleuation of the Pole in any place: if ye subduct the same eleuation from 90. degrees, it shall leaue and she [...] the eleuation of the aequator in the sayd place. So then the eleuation of the aequator at Oxford, is 38. degrees. 10. minuts.

Propositio. 35. An other way of working the same, with more praecisenes.

FIrst learne by some good Ephemeris the precise place of the Sunne at noone [Page] in the day of your obseruation: then againe learne ye exact declination of the said place. Lastly, with your [...] take the Me­ridian height of the Sunne that day: And if the declination bee Northerne, then sub­duct it from the Meridian Altitude: but if it be Southerne, then ad it to the Meridian Altitude: so shall wee bring forth the Alti­tude of the aequator: and this Altitude be­ing subducted from 90. degrees, leaueth the Altitude of the Pole: but if the Sunne in the time of obseruation be in the Aequi­noctiall point, then is the Meridian Alti­tude, the Altitude also of the aequator, and it subducted from 90. degrees, leaueth the Altitude of the Pole.

Propositio. 36. To make a Horizontall Diall by the Globe.

A Horizontall Diall is such a one as is made in a plaine Superficies, and lyeth leuell with the Horizon. For making whereof ye are to consider, that from one Pole of the Globe to the other goe twelue great Circles, called hower Circles, and [Page] diuide the aequator into 24. aequall parts: And two of these bee two Colures. Put therefore the Solstitiall Colure precisely vnder the Meridian of your Globe, (the Globe being first perfectly rectified) and fixe ye Globe so that he cannot mooue. Now marke how many degrees of the Horizon are inclosed betwixt the Meridian and the next hower Circle toward the East (which for distinction sake I call the second hower Circle) so likewise betwixt the first & third, the first & fourth, the first and fifth, the first and sixt, the first and seuenth: (which is he that cutteth in the true East point) and set them all downe in tables: then drawe on some plaine thing a Circle, and diuide it into fower quarters, by drawing two crosse lines: Now take the one ende of any of the two lines, and terme it the North point, so shall his other end be the South point, and the endes of the other line East and West. Againe, diuide that quarter of this Circle which is betwixt the North point and East into 90. aequall parts, and let 90. stand at the East. So doe by the quarter betwixt North and West. Lastly, recken from the North point toward East, so many degrées [Page] as your tables shewe to haue [...] betwixt the first and second hower line: and from the point where they ende, drawe a line by the Center of the saide Circle: and so doe by all the numbers of your tables: for so shall ye haue your hower lines drawne for a Horizontall Diall. In whose Center must be a stile exected, according to the ele­uation of your Pole. But this I leaue ob­scure, as meaning to set out an ample trea­tise of Dialling by it selfe.

Propositio. 37. How the Starres may be knowne by the Globe of Heauen.

REctifie your Globe in the open ayre by the 4. proposition, thē take the height of any knowne Starre by your Instrument, afterward looke the same Starre on the Globe, and by helpe of your Quadrant of Altitude put the same Starre at his height taken before, and in the same Coast, & then fixe the Globe. Now if ye would knowe a­ny other Starre of Heauen, then take the same Starre his height with your Instru­ment: lastly, turne your Quadrant of Alti­tude [Page] toward the same Coast of the Globe in which the Starre was in: & looke what Starre ye finde in that Coast, to haue that Altitude, the same is he whom ye seeke. The like is to be done by all others.

Propositio. 38. To finde the Longitude of any fixed Starre.

THE Longitude of a Starre, is the por­tion of the Ecliptick line, taken from the head of Aries, (according to the order of the Signes) to the point of the Ecliptick, cut by a Circle which passeth frō the Pole of the Ecliptick, by the Center of the sayd Starre: and is thus found. Take the Globe from his Horizon, and take of his Meri­dian Circle, and fixe the same Circle by some meanes on the Poles of the Zodiack, then turne the Starre whose Longitude ye seeke, vnder the Circle: and recken all the Signes and parts from the head of A­ries, to that point of the Ecliptick which is vnder the Circle with the Starre: for so much is his Lōgitude. And the same point of the Ecliptick which is so vnder the Cir­cle, shalbe called the place of that Starre. And the Starre is sayd to bee vnder that [Page] Signe, of whom the aforesaid point is a part. The Longitude may also be taken, if ye doe but fixe the Quadrant of Altitude in the Pole of the Ecliptick, and stirre not at all the Meridian Circle.

Propositio. 39. To finde the Latitude of any Starre.

THE Latitude of a Starre, is the por­tion of the Circle that passeth from the Poles of the Ecliptick line, by the Center of any Starre, which is inclosed betwixt the Ecliptick line and the Center of the Starre, and is found thus. Your Circle standing in the Poles of the Zodiack as before: turne the Starr vnder the said Cir­cle: for then the portion of that Circle be­twixt the Starre and the Ecliptick, is his Latitude. And this Latitude is Northern, when the Starre is North from the Eclip­tick: and Southerne of contrary.

Propositio. 40. To finde what Starres be aboue ground at any time of the day or night.

IF ye would know it in the day time whē the Sunne shineth, then take the height of the Sunne by the 2. proposition: after­ward [Page] finde his place by the 5. proposition: lastly, by help of the Quadrant of Altitude, set the Sunne at his owne height & Coast, and then all the Starres aboue the Hori­zon doe appeare in the Globe. Now if it be in the night, and the Starres appeare, then take the height of some knowne Starre, and place the same Starr at his due height in the Globe, so shall ye see the same.

Propositio. 41. To doe the same without Sunne, or appearaunce of any Starre.

YE must knowe what it is of the clocke at that time when ye would worke this conclusion: then rectifie the Index by the 14. proposition: Lastly, turne the Globe till the Index come on the same hower as is giuen by the clocke, for then the Starres appeare as they should.

Propositio. 42. To finde what Starres will passe directly ouer our heads in the motion of the heauen.

AFter that the Quadrant of Altitudes is fixed in his due place, as is spoken of before, so that he now doe shewe the Zenith or Verticall point: then mooue about the [Page] Globe, and marke what Starres passe vn­der the Zenith in this motion, for those bee such as goe by our heads, & are called some­times Culminant starres, sometimes Ver­ticall starres, and haue their cheefest vse in Astrologie.

Propositio. 43. To knowe with what degree of the E­cliptick any Starre rised, commeth to the Meridian: or setteth.

MOue the Globe till the Starre whom ye propose, ascend aboue the Horizon, and then marke the degrée of the Ecliptick that riseth with him. Againe mooue him to the Meridian, and marke the degree of the Ecliptick, so doe by him in the West side of the Horizon, and ye shal haue your intent.

Propositio. 44. To knowe the hower of any Starres rising.

REctifie the Index by the 14. propositiō, then turne the Globe til the said Starre (whose time of rising ye desire,) touch the East side of the Horizon: for then the In­dex giueth his time of rising. And if ye turne him to the Meridian, the Index will shewe his time of comming the ther: or if ye [Page] turne him to the West side of the Horizō, the Index sheweth his setting.

Propositio. 45. To find in how long time any whole signe ariseth.

REctifie the Index by the fowerteenth proposition: then put the beginning of the signe (whose time of rising ye seeke) to the East part of the Horizon: and marke what the Index standeth on then: againe, put the last degree of the sayde signe to the Horizon, and see what the Index sheweth: for the differēce of the two times by the In­dex, is the time in which that signe riseth.

Propositio. 46. To find in what coast any starre is, and how many degrees from the Meridian.

FInde the Starres aboue ground by the 40. proposition: then the Globe beeing fixed: put the Quadrant of altitude to any State. Then shall the foote of the Qua­drant shewe in the Horizon, how farre the same Starre is from East, West, North or South. But if ye first rectifie your Index by the 14. proposition: and then finde the starres aboue by the 40. propositiō. Agayn [Page] at the same time marke where the Index standeth: lastly put any Starre vnder the Meridian, and againe note the standing of the Index: the differēce of those two times shewed by the Index, is the distance of that starre from the Meridian, in the time of your obseruation.

Propositio. 47. To find what Starres rise or set any day, Cosmically, Achronically or Helically.

SVch starres as bee neare to the sunne in any day, and ascende aboue the Horizon a little before the appearance of the same: are said to ryse helically, and such Starres as set very little after the Sunne, are sayd to set helically. Againe such Starres as ascend together with the Sunne, and such as set at the same time, are sayd to rise and set cosmically. Lastly, such starres as set together with the Sunne: and such as rise at the same time: are sayde to set and rise achronically, and such may bee thus found. Rectifie the Index by the 14. propo­sition: and turne the place of the Sunne to the East side of the Horizon: for the starres going immediatly before the Sunne, rise [Page] helically. and those in the Horizon rise cos­mically: and they that are in the Horizon in the west, doe set cosmically, and such as immediatly rise after the Sunne, doe sette helically. Lastly turne the Sunne to the West point of the Horizon, and looke what starres touch the Horizon with him, such set achronically: and such as are at the same time rising in the East, rise Achroni­cally.

Propositio. 48. To knowe the hower of the night, at any time by the Starres.

REctifie the Index by the 14. propositi­on, then againe finde what starres bee aboue ground at the same time, when yee would know ye hower, by ye 40. proposition: for then the Index will shewe the hower.

Propositio. 49 To find the fower Cardinall points of heauen at any time of day or night.

THe fower Cardinall points, bee the fo­wer degrees of the Ecliptick, where of one is in the East rising: an other is in the South or vnder the Meridian, aboue at the same time: the third in the West setting, [Page] and the fourth vnder the Meridian beneath ground, all at one instant, in the time of any geniture, or motion of any question, and are thus knowen. If yee seeke them in the day (the Sunne shining) then find the starres aboue ground by the 40. proposition: and with all marke the degree of the Ecliptick in the East. so likewise in the South, West and North, for those be then the Cardinall points. Againe, if it be in the night, then find the starres aboue by the same 40. pro­position. and the pointes shall likewise ap­peare. Lastly, if nether the Sunne shine, or starre: then knowe the hower by the clock, and afterward find the starres aboue groūd at the sayd hower by the 41. proposition. so shall the pointes be geuen as before.

Propositio. 50. To find the bignes of the angle, made betwixt the Meridian Circle, and any Circle of position.

CIrcles of Position bee all such, as are drawen from the North point of any Horizon by the Center of any starre, and so to go to the South point of the same Horizon, to returne to the North againe. And euery one of these Circles doth make some [Page] with the Meridian, and the sayd angle hath his bignes shewed, by a portion of the fixed Verticall: so that to find the bignes of the angle made betwixt the Meridian and any Circle of position: is to find the portion of the fixed Vertical, inclosed betwixt the Me­ridian and the said Circle of position. that portion is thus found. Put your quadrant of altitude, to the true East point, then raise vp your Brasse halfe Circle as high aboue the Horizon as yee please: so that it may nowe represent some circle of position. for then the degrees of the Quadrant of al­titude from the Meridian to this circle: be the bignes of the angle made betwixt the Meridian, and the Circle of position. but if your circle of position fall on the West side of the Meridian, then put the Quadrant to the West point; and worke as before.

Propositio. 51. To find the beginnings and endes of the 12 howses of Heauen.

COncerning the erecting the scheme of heauen, or as we commonly call it the twelue howsen: though fower diuers waies haue bene receaued, touching the howsen, how they ought to bee taken: yet it is not [Page] our entent to discourse of that question, but to shewe howe they ought to be erected, ac­cording to the most vsuall way, set downe by Regiomontanus, & called reasonable. Wherefore first ye are to knowe, that in a­ny Horizon wheresoeuer wee be, wee doe imagine sixe circles to be drawen from the North point of the Horizon to the South of the same, and diuiding the Aequinoctiall into 12 aequall partes, and the 12. spaces betwixt these circles, are called the twelue howses. (& two of the 6. circles are alwaies the Meridian and Horizon.) in euery one of these howsen is inclosed some portion of the Zodiack, and one portion is greater thē an other. so that to erect the twelue how­sen, is to find out the portion of the Eclip­tick inclosed in ech space, & to do it, we thus proceede. First find out the fower Cardinal points by the 49. proposition, for those be the beginnings of 4. howsen of the twelue: the Cardinall point vnder the Meridian a­boue ground, is the beginning of the tenth howse. This done, fixe the Globe, then rec­ken from the degree of the aequator (being then vnder the Meridian) 30. degrees to­ward the East point, & raise vp your brasse [Page] halfe circle to stand on the point of the ae­quator on which yee left. For looke then what degre of the Ecliptick is cut then by the brasse halfe Circle: the same is the end of the tenth howse, and beginning of the e­leuenth. Againe, yet recken 30. degrees more in the aequator toward the East, and put the brasse halfe circle to it, and thē take the degree cut in the Ecliptick, for that is the end of the eleuenth howse, and begin­ning of the twelfth. Againe the Cardinall point of the East, is the end of the twelfth howse, and beginning of the first howse. Now if in like sort ye goe from the degree of the aequator vnder the Meridian, by ech 30. degree of the same toward the West point, and still obserue the degres cut in the Ecliptick: yee shall haue the beginnings and ends of the ninth, eighth and seauenth howse. Thus hauing erected sixe howsen, the degrees of the Zodiack which are op­posite to these in a Diameter, (one to an o­ther) bee the beginnings and ends of the o­ther sixe howsen, which were to be found. And here must yee note, that the first howse beginneth at the East point, and goeth vnder the ground toward the Meridian [Page] Circle, the second and the third succeede. the fowerth, beginning at the Meridian vnder ground comming toward West, the fifth and sixth succeed, the seuenth begin­neth in the West, and goeth aboue ground toward the Meridian, the eight and ninth succeed. Other conclusions lesse profitable I wittingly auoyded: and the more excel­lent, deferred to a more conuenient time.



Pa: 3. li: 13. indicem, lege iudicem.
Pa: 23. li: 1. same, lege Sunne.
Pa: 24. li: 1. lege Ver.
Pa: 46. li: 16. till ye, lege till it.

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