## 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 y^{e} 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 y^{e} 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 y^{e} 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 y^{e} 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 y^{e} Pole. As at Oxford I tooke y^{e} 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 y^{e} Meridiā in a crooked Sphaere: for that y^{e} 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 y^{e} 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 y^{e} East point toward y^{e} 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 y^{e} 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 y^{e} Ecliptick is vnder the Meridian, that is the place of the Sun. As the declination of the Sunne in y^{e} 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 y^{e} 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 y^{e} 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 y^{e} 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 y^{e} hower, by y^{e} 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.