The description and vse of the sphaere· Deuided into three principall parts. Whereof the first intreateth especially of the circles of the vppermost moueable sphære, and of the manifold vses of euery one of them seuerally

THE DESCRIPTION AND VSE OF THE SPHAERE. Deuided into three principall Parts. WHEREOF The first intreateth especially of the Cir∣cles of the vppermost moueable SPHAERE, and of the manifold vses of euery one of them seuerally. The second sheweth the plentifull vse of the vppermost Sphaere, and of the Circles thereof joyntly. The third contayneth the Description of the Orbes whereof the Sphaeres of the Sunne and Moone haue beene supposed to bee made, with their Motions and Vses.

By EDVVARD WRIGHT.

The Contents of each Part are more particularly set downe in the Table.

LONDON, Printed by B. A. and T. Fawcet, for Iohn Tap, and are to bee sold at his Shop at S. Magnus corner. 1627.

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CONTENTS

A TABLE OF THE CONTENTS OF this Booke.
The first Part. Of the Circles of the vppermost SPHAERE, and their seuerall vses.
The second Part. Of the vses of the vppermost Sphaere, and of the Circles thereof joyntly.
Of the vse of the SPHAERE and GLOBE. Pars, 1.
CHAP. I. The definition and diuision of the Sphaere.
CHAP. II. The Description of the Horizon.
CHAP. III. The vses of the Horizon.
CHAP. IIII. The description of the Meridian.
CHAP. V. The vses of the Meridian.
CHAP. VI. The description of the Houre-circle, and Poles.
CHAP. VII. Of the Equinoctiall Circle.
CHAP. VIII. The description of the Zodiacke.
CHAP. IX. The vse of the Zodiack.
CHAP. X. The description of the two Colures.
CHAP. XI. Vses of the Equinoctiall Colure.
CHAP. XII. Vses of the Solstitiall Colure.
CHAP. XIII The Description of the two Tropickes.
CHAP. XIIII. Vses of the Tropickes.
CHAP. XV. The Polar Circles.
CHAP. XVI. Vses of the Polar Circles.
CHAP. XVII. Of the Zones.
CHAP. XVIII. The difference of Shadowes that the Sunne maketh in these Zones.
THE SECOND PART. Of the vses of the vppermost SPHAERE, and of the Circles thereof joyntly.
PROP. I. To rectifie the Sphaere to the Latitude. &c.
PROP. II. To know the place of the Sunne; &c.
PROP. III. To know the declination of the Sunne, &c.
PROP. IIII. To know the right ascention of the Sunne, &c.
PROP. V. To know the oblique ascension of the Sunne, &c.
PROP. VI. To finde the difference of Ascension.
PROP. VII. To finde at what time the Sunne riseth or setteth.
PROP. VIII. To finde the length of the artificiall day or night.
PROP. IX. To know the time of the Sun rising and Sun setting.
PROP. X. To finde the length of the artificiall day or night.
PROP. XI. To know the Meridian altitude, or the height of the Sunne at noone, for any time and place.
PROP. XII. To know how high the Sunne is aboue the Horizon at any time of the day.
PROP. XIII. To finde the houre of the day by the height of the Sunne; &c.
PROP. XIIII. To finde the Amplitude or bredth of the Sunnes rising, or setting, &c.
PROP. XV. To finde the place of the Sunne, &c.
PROP. XVI. To finde what day of the moneth it is, &c.
PROP. XVII. The day of the moneth being knowne, to finde at what time the day breaketh.
PROP. XVIII. To finde how long the twylight continueth.
PROP. XIX. To finde how much the declination of the Sunne must alter at any time of the yeare, to make the day an houre lon∣ger or shorter.
PROP. XX. To find how many dayes it is ere the day lengthen or shor∣ten an houre.
PROP. XXI. To make an Horizontall Diall.
PROP. XXII. How to make a direct mural Diall.
PROP. XXIII. How to make any direct inclining, or direct reclining Dial.
PROP. XXIIII. To know at what time the Moone, or any other of the Pla∣nets or fixed Stars, that are within the bredth of the Zodiack; rise or set, or come to the Meridian, &c.
PROP. XXV. To know how long the Moone, or any of the Planets of fixed Stars doe shine or continue aboue the Horizon.
PROP. XXVI. To finde which of the Planets or fixed Starres are aboue or vnder the Horizon at any time, &c.
PROP. XXVII. To finde in what time any Signe or part of the Ecliptick riseth or setteth.
PROP. XXVIII. To finde the houre of the night by any of the Planets or fixed Starres in the Zodiack, &c.
PROP. XXIX. To know at any time of the yeare, what Stars in the Zodi∣ack, arise or set, Cosmically, Achronically, or Heliacally.
PROP. XXX. To finde the foure principall or Cardinall points of Hea∣uen (as the Astrologians call them) at any time.
PROP. XXXI. To finde out the bredth of any climate, &c.
PROP. XXXII. The reason of the inequalitie of naturall dayes, &c.
PROP. XXXIII. To finde by the Sphaere how much the naturall dayes are longer at one time of the yeare then at another.
The third Part.
CHAP. I. Of the Orbes whereof the Sphare of the Sunne is made.
CHAP. II. Of the vppermost and nethermost Orbes of the Sphaere of the Sunne, more particularly.
CHAP. III. To finde how much the Sunne is nearer or further from the earth, at one time then at another.
CHAP. IIII. Of the situation and motion of the uppermost, and ne∣thermost Orbes of the Sunne.
CHAP. V. How to find the place of the Suns Aux or Apogaeum, &c.
CHAP. VI. Of the eccentrick of the Sunne, &c.
CHAP. VII. Of the vses of the Sunnes eccentricall Orbe.
CHAP. VIII. The definitions of certaine Astronomicall wordes of art, for the better vnderstanding of the Theorick of the Sunne.
CHAP. IX. Of the vppermost Orbe of the Sphaere of the Moone cary∣ing the Dragons head and tayle.
CHAP. X. Of the Orbes carying the Moones Apogaeum and Peri∣gaeum.
CHAP. XI. Of the eccentricke of the Moone.
CHAP. XII. In what proportion the Moones eccentrick, and Orbe, ca∣rying her Apogaeum are moued.
CHAP. XIII. Of the Epicycle of the Moone, and how it is moued.
CHAP. XIIII. The definitions of certayne Astronomicall wordes of Art, for the better vnderstanding of the Theoricke of the Moone.
CHAP. XV. The reason of the variety of the Moones equation, &c.
CHAP. XVI. The reason Moones proportionall minutes, &c.
CHAP. XVII. The reason of the Eclipses of the Sunne and Moone, &c.
CHAP. XVIII. Of the diuersity of the bounds or spaces, within which an Eclipse may happen: and the reason of that diuersity.
CHAP. XIX. How to find the place of the Dragons head and taile for a∣ny time.
CHAP. XX. A table for finding the place of the Dragons head and taile more exactly and the declaration thereof.
CHAP. XXI. To finde the place of the Dragons head or tayle, by the former table.
CHAP. XXII. To know at what time there shall be an Eclipse of the Moone.

A TABLE OF THE CONTENTS OF this Booke.

The first Part. Of the Circles of the vppermost SPHAERE, and their seuerall vses.

THe Definition and deuision of this Sphaere, Chap. 1.
The description of the Horizon, Chap. 2.
The vses of the Horizon, Chap. 3.
The description of the Meridian, Chap. 4.
The vses of the Meridian, Chap. 5.
The description of the Houre-circle, and Poles of this Sphaere, Chap. 6.
Of the Equinoctiall circle, and why it is so called and how di∣uided, together with his manifold vses, Chap. 7.
The description of the Zodiacke of this Sphaere, Chap. 8.
The vses of the Zodiacke, Chap. 9.
The description of the two Colures, together with the vses common to them both, Chap. 10.
The vses of the Equinoctiall colure, Chap. 11.
The vses of the Solstitiall colure, Chap. 12.
The description of the two Tropickes, Chap. 13.
The vses of the Tropickes, Chap. 14.
The Polar circles, Chap. 15.
Vses of the Polar circles, Chap. 16.
Of the Zones, Chap. 17.
The difference of shadowes that the Sunne maketh in these Zones, Chap. 18.

The second Part. Of the vses of the vppermost Sphaere, and of the Circles thereof joyntly.

TO rectifie the Sphaere, that is to sett the Sphaere to the Latitude of that place for which you would vse it, Prop. 1.
To know▪ the place of the Sunne by this Sphaere, Prop. 2.
To know the declination of the Sunne, or of any point of the Ecliptick, Prop. 3.
To know the right Ascention of the Sunne, or any point of the Zodiack, Prop. 4.
To know the oblique ascension of the Sunne, or of any Starre or point in the Zodiack, Prop. 5.
To finde the difference of Ascension, Prop. 6.
To finde at what time the Sunne riseth or setteth, Prop. 7.
To finde the length of the Artificiall Day or Night, Prop. 8.
To know the time of the Sunne rising, or Sunne setting, Prop. 9.
To find the length of the artificiall Day or Night, otherwise by the Sphaere, Prop. 10.
To know the Meridian altitude of the Sunne at any place, whose latitude is knowne, Prop. 11.
To know how high the Sunne is about the Horizon at any time of the day, Prop. 12.
To find the houre of the day by the height of the Sunne, the place of the Sunne, and height of the Pole being giuen, Prop. 13.
To find the bredth of the Sunnes rising or setting, that is, how farre he riseth or setteth from the point of true East or West at any time, Prop. 14.
...

To finde the place of the Sunne, his declination, and the quar∣ter of the yeare being knowne, Prop. 15.
To finde what day of the moneth it is by knowledge of the Sunnes declination, Prop. 16.
The day of the moneth being knowne to find at what time the day breaketh, Prop. 17.
To finde how long the twylight continueth, Prop. 18.
To finde how much the declination of the Sunne must alter at any time of the yeare, to make the day one houre longer or shorter, Prop. 19.
To finde how many dayes it is ere the day lengthen or shorten an houre, Prop. 20.
To make an horizontal Diall by the Sphaere, Prop. 21.
How to make a direct murall Diall by the Sphaere, Prop. 22.
To make any direct inclining, or direct reclining Dyall by the Sphaere, Prop. 23.
To know at what time the Moone, or any other of the Planets, or fixed Starres that are within the bredth of the Zodiack rise or sett, or come to the Meridian: as also with what degree of the ecliptick they rise set or midde Heauen, toge∣ther with their declinations, and their right and oblique ascensions, and descensions, and their amplitudes or bredths of rising or setting, Prop. 24.
To know how long the Moone, or any of the Planets or fixed Starres doe shine, or continue aboue the Horizon, Prop. 25.
To find which of the Planets of fixed Starres (that are with∣in the compasse of the Zodiack) are aboue or vnder the Horizon at any time of the day or night, Prop. 26.
To find in what time any Signe, or part of the Ecliptick, riseth or setteth, Prop. 27.
To finde the houre of the Night by any of the Planets, or fixed Starres in the Zodiack, that appeare aboue the Horizon, Prop. 28.
To know at any time of the yeare, what Starres in the Zodi∣ack arise or set Cosmically, Achronycally, or Heliacally, Prop. 29.

[illustration]
The Meridian Line.

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Of the vse of the SPHAERE and GLOBE. Pars, 1. (Book 1)

The Description of the Sphaere and Globe, diuided into three principall parts..

Whereof this first intreateth specially of the Circles of the vppermost moueable Sphaere and of their peculiar vses.

CHAP. I. The definition and diuision of the Sphaere.

THis Sphaere, is nothing else but a representation of the Coelestiall orbes and circles, that haue beene imagined for the easier vnderstan∣ding, expressing, and counting of the motions and appa•ences, ey∣ther common to the whole Hea∣uens, or proper to the Sunne and Moone.

The circles of this Sphaere are eyther inmoueable, as the two greatest and vtmost circles, the Horizon and Meridian, (whereto is adioyned the little houre circle that is fixed to the Meridian) or else moueable▪ as all the rest contayned within these.

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CHAP. II. The Description of the Horizon.

THe greatest and vtmost circle of the Sphaere that lyeth leuell on all sides from the ground, is called the Horizon, which is deuided into 7. limbs, or bor∣ders. The first and vtmost of them conteyneth the 32. points of the Compasse, or the windes (as they are at this day deuided and vsed by Sea-men) with their Latine names adjoyned vnto them. The second limbe conteyneth the names and diuisions of the 12. Windes as they were wont to bee deuided in old time. The third is deuided into the moneths and dayes of the new Kalender, first established by Pope GREGORIE the XIII. and now vsed in many places beyond the Seas. In the fourth limbe are set downe the moneths and dayes of the ordinarie Kalender vsed in England. Next within this, are placed the 12. Signes and degrees of the Zodiacke, that so the place of the Sunne might bee presently knowne for any day of the yeare giuen, or contrariwise, that the day of the Moneth might be readily found by the place of the Sunne. After this, followeth the sixt limbe conteyning the 32. Windes or points of the Compasse, with letters representing the names now in vse amongst English Marriners. The seuenth and last limbe next the innermost edge of the Horizon, is deuided into 360. degrees with figures set to eue∣ry tenth degree, beginning from the points of East and West, and ending at North and South; that so the number of any degree of the Horizon might bee the easilier knowne: Which Circle appeareth

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most plainely to them that are in a plaine Champi∣on Countrie, or vpon the Sea close by the water in a cleare calme day.

CHAP. III. The vses of the Horizon.

1. IT deuideth the vpper and visible part of the Heauens from the nether halfe that is hidden out of our sight.

2. It sheweth partly the difference of a right and oblique Sphaere, for when this circle and the Equi∣noctiall, crosse each other at the right Angles, it is said to be a right Sphaere, otherwise when they make oblique Angles one with another, it is called an ob∣lique Sphaere.

3. In an oblique Sphaere this circle seuereth those Starres which neuer rise nor set, but are alwayes ey∣ther aboue or beneath the Horizon, from such Starres as rise and set in euery 24. houres. For all the Nor∣therly starres that are no further distant from the North pole, then the North pole is from the Hori∣zon, doe neuer set, but are alwayes aboue the Hori∣zon: And contrariwise, those Starres that bee about the South pole, no further distant from it then it is from the Horizon, doe neuer rise, but are alwayes hid∣den out of sight vnder the Horizon.

4. In respect of this circle, the Sunne, Moone and Starres, or any other part or point of the Heauens, are sayd to rise or set: For when they come vp from vnder the Horizon, they are sayd to rise; otherwise when they goe from aboue the Horizon downe vn∣derneath the same, they are sayd to set.

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5. And hereof it commeth that the ascendent, and descendent are found by this Circle: for that part of the Ecliptick that is at the East part of the Horizon arising, is the Ascendent; and the point opposite to this at the West part of the Horizon, may be called the Descendent.

6. This Circle partly sheweth the difference of as∣cention of any part or point of the Heauens.

7. In this Circle we reckon how farre the Sunne, the Moone, or any Starre, or point of Heauen, ariseth from the point of due East.

8. The Horizon determineth the time of the arti∣ficiall day and night: for we call the time w••rein the Sunne abideth aboue the Horizon, an artificiall day: And the time that he continueth vnder the Horizon, is the artificiall night.

9. This Circle sheweth the reason of the equality of artificiall dayes and nights, in a right Sphaere: and of the inequality of them in an oblique Sphaere. For in a right Sphaere, the Horizon deuideth all the pa∣ralels of the Sunne or Circles of the naturall dayes, into equall parts: But in an oblique Sphaere, it deui∣deth them into vnequall parts.

10. By meanes of this Circle, wee know what Starres, and what Eclipses, Coniunctions, or other aspects of the Planets may bee seene in our Hemi∣sphere at any time.

11. From the Horizon is measured the twilight: For in the morning the Sunne being vnder the Hori∣zon about 18. degrees of the verticall, Circle, the twi∣light beginneth: And when the Sunne is so much vn∣der the Horizon at Euening, the twilight endeth.

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12. This Circle is of especiall vse in Geography, for from it wee begin to account the eleuation of the Pole, and of the Equinoctiall circle, whereby the La∣titude of any place is knowne.

13. In Astrologie for erecting a figure, this Cir∣cle sheweth the beginning of the first and seauenth Houses.

CHAP. IIII. The description of the Meridian.

NExt the Horizon, succeeds the Meridian stan∣ding vpright on edge, and crossing the Horizon at right angles in the points of North and South. This circle is diuided on both sides at the inner edge into 360▪ Degrees, with figures set to euery tenth de∣gree, beginning at the Equinoctiall, and ending at the Poles with 90. and beginning also at the Poles, and ending at the Equinoctiall with 90. The num∣bers beginning at the Pole, serue to set the Sphaere readily to any eleuation desired. The other numbers beginning at the Equinoctiall, shew presently the de∣clination of any degree of the Zodiacke, or of any point assigned in the Sphaere, one quarter of the Me∣ridian on eyther side thereof from the Equinoctiall to both Poles, sheweth the Climates, and the quantities of the longest dayes.

CHAP. V. The vses of the Meridian.

1. IT deuideth the World into two halfes or He∣misphaeres: that is, the East and the West hemisphaeres. The Easterly hemisphaere is all that

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part of the world which is on the East-side of the Meridian, and the other halfe may bee called the West hemisphaere.

2. It sheweth the North and South parts of the world, for the two intersections of the Meridian with the Horizon, shew the very points of North and South. The South point is that which is directly vn∣der the Sunne at noone: And the point right ouer a∣gainst this, is called the North-point.

3. It deuideth the arches of the Equinoctiall, and of all his Paralels, into two equall parts both aboue and beneath the Horizon.

4. And therefore it deuideth the artificiall Day and Night into two equall parts.

5. And consequently, it sheweth midday and mid∣night.

6. In an oblique Sphaere it serueth in stead of a right Horizon (that is) an Horizon that maketh right angles with the Equinoctiall.

7. Therefore the Astronomers begin their ac∣count of times (which are measured by the equall motion of the Equinoctiall) from the Meridian: the principall of which times, is the naturall day which is vsually begun from midday, or mid∣night.

8. This Circle sheweth the highest and lowest heights of the Sunne and Starres, which is most ma∣nifest in those Starres that are alwayes aboue the Ho∣rizon. These heights are called the Meridian alti∣tudes of the Sun or Starres, which heights are chiefe∣ly obserued by Astronomers and Nauigators with great diligence.

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9. In this Circle, wee obserue the distance of the Tropickes, and the greatest obliquitie of the Zodi∣acke.

10. In this Circle, wee obserue and count the La∣titudes of places, the height of the Pole, and of the Equinoctiall. For the height of the Pole or Equino∣ctiall, is nothing else but the arch of the Meridian contained betweene the Pole or Equinoctiall and the Horizon. The height of the Pole is alwayes equall to the Latitude of the place. The height of the Equino∣ctiall is equall to the Complement of the Latitude and therefore it being substracted out of 90. 〈◊〉 shall remaine the height of the Pole.

11. The Meridian sheweth the longit••• of pla∣ces in Geographie.

12. In the Meridian, are measured the bredth of the Zones and Climates.

13. This circle in Astrologie, sheweth the highest and lowest parts of Heauen, which are the beginnings of two principall Houses: that is, the fourth and the tenth houses.

CHAP. VI. The description of the Houre-circle, and Poles.

THe little Circle fastned to the Meridia• is called the Houre-circle, which is deuided into 24. e∣quall parts, signifying and representi•• vnto vs so many equall houres, whereof both the 〈◊〉 houres are fixed iust vpon the Meridian, becaus•• •hen the Sunne commeth to the Meridian, it is iust twelue a clocke: the vpper XII. serueth for the Day; and the other XII. beneath serueth for the Night.

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The Index, or the Painter in forme of an Arrow, fastned vpon the Pinne that commeth through the midst and Center of this circle, is made to shew and point out the said houres as need shall requite, in the vse of the Sphaere.

The vse of this houre Circle shall be shewed here∣after, when we shall speake of the common vse of ma∣ny circles of the Sphaere together. And these two Circles (that is, the Meridian and Horizon) are cal∣led immoueable, because they keepe themselues al∣wayes, and in all places ouer the same parts of the Earth; where as all the rest (conteyned within these two) moue round about altogether with one motion in the space of foure and twenty houres.

This motion (being common to the whole Hea∣uens) is made about two Points or Poles, represen∣ted in this Sphaere, by the two Wyre pinnes about which the Sphaere is turned; whereof the one that commeth through the middest of the little Circle fastned to the Meridian (which wee call the houre Circle) representeth vnto vs the Pole Articke or the North Pole: the other because it is opposite to this, is called the Antartick pole, that is the right opposit, to, or right ouer against the North pole, which is al∣so the South pole.

CHAP. VII. Of the Equinoctiall Circle.

THat Circle which compasseth about the midst of the Sphaere,* 4.1 and is euery where of equall di∣stance from both Poles, is called the Equinoctiall circle, or the Equator; either because it is equally

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distant from both Poles of the world; or ••se because the Sunne comming vnder this Circle maketh equa∣lity of dayes and nights throughout the world.

It is deuided at the vtmost edge, or both sides thereof into 360. Degrees, with figures 〈◊〉 to euery tenth degree, beginning at the beginning of Aries, and proceeding Eastwards, till you become about to the same point againe.

This Circle hath many vses.

1. It is the measure of the first 〈◊〉. For this onely amongst all the Circle of the Sphaere is moued equally both in a right and 〈…〉 Sphaere, because • alone being perpendicular to the 〈…〉 world, about which the Sphaere is equally turned, is deuided into two haltes by euery Horizon in the same points.

2. It is the measure of time; because it measureth the quantitie of the artificiall and naturall dayes, of which Moneths and Yeares are made: It measureth also the quantitie of Houres and of other times which the Sunne maketh going vnder the Zodiacke. And therefore the degrees of the Equinoctiall are called tempora (that is) times.

3. It sheweth the two Equinoctiall points in the Eclipticke, cutting the Ecliptick in two places, which are the beginnings of Aries and Libra: and the Sun when hee commeth to those two points, is equally distant from both Poles of the World, and maketh equalitie of dayes and nights in all places; which hap∣neth in our time about the 10. or 11. day of March, and the 13. or 14. of September.

4. The irregularitie of the Zodiacke, and of all

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the Signes and degrees thereof, is measured by this Circle. For seeing the most part of the apparences of the first motion are referred to the Zodiacke, which is not turned about his owne Poles, but about the Poles of the Sphaere, and therefore must needs bee vnequally turned about; it was needfull that this ine∣qualitie should be ruled and measured by some other equall motion.

5. It deuideth the Sphaere into two halfes (which they call Hemisphaeres) that is, into the North halfe or hemisphaere, wherein is the North pole, and into the South hemisphaere, wherein is the South pole.

6. So it deuideth the Zodiacke into the North halfe, and the South halfe; or into the North signes, and the South signes.

7. From this Circle are numbred the declinations of the Starres, and of the degrees and parts of the E∣clipticke, and of any other point of Heauen.

8. And in this Circle are counted the right ascen∣tions of the same Degrees and Starres, &c. For the right ascention of any starre or point of the Heauens, is nothing else but the Arch of the Equinoctiall circle contained betweene the beginning of Aries and the Meridian, the same Starre or point being first brought vnder the Meridian.

9. In the Equinoctiall is counted the ascentionall difference and the oblique Ascention and Descention of any point of Heauen. And from the same Circle is reckoned the distance of the Sunne rising from the true East point. For the oblique ascention or descen∣tion is nothing else but the arch of the Equinoctiall, contained betweene the beginning of Aries, and that

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point of the Equinoctiall Eastwards, which ariseth or setteth together with the Starre or point that is giuen, in an oblique Sphaere. And the difference ascentio∣nall or descentionall is nought else but the arch of the Equator, whereby the right and oblique ascention or descention of a Starre, or any other point in Heauen doe differ each from other. The distance of the sunnes rising from the true East point (which in Latine is called Amplitudo ortiua,) is the arch of the Horizon contayned betweene the Equinoctiall and the paralell of the Sunne, or his Center when he riseth.

10. In Geographie wee count the Longitudes of places in this Circle; and from it we reckon the Lati∣tudes, in the Globe of the earth, and in Maps, and sea Charts. For the longitude of a place is nothing else but the arch of the Equinoctiall circle contayned be∣tweene two Meridians, whereof one goeth by the ca∣nary Ilands, and the other by the place that is giuen, And the latitude of a place is the arch of a Meridian contayned betweene the Equinoctiall, and the Zenith of the place that was giuen.

11. In Dialling this Circle is of especiall vse. For by meanes of it the spaces of the houres are deuided in all kindes of Dials, horizontall, erect, direct, decli∣ning, inclining, reclining, &c.

12. In Astrologie the twelue Houses are set out by the equall diuisions of this Circle into twelue parts, according to the way deuised by Regiomontanus, which way is commonly called rationall or reasona∣ble. And this Circle gouerneth the directions, where∣by things to come are artificially fore-told.

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CHAP. VIII. The description of the Zodiacke.

THe great broad Circle that compasseth about the Sphaere obliquely, comming nearer the Pole of the Sphaere in one place then in another, is called the Zodiacke.

Round about through the middest of this Circle, is drawne the Circumference commonly called the Eclipticke line, deuiding the whole Sphaere, and the whole bredth of the Zodiacke throughout, into two equall parts.

In this Sphaere there are represented vnto vs two Eclipticke lines. The one may be called the middle, or fixed Eclipticke, which keepeth alwayes the same distance or obliquitie from the Equinoctiall. The o∣ther may bee called the true or moueable Eclipticke, because it maketh not alwayes the same angles of intersection with the Equator, but sometimes grea∣ter, sometimes lesse. For the greatest obliquitie of the Zodiacke, which not long before Ptolomees time was obserued to bee 23. Degrees and 52. Minutes; in Copernicus his time, was hardly found to exceed 23. degrees 28. minutes, according to his obseruati∣on, and therefore hee thought that the difference be∣tweene the greatest and least obliquitie of the Zo∣diacke, was 24. Minutes: and the middle or meane obliquitie betweene both these, to bee 23. Degrees 40. Minutes.

The manner of the variation of this obliquitie may in some sort bee shewed by this Sphaere, if we suppose the fixed Eclipticke drawne round about through

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the middest of the Zodiack to be 23. degrees 40. min. distant from the Equinoctial at the beginning of Can∣cer and Capricorne: and the moueable Eclipticke (fast∣ned as it were vpon two Poles at the beginning of A∣ries and Libra, and so hauing alwayes the same points of intersection with the middle Eclipticke and Equi∣noctiall) to bee moued vp and downe aboue and be∣neath the middle Eclipticke, by the space of 12. Mi∣nutes at the beginning of Cancer and Capricorne: and this motion to finish his reuolution once in 3432. Iu∣lian yeares.

The bredth of the Zodiacke is bounded by the greatest latitudes of the Planets, especially of Venus and Mars, which sometimes hath almost 7. degrees of latitude.

The Zodiacke is diuided by the Equinoctiall into two semicircles.

The one aboue the Equinoctiall is called the Nor∣therly semicircle: the other halfe beneath the Equi∣noctiall, is the Southerne semicircle of the Zodiacke.

So long as the Sunne moueth vnder the first of these semicircles, the dayes are longer then the nights, otherwise they are shorter.

Each of these semicircles is againe deuided in∣to two parts, and so the whole Zodiack into foure quarters: the first from Aries to Cancer, may be cal∣led the vernall or Spring-quarter, which in this Sphaere is also shewed by the word Ver (signifying the Spring:) The next from Cancer to Libra, the Summer quarter, wherein is written the word Ae•tas signifying the Summer. The 3. from Libra to Capri∣corne, is the Haruest quarter, wherein you shall finde

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in this Sphaere the word Autumnus which signifieth Autumne or Haruest. The fourth and the last, from the beginning of Capricorne to Aries, is called the win∣ter Quarter, which in this Sphaere is shewed by this word Hiems, which signifieth the Winter. And these foure quarters of the Zodiacke are thus called by the names of the Quarters of the yeare, because the Sunne mouing vnder those quarters of the Zodiacke, maketh those foure Quarters of the yeare. Euery one of these quarters of the Zodiacke is againe deuided into three parts, and so the whole compasse of the Zodiacke in∣to 12. which are called the 12. Signes, whereof euery one contayneth 30. Degrees in length from West to East, and is in bredth equall to the bredth of the Zo∣diacke. These Signes, and the Zodiacke it selfe haue their beginning from that common meeting, or cros∣sing of the Eclipticke, and the Equinoctiall, where the Eclipticke beginneth to arise aboue the Equino∣ctiall towards the North pole: and they are called by these names; Aries, Taurus, Gemini, Cancer, Leo, Vir∣go, Libra, Scorpio, Sagitarie, Capricorne, Aquarie, Pisces. That is to say, The Ramme, the Bull, the Twinnes, the Crab, the Lyon, the Virgin, the Ballance, the Scorpion, the Shooter, the Goat, the Water-pourer, the Fishes. And they are signified by these Cha∣racters, ♈ ♉, ♊, ♋, ♌, ♍, ♎, ♏, ♐, ♑, ♒, ♓. This deuision of the Zodiacke into 12. Signes and of euery signe into 30. Degrees, nature it selfe seemeth to haue shewed by the motions of the Sun and Moone. For in what time the Sunne moueth once about the whole compasse of the Zodiacke, the Moone maketh twelue reuolutions through the same. Therefore as

Page 15
the time of a yeare is deuided into 12. Moones, so the Zodiacke is deuided into 12. Signes: And as euery Moneth contayneth 30. dayes, so euery signe is deui∣ded into 30. parts, which they call Degrees, which signifieth as much as steps, because the Sunne step∣peth, or goeth forwards almost so much as a degree in euery day, from the West Eastwards vnder the Zodiacke.

The Zodiacke is otherwise also deuided into two semicircles, the one (from Capricorne to Cancer) ascen∣ding, because that so long as the Sunne or any of the Planets are in that semicircle, they still ascend and rise higher and higher aboue the Horizon. The other se∣micircle of the Zodiacke, from Cancer to Capricorne, is called descending, because the Sunne or Planets being in that semicircle, come downe euery day low∣er then other.

The 12. Signes are by the Astrologians diuersly deuided, first into chiefe, meane, and common signes. The chiefe signes (which are also called Cardinall, that is the principall signes) are Aries, Cancer, Libra, and Capricorne, because they come next after the prin∣cipall points of the Zodiacke, that is, the two Equi∣noctiall points at the beginnings of Aries, and Libra; and the two solstitiall points of Cancer and Capricorne. The meane signes (which are also called fixed) are Taurus, Leo, Scorpio, and Aquarius. They are called meane, because they are placed betweene the chiefe or principall, and the common signes. They are cal∣led fixed signes, because that when the Sunne is in those signes, wee finde a more perfect temperature of the Ayre, then when he is in the other signes.

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The common signes (which are also called double bodyed) are Gemini, Virgo, Sagitarie, and Pisces. They are called common, because they take part of the na∣ture of the fixed signes going before them, and of the Cardinall signes following after them. They are cal∣led double bodied, by reason of their Images, as they are imagined in the eight Sphaere, which are com∣pounded of two bodies: For there be two Twinnes; and the Virgin holdeth an eare of corne in her hand; Sagitarie is made of a Man and an Horse; and there are two Fishes. The placing, and nature of these signes brought in this diuision.

The Astrologians also deuide the 12. Signes into foure trigons of triplicities, so called because they are distant the third part of a Circle, one from another. The first triplicitie contayneth Aries, Leo, and Sagita∣rius; and is called the fiery trigon, or triplicitie: The second triplicitie contayneth Taurus, Virgo, and Ca∣pricorne; and is called the earthly trigon. The third triplicitie contayneth Gemini, Libra, and Aquarius; and is called the ayrie trigon. The fourth triplicitie contayning Cancer, Scorpio, and Pisces; is called the watrie trigon. Nature it selfe is the cause of this diui∣sion of the Signes also. For into these Trigons of the signes, shee hath distributed the Coniunctions of the three superiour Planets: especially the coniunctions of Saturne and Iupiter, which the Astrologians call great coniunctions. For examples sake, if there bee a great coniunction in Aries, the same shall be twenty yeares after in Sagitarie, and other twenty yeares after in Leo; and after as many more yeares, it returneth a∣gaine into Aries. The reuolution of one Trigon con∣tayneth

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almost 200. yeares, after which time the same great conjunctions remoue into the next trigon.

CHAP. IX. The vse of the Zodiack.

1. THe Zodiack is the measure of the second motions, as the Equinoctiall is the measure of the first motion.

2. For in this Circle wee reckon the longitudes, and from it we count the latitudes of all the Starres. For the longitude of a Starre is nothing else but the arch of the Ecliptck conteyned betweene the begin∣ning of Aries, and the circle of the Starres latitude. And the latitude is the Arch of a great circle, drawne by the poles of the Ecliptick, conteyned betweene the Starre and the Ecliptick.

3. According to this circle, the whole Heauen, yea, the whole world is deuided into twelue Signes. Whereof it commeth that because of this Circle, as∣well the fixed, as the wandring Starres which we call Planets, yea, and those Starres also that appeare of a sudden, as blazing Starres or Comets, and other Meteors, are said to be in this or that signe; and that three manner of wayes.

First, to be in a signe, is to be vnder some one of the 12. parts of the Ecliptick. Thus the Starres which are vnder the Ecliptick, but especially the Sunne which runneth alwayes vnder it, are said to be in the Signes.

Secondly, because the Zodiack hath latitude, those Starres are said to be in a signe, which although they be beside the Ecliptick, yet are vnder the Zodiack, and so any of the other Planets, which for the most

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part wander beside the Ecliptick, may be said to bee in some signe.

Thirdly, if we vnderstand six great Circles to bee drawne by the beginnings of the twelue signes, and by the poles of the Eclipticke; by these circles the whole heauen (or rather the whole world) is deuided into twelue parts, which with a generall name are cal∣led signes: Thus all the Starres aswell fixed as Planets and Comets, which are without the Zodiacke in any of these parts, may be said to be in some signe.

4. In this circle are noted the degrees of the signes, with which the Starres doe rise and set, as well in a right as in an oblique Sphaere. For because this circle is the chiefest, all Caelestiall apparances (or at least the most part of them) are referred vnto it, and not vnto the Equinoctiall. But the Equinoctiall measu∣reth the times of their risings and settings.

5. The obliquitie of the Ecliptick is the cause of the inequalitie, aswell of naturall dayes in both Sphaeres, as of artificiall dayes in an oblique Sphaere. For seeing it is moued vnequally, because it is moued vpon other Poles then his owne, the Sunne which is the author, and maker of times mouing vnder it, must needs make vnequall dayes.

6. The chiefe times are defined by this circle, as the time of a yeare, by the motion of the Sunne; the time of a moneth by the motion of the Moone, through the whole compasse of this circle. Also the foure quar∣ters of the yeare, Spring, Summer, Autumne, and Winter, whereto may be added Plato his great yeare, which is the time wherein the fixed Starres make one reuolution about the axtree and poles of the Zodi∣ack,

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if God would haue the world to last so long.

7. The Eclipticke line sheweth the places, and times of the Eclipses: For the Sunne and Moone, are Eclipsed onely vnder it, or neere vnto it.

8. As the description of the Tropicks dependeth on the obliquitie of the Eclipticke, so the polar Cir∣cles are described by the Poles thereof.

9. Hereof it commeth, that by reason of the same obliquitie, the Zones and Climats are set forth and bounded.

10. This Circle is of especiall vse in Astrologie, for it distinguisheth the points of the 12. Houses, and in it the Aspects and configurations of the Pla∣nets are obserued. The chiefest judgement aswell in casting Figures as in reuolutions and directions is ta∣ken from this circle.

CHAP. X. The description of the two Colures.

THe two circles crossing each other at right An∣gles in the poles of the Sphaere, are called the Colures: whereof the one that passeth by the com∣mon meeting of the Eclipticke and Equinoctiall, is called Colurus aequinoctiorum, that is the Equinoctiall Colure, or the colure of equall dayes and nights. The other passing by the poles of the Eclipticke, and the Solstitiall points, is called Colurus solstitiorum, the Solstitiall colure, or colure of the Sunne-stan∣dings.

Vses common to both Colures.
1. By meanes of these two Colures, all the moua∣ble circles of the materiall Sphaere are framed toge∣ther,
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that so they might be turned about, like as the whole Heauens are moued.
2. The Poles are fastened in the common meeting of these two Circles: and the Poles are also shewed by the same common meetings.
3. They shew the foure principall points of the Eclipticke; that is, the two Equinoctiall, and the two Solstitiall points.
4. These circles shew those points of the Eclip∣ticke, wherein the Sunne is either equally distant from both poles of the Sphaere, or commeth neerest to either of them: In which points the Sunne maketh the dayes longest or shortest, or of a meane length betweene both these in an oblique Sphaere.
5. They deuide the Ecliptick into foure quarters, in which the Sunne maketh foure quarters of the yeare, the Spring, the Summer, Autumne, and Winter.
6. They deuide the Ecliptick and Equinoctiall in∣to such foure quarters, as in a right Sphaere doe rise together in equall time.

CHAP. XI. Vses of the Equinoctiall Colure.

1. THe section of this Circle with the Ecliptick; sheweth the Equinoctiall points, wherein the Equinoctiall and the Eclipticke doe deuide and crosse each other. In which points the Sunne maketh equality of dayes and nights throughout the whole world: whereof this circle is also called Colurus Aequinoctiorum; that is, the colure of equall dayes and nights, or the Equinoctiall colure.

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2. It deuideth the Eclipticke into the North and South halfes.

3. It deuideth the Signes wherein the Sunne maketh the dayes longer then the nights, from those signes wherein the dayes are made shorter then the nights.

4. It sheweth which halfes of the Eclipticke and Equator, doe arise together in equall time in an ob∣lique Sphaere.

5. It sheweth the two high Sunne-standings in a right Sphaere, in the time of which Sunne-standings, the Sunne passeth by the Zenith.

CHAP. XII. Vses of the Solstitiall Colure.

1. THe common meetings of this circle with the Ecliptick, shew the Solstitiall or Tropi∣call points; in which points the Sunne seemeth to stand, and then returneth backe againe: for which cause this circle is called the Colure of the Sun-stan∣dings. These points are called tropicall (which is as much to say as turne-points, or points of returne) be∣cause that when the Sunne going alwayes vnder the Eclipticke commeth to these points, which are fur∣thest distant from the Equinoctiall circle, it returneth againe towards the same circle. But they were called Solstitiall or Sun-ding points, because that whilest the Sunne is about those points, the difference of the Sunnes returning is (for certaine dayes) insensible. Hereof the Sunne is said to make his station, or to stand, when he commeth to either of those points. They that dwell without the Tropickes, haue two

Page 22
sunne-standings, that is the Summer sun-standing, or high sun-standing (when the Sunne in Summer time is at the highest, and next vnto our Zenith being in the beginning of Cancer) and the winterly, or low sun-standing, when the Sunne in Winter time is low∣est in the Meridian, and furthest from our Zenith. But they that dwell within the Tropicks (by a certaine si∣militude taken from our sun-standings, wherein the Sunne is either highest or lowest) are said to haue foure sun-standings; that is two high sun-standings, when the Sunne passeth by their Zenith (the highest point in the Heauens) which hapneth twice euery yeare in two places, equally distant from the begin∣nings of Cancer and Capricorne: and two low sun-stan∣dings, when the Sunne is in the beginning of Cancer and Capricorne.

2. In this Circle by the arch conteyned betweene the Equator and Eclipticke, we measure the greatest declination of the Sunne, or obliquity of the Eclip∣ticke, which in Ptolomees time was 23. degrees 51. mi∣nutes, and one third part of a minute. But euer since that time it hath beene found by obseruation to de∣crease; so as in this our age, it is no more then 23. de∣grees and one halfe, or little more: Notwithstanding Copernicus thought that the greatest obliquity was 23. degrees 28. minutes.

3. It sheweth the places of the Eclipticke, in which the Sunne (comming neerest to our Zenith) maketh the artificiall day longest; or going furthest from the same point, maketh the same shortest.

4. It deuideth the Zodiacke into two halfes, the one ascending, and the other descending.

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5. Hereby also the signes are distinguished, which doe rise rightly, and which rise obliquely in an ob∣lique Sphaere. For the descending halfe riseth right∣ly, and the ascending halfe riseth obliquely.

6. So the points of the Eclipticke are shewed by this Circle, wherein the greatest difference of right and oblique ascensions happeneth. It distinguisheth those signes in which when the Sunne moueth, the ar∣tificiall dayes are increased, and the nights decrease; from those signes wherein the dayes are diminished, and the nights increase.

7. In this circle are the bredths of the Zones boun∣ded; for the obliquity of the Eclipticke doubled, sheweth the bredth of the torrid or burnt Zone: the distance of the poles of the Ecliptick, and of the Poles of the Equator, shew the bredth of the cold or frozen Zones; and the other two Arches remaining, shew the bredths of the temperate Zones.

CHAP. XIII The Description of the two Tropickes.

THe two smaller Circles Equidistant in all places from the Equinoctiall, and comming vnder these Solstitiall points of the Eclipticke on both sides, are called the Tropicks, that is circles of returne.

And they are so called, because that when the Sun commeth to them, it beginneth to returne backe a∣gaine towards the Equinoctiall circle. Or else they may be so called, because they are described by the turning about of the Tropicall points of Cancer and Capricorne. They are also called solstitiall Circles; that is Circles of the sun-standings; because that by

Page 24
reason of the insensible alteration of the declination of the Ecliptick, for some space both before, and after the Tropicall points, the Sunne (in respect of his Me∣ridian altitudes, or in respect of the motion he hath towards the North or South, by reason of the obli∣quity of the Eclipticke) seemeth to stand (as it were) for certaine dayes in those places.

There be two Tropicks, the Tropick of Cancer, and the tropicke of Capricorne.

The tropick of Cancer, toucheth the Ecliptick in the beginning of Cancer, which is the most northerly point of the Ecliptick: or it is the Tropick described in the first mouable Sphaere, by the Summer solstitiall point.

This circle is called the Tropick of Cancer, be∣cause it toucheth the Ecliptick in the beginning of Cancer.

It is also called the Summer Tropick, and the Tro∣pick of the Summer sun-standing, because that when the Sunne commeth to it, the Summer beginneth. It is called the North tropick, because it is in the North part of the world: and the Circle of the high sunne-standing, because the Sunne comming to it, is highest in the Meridian, and next vnto our Zenith which dwell in the North part of the world, without the Tropicks. The Tropick of Capricorne is the Tro∣pick which toucheth the Ecliptick in the first point of Capricorne. It is called the Tropick of Capricorne, be∣cause it toucheth the Ecliptick in the beginning of Capricorne. It is called the winter Tropicke and Tro∣pick of the Winter sun-standing, because the Sunne commeth to it in Winter.

Page 25
It is also called the circle of the lowest Sunne-stan∣ding, because that when the Sunne commeth to this Tropicke, it is furthest distant from our Zenith, and hath his lowest height in the Meridian.

CHAP. XIIII. Vses of the Tropickes.

1. THe Tropicks shew the Tropicall, or Solsti∣tiall points of the Eclipticke: that is, the points wherein the Sunne seemeth to stand, and be∣ginneth to returne backe againe.

2. They bound out the greatest declinations of the Sunne, which in our times is about 23. degrees and an halfe.

3. Therefore they doe also bound out the obliqui∣ty of the Ecliptick, for they are the bounds of the Sunnes way, beyond which the Sunne goeth not at any time.

4. The Sunne comming to either of these circles, is either neerest, or furthest distant from our verticall point.

5. In an oblique Sphaere, they measure out the shortest, and longest artificiall day and night.

6. The Tropicks (aswell in Heauen as in Earth, conteyne betwixt them the Torrid Zone, and sepa∣rate it from the temperate.

CHAP. XV. The Polar Circles.

THe two smallest circles that are next about the poles of the Sphaere, are called the polar circles. They are drawne by the poles of the Eclipticke,

Page 26
and are euery where Equidistant from the Equinocti∣all, and from the poles of the Sphaere.

They are called polar Circles, either because they are neere the poles of the Sphaere, or else because they are described by the motion of the poles of the E∣clipticke.

And therefore there be two polar Circles, that is, so many as there are poles of the Ecliptick: the Polar circle Artick, and the Polar Antartick.

The Articke polar circle, is that which passeth by the North pole of the Ecliptick, or which is descri∣bed by the North pole of the Ecliptick being carried about with the motion of the first moueable Sphaere.

The Antartick polar circle, is that which goeth by the South pole of the Eclipticke, being described with the first motion by the Antartick pole of the Ecliptick.

The distance of these polar Circles from the poles of the Sphaere, is equall to the distance of the tropicks from the Equinoctiall, which in our time is about 23. degr. and an halfe: for so much as is the obliquity of the Zodiack (whereto the distance of the Tropicks from the Equinoctiall is alwayes equall) so much are the poles of the Ecliptick distant from the Poles of the world.

CHAP. XVI. Vses of the Polar Circles.

1. THe Polar Circles shew the poles of the Zo∣diack, and shew their distance from the poles of the Equinoctiall.

2. The temperate Zones are bounded by these

Page 27
polar circles; for the Articke circle boundeth the North side of the North temperate Zone; and the Antartick circle boundeth out the South side of the South temperate Zone.

3. The Polar circles separate the temperate Zones, from the cold Zones which they compasse round about, and inclose within them.

Therefore the foure lesser circles, that is the two Polar circles, and the Tropicks, deuide Heauen and Earth, into fiue Zones.

CHAP. XVII. Of the Zones.

A Zone is a space of Heauen, or Earth, con∣teyned betweene two of the smaller Circles; or inclosed within the compasse of either Polar circle.

They are called Zones (that is as much to say as girdles) because they compasse about Heauen or Earth like a girdle.

The Zones are deuided by auncient Writers into two kindes; that is into temperate, and vntemperate Zones.

A temperate Zone is the space of Heauen or earth, conteyned betweene either of the Tropicks, and the next Polar circle.

There be two temperate Zones; the one North, the other South.

The North temperate Zone is conteyned be∣tweene the Tropicke of Cancer, and the Artick polar circle.

The South temperate Zone is that which is con∣teyned

Page 28
betweene the Tropicke of Capricorne, and the Antartick polar circle.

They are called temperate Zones, because they haue a better temperature of the ayre for the most part, and more meer for habitation, then the vntem∣perate Zones. The bredth of eyther temperate Zone is alwayes equall to the complement of the distance of the Tropicks, and therefore in this age is about 43. degrees, that is 2580. English miles.

There be two kinde of vntemperate Zones, the one exceeding in heat, the other in cold, for the most part.

The hot vntemperate Zone, (called also the Tor∣rid; that is, the burnt or broyled zone) is that space of Heauen or Earth, which is conteyned betweene the tropicks.

It is called the burnt Zone, because that by reason of the Sunnes continuall going ouer that zone; and casting his beames directly downe thereupon, it is scorched with ouer-much heat, and is not so meet to be inhabited as the temperate zones.

The bredth of this Zone is alwayes equall to the obliquitie of the Zodiack, or greatest declination of the Sunne, doubled; which in our time is about 47. degrees, that is 2820. English miles.

The cold or frozen zones, are the spaces of Heauen or earth, conteyned within the Polar circles.

There be two cold zones, the one North, contey∣ned within the compasse of the Articke circle: the other South, conteyned within the compasse of the Antartick Polar circle.

These zones exceed in cold, because they want

Page 29
the sight of the sunne for a great part of the yeare, and when the Sunne appeareth vnto them, his beames fall so obliquely vpon them, that they can (in all like∣lyhood) receiue but small heat thereby for the most part.

The bredth of these Zones is measured from the Poles of the world to the Polar circles, and therefore must alwayes bee so much as the Polar circles are di∣stant from the Poles: that is, in our age about 23. Degrees and a halfe, which make 1410. English miles.

CHAP. XVIII. The difference of Shadowes that the Sunne maketh in these Zones.

THey that dwell in the torride Zone, doe cast their shadowes which the Sunne maketh at noone (which we may therefore call their noone shadowes) both towards the North, and towards the South: towards the North, when the sunne is betwixt their zenith and the south point of the Horizon; and to∣wards the South, where the sunne is betweene their Zenith and the North.

For seeing the zenith of them that dwell in that Zone is betweene the Tropicks, the sunne must needs bee sometimes Northwards from their zenith, and so make a south shadow: and sometime South∣wards, and then make a north shadow. For which cause they that inhabite this Zone are called Am∣phiscij; that is, such as cast their noone shadowes on both sides.

But they that dwell in the temperate Zones, are

Page 30
called Heteroscij; that is, such as cast their shadowes at noone, one way onely. For they that dwell in the North temperate Zone, haue the Sunne alwayes at noone from their Zenith Southwards, and therefore must needs alwayes cast their noone shadowes Northwards. Whereas contrariwise they that inha∣bit the South temperate Zone, hauing the Sunne at noone alwayes Northwards from their Zenith, must needs haue their shadowes at noone, alwayes to∣wards the South.

And they that are in the cold Zones, are called Periscij; that is, such as cast their shadowes round about them. For seeing the Sunne continueth eue∣ry yeare for certaine dayes together, alwayes aboue their Horizon, and therefore moueth round about them without setting: it must needs bee, that their shadowes also are carried round about them, falling towards all parts of the world in the space of 24. houres. {inverted ⁂}

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THE SECOND PART. Of the vses of the vppermost SPHAERE, and of the Circles thereof joyntly. (Book 2)

PROP. I. To rectifie the Sphaere to the Latitude. &c.

FIrst finde by obseruation, or other∣wise the height of the Pole, or La∣titude of that place for which you would rectifie the Sphaere. Then (by turning about the Meridian of the Sphaere; lift vp or put downe the North Pole of the Sphaere (about which the houre circle is fastened) till the arch of the Meridian from the North part of the Ho∣rizon vpwards vnto the Pole, be iust so many degrees as the eleuation of the Pole or latitude of the place was found to be: for so haue you the Sphaere duly rectified.

As for example, the Latitude of the Citie of London is 51. degrees and 32. minutes, therefore if you lift vp the North Pole of the Sphaere, aboue the North part of the Horizon, so many degrees and minutes you shall haue your Sphaere rectified for that place.

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PROP. II. To know the place of the Sunne; &c.

LOoke the day of the moneth (for which you de∣sire to know the place of the Sunne) in the Hori∣zon, and see what signe and degree of the Zodiacke vpon the Horizon answereth thereto; for there haue you the place of the Sunne.

Take for example the 25. of December: looke this day therefore in the Horizon, and you shall finde answerable thereto 13. degrees, and about 40. mi∣nutes of Capricorne, which is the place of the Sunne at that time.

PROP. III. To know the declination of the Sunne, &c.

BRing the point whose declination you desire to know, vnto the Meridian of the Sphaere, and look what number of degrees and minutes of the Meridi∣an is conteyned betweene that point, and the Equi∣noctiall, for so much is the declination.

As if you would know the declination of the 10. degree of Taurus, bring that degree to the Meridian, and you shall finde the arch of the Meridian between that degree and the Equinoctiall, to be 14. degrees and about 51. minutes.

PROP. IIII. To know the right ascention of the Sunne, &c.

BRing that point (as before) to the Meridian, and see then how many degrees and minutes of the Equinoctiall are conteyned betweene the beginning

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of Aries and the Meridian: for that is the right ascen∣sion of that point. So you shall finde the right ascen∣sion of the 10. degr. of Taurus to be 37. degr. 35. min. for if you bring that degree of Taurus to the Meridi∣an, you shall finde so many degrees and min. between the beginning of Aries, and the Meridian.

PROP. V. To know the oblique ascension of the Sunne, &c.

SEt the Sphaere to the eleuation of the place for which you desire to know the oblique ascension; then bring the Sunne, Starre, or point whose oblique ascention you would know, vnto the East semicircle of the Horizon, and looke how many degrees and mi∣nutes of the Equinoctiall circle, are conteyned be∣tween the East point of the Horizon, and the begin∣ning of Aries; for so much is the oblique ascension desired: As for example, if you see the Sphaere to the Latitude of London 51. degr. 32. min. and then bring the 10. degree of Taurus to the East part of the Hori∣zon, you shall finde about 19. degrees and an halfe of the Equinoctiall, at the same East part of the Hori∣zon; which is the oblique ascension of that degree of Taurus, for the Latitude of the Citie of London.

PROP. VI. To finde the difference of Ascension.

COmpare the right and oblique ascensions of the Sunne, (or of any point of the Zodiacke) toge∣ther, and subtract the lesse from the greater, for the remainder shall bee the difference of ascension. As for example, the right ascension of the 10. degree

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of Taurus, being found by the 4. Propo. to be 37. de∣grees, 35. min. and the oblique ascention of the same degree at London, by the 5. Prop. 19. degree 30. min. by subtraction of the lesse out of the greater, the dif∣ference shall be found to be 18. degr. and 5. minutes, which is the difference of ascension sought for.

PROP. VII. To finde at what time the Sunne riseth or setteth.

REduce the difference of Ascention into houres and minutes (taking for euery 15 degrees 1. houre, and for euery one degree that remayneth 4. minutes, and for euery minute of a degree 4 seconds) for these houres, minutes and seconds, being added to 6. houres, if the Sunne bee in any of the South signes; or subtracted, if hee be in the North signes, sheweth the time of the Sun-rising. And contrari∣wise, the same houres and minutes subtracted from sixe houres when the Sunne is in the South signes, or added when he is in the North signes, sheweth the the time of the Sunne-setting.

As for example, the Sunne being in the 10. degree of Taurus which happeneth about the 20. or 21. day of Aprill) I would know at what houre and mi∣nute the Sunne riseth, and setteth at London: Ha∣uing therefore found by the former Proposition the difference of ascention to be 18. degr. and 5. minutes I take for 15. degrees thereof one houre, and for the three degr. remaining, 12. minutes of an houre, and for the 5. minutes, 20. seconds of an houre. Which houre, minutes and seconds being subtracted out of 6. houres, because the Sunne is in a North signe,

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there remaineth the time of the Sunnes rising at 4. a clocke 47. minutes, 40. seconds. And adding the same houre, min. and seconds to 6. houres, you haue the time of the Sun-setting that day at 7. a clocke, 12. min. and 20. seconds.

PROP. VIII. To finde the length of the artificiall day or night.

THe artificiall day, is the time conteyned between the Sun-rising and the Sun-setting: and the arti∣ficiall night is the time betweene Sunne-setting and Sun-rising. The length of both these is found after this manner: hauing found the difference of ascen∣sion, and reduced it into houres and minutes (as in the former Proposition) double th•se houres and mi∣nutes, and adde them to 12. houres if the Sunne be in the North signes, or subtract them from 12. houres if the Sunne be in the South signes, for so shall you haue the length of the day: But (contrariwise) sub∣tract the same houres and minutes (being doubled) from 12. houres, the Sunne being in the North signes; and adde them to 12. houres when he is in the South-signes; so haue you the length of the night.

Or else, double the time of the Sun-setting, so haue you the length of the day. And double the time of the Sun-rising, so haue you the length of the right.

As the time of the Sun-rising being found by the former Proposition to be 4 houres 48. minutes after mignight at London, the Sunne being in the 10. degr. of Taurus, by doubling the time of the Sun-rising, the length of the night shall be found to be 9. houres and 36. minutes. And doubling the time of the sun-setting

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that is 7. houres, and 12. minutes, you haue the length of the day, 14. houres; and 24. minutes.

PROP. IX. To know the time of the Sun rising and Sun setting.

THe place of the Sunne being found by the 2. Pro∣position, bring the same to the Meridian, and withall set the point of the Index of the houre circle, to the 12. houre in the same circle: Then bring the place of the Sunne to the Horizon Eastwards; and the point of the houre Index shall shew you in the houre circle, the time of the Sun-rising. But if you bring the place of the Sunne to the Horizon West∣wards, the point of the Index will shew in the houre circle the time of the Sun-setting.

As for example, the Sunne being in the 10. degree of Taurus, bring the same degree to the Meridian, and bring the point of the houre Index also to the Meridian: then (the Sphaere being set to the Latitude of London) bring the same 10. degree of Taurus to the East part of the Horizon, for then the houre Index will shew you in the houre circle, that the Sunne ri∣seth at 4. of the clocke and 48. minutes.

And bringing the same degree to the West semi∣circle of the Horizon, the same Index will shew the time of the Sun-setting to be 7. houres and 12. min. after noone.

PROP. X. To finde the length of the artificiall day or night.

BRing the place of the Sun (being found as before to the East semicircle of the Horizon: set the

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houre Index 12. a clocke in the Houre circle: turne about the Sphaere from the East Westwards, till the place of the sunne come to the Horizon, and marke how many houres the Index hath runne ouer vpon the Houre circle in the meane time, for so much is the length of the day.

And to finde the length of the night: Bring the place of the sunne to the West semicircle of the Ho∣rizon, and set the Index to 12. a clocke as before; Then turning forwards the Sphaere from East West∣ward till the place of the sunne come to the East se∣micircle of the Horizon; see how many houres the Index passeth ouer in the Houre-circle, for so many houres long is the night.

As for example; supposing the Sunne to be as be∣fore in the 10. degree of Taurus, bring the same de∣gree to the East part of the Horizon, and the point of the Index to the Meridian: then turning about the Sphaere, till the same degree come to the West part of the Horizon; you shall finde that in the meane time, the point of the Index shal passe ouer 14. houres and 24. minutes, which is the length of the day. Like∣wise, if you bring the same 10. degr. of Taurus to the West part of the Horizon, and the Index to the Me∣ridian, and turne about the Sphaere, till that degree come to the East semicircle of the Horizon, the num∣ber of houres that the Index runneth ouer in the meane time vpon the Houre circle, shall be found to bee 9. Degrees, and 36. Minutes.

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PROP. XI. To know the Meridian altitude, or the height of the Sunne at noone, for any time and place.

SEt the Sphaere to the latitude of the place where you d•sire to know the Sunnes height at noone: bring the place of the Sunne (being found as before by the 2. Prop.) to the Meridian, then see how many degrees of the Meridian, are contayned betweene the Horizon, and the place of the sunne, for so much is the height of the Sunne at noone.

In like sort it may be knowne how much the Sunne is vnder the Horizon at midnight, after this manner: Bring the place of the sunne in the Zodiacke to the Meridian vnder the Horizon, and see how many de∣grees of the Meridian, are contayned betweene the vpper-side of the Horizon, and the place of the Sunne downewards: and so shall you haue that you sought for.

Or else if you cannot well come to the Meridian vnder the Horizon: bring that point of the Eclip∣ticke which is opposite to the place of the sunne, vn∣to the Meridian aboue the Horizon; for the arch of the Meridian, or the number of degrees and minutes of the Meridian, betweene that point and the Hori∣zon sheweth how much the sunne is vnder the Hori∣zon at midnight.

After this manner▪ the Sunne being in the 10. degr. of Taurus, you shall find that his Meridian altitude at London is 53. degrees, and about one halfe.

As also that hee is vnder the Horizon at midnight about 23. degrees and a halfe at London.

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PROP. XII. To know how high the Sunne is aboue the Horizon at any time of the day.

BRing the place of the Sun (found by the 2. Prop.) to the Meridian: set the houre Index to 12. a clock vpon the houre circle: turne the Sphaere about till the Index come to the houre at which you desire to know the height of the Sunne aboue the Horizon; take the distance of the place of the Sunne from the Horizon with a large payre of Compasses: then set both feet of the Compasses in the Ecliptick, and looke how many degrees are conteyned betweene them, for so much is the height of the Sunne.

Thus may you finde by the Sphaere, that when the Sunne is in the tenth degree of Taurus, his height at 10. of the clocke in the fore-noone (the Sphaere be∣ing duly rectified by the first Proposition) shall be a∣bout 45. degrees and an halfe at London.

PROP. XIII. To finde the houre of the day by the height of the Sunne; &c.

SEt the pole Artick of the Sphaere to his eleuation for that place where you desire to know the houre of the day: bring the place of the Sunne in the Zo∣diack to the Meridian, and the houre Index to 12. a clocke of the houre circle: take so many degrees of the Ecliptick betweene the feet of your Compasses, as the height of the Sunne amounteth vnto.

Then set one foot of your Compasses in the place of the Sunne, and turne the Sphaere about, East∣wards, if it be in the fore-noone, or West-wards, if

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in the after-noone, till you can but onely touch the Horizon with the other foot of your Compasses; for then the Index pointeth out the houre of the day in the Houre circle.

As suppose you obserue the height of the Sun be∣ing in the 10. degr. of Taurus, and find him to bee 30. degrees high in the fore-noone: you shall find (fol∣lowing the directions prescribed in this Proposition) that it shall then be about 8. of the clocke in the mor∣ning.

PROP. XIIII. To finde the Amplitude or bredth of the Sunnes rising, or setting, &c.

THe pole of the Sphaere being set to his eleuation, and the place of the Sunne to the East semicircle of the Horizon: see how many degrees of the Hori∣zon, are contayned betweene the place of the Sunne, and the true East point, for so you shall haue the bredth of the sunnes rising.

Thus the sunne being in the 10. degree of Taurus, you shall find by the Sphaere, that (for the latitude of London) hee riseth about 23. degr. and a halfe North∣wards, from the true East point, and that hee setteth as many degrees towards the North, from the true West point.

PROP. XV. To finde the place of the Sunne, &c.

THe quarter of the yeare being knowne, bring the quarter of the Eclipticke that is answerable there∣to, vnder the Meridian; and turne the Sphaere to or fro, till there bee so many degrees and minutes of the

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Meridian, conteyned betweene the Ecliptick and the Equator, as the declination commeth to: then looke what degree of the Ecliptick is vnder the Meridian, for that is the place of the Sunne.

As suppose the declination of the Sun in some day of the Spring-time of the yeare be found to bee 14. degr. 51. min. (turning therefore the Sphaere to and fro, till some part of the spring quarter of the Eclip∣tick, come right vnder that degree and minute of de∣clination in the Meridian) you may finde that the Sunne is then in the tenth degree of Taurus.

PROP. XVI. To finde what day of the moneth it is, &c.

THe place of the Sunne being found by his decli∣nation (as is already shewed) seeke the place of the Sunne in the Horizon of the Sphaere, and looke what day is answerable thereto, for that is the day of the moneth which was sought for.

As the place of the Sunne being found by his de∣clination (as is shewed in the former Proposition) to be in the 10. degree of Taurus, the day of the moneth shall thus be found to be the 21. of Aprill.

PROP. XVII. The day of the moneth being knowne, to finde at what time the day breaketh.

FInde the place of the Sunne (by the 2. Prop.) and bring it to the Meridian, then bring the houre Index, to 12. a clocke vpon the houre circle.

Finde out also the point of the Eclipticke that is right ouer against the place of the Sunne: then take

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betweene the feet of your Compasses 17. degrees of the Eclipticke, and setting one foot of the Compas∣ses in the point opposite to the place of the Sunne, turne the Sphaere Westwards, till you can but onely touch the Horizon with the other foot, for then the Index sheweth in the houre circle at what time the day breaketh.

So the 21. of Aprill, the Sun being in the 10 degr. of Taurus, you shall finde that the day breaketh about halfe an houre past 2. of the clocke in the morning.

PROP. XVIII. To finde how long the twylight continueth.

FInde out by the former Prop. at what time the day breaketh, and learne also at what time the Sunne riseth by the 7. or 9. Prop.

Then subtract the lesser from the greater, and there shall remayne the length of the twylight.

Or else thus: hauing brought the point that is opposite to the place of the Sunne to be 17. degrees aboue the Horizon West-wards, in such sort as is shewed in the former Proposition; and keeping the Sphaere in that position, bring about the point of the houre Index vnto 12. a clocke vpon the houre circle; then tune the Sphaere Westwards vntill the degree or point of the Eclipticke that is opposite to the place of the sunne come to the Horizon: and see how ma∣ny houres the point of the Index hath runne ouer in the meane time vpon the houre circle: for so many houres continueth the twylight.

By eyther of these wayes, the Sunne being in the 10. degr. of Taurus, you shall finde that the twylight

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(that is the time from the breake of the day till Sun∣rise) is about 2. houres and 20. minutes.

PROP. XIX. To finde how much the declination of the Sunne must alter at any time of the yeare, to make the day an houre lon∣ger or shorter.

BRing the place of the Sunne (found by the second Prop.) to the East semicircle of the Horizon, and marke what degree or point of the Horizon it falleth vpon; bring one of the Colures to the same degree or point, and there make a pricke in that colure; and holding the Sphaere immoueable,) marke withall what degree of the Equinoctiall, or of eyther of the Tropickes is then at the Horizon: Then turne the Sphaere 7. degrees and an halfe forwards, towards the West, if the dayes shorten: but contrariwise if the dayes lengthen; and holding the sphaere there im∣moueable, make another prick in the colure at the Horizon: for the distance of these two prickes in the colure taken with the Compasses and brought to the Ecliptick, or Equinoctiall, sheweth how much the Sunnes declination must alter to make the day an houre longer, if the dayes increase; or shorter, if they decrease.

After this manner you shall finde that the sunne be∣ing in the 10. degree of Taurus, his declination must increase about 5. degrees, (or little more) to make the day an houre longer; but when the sunne is in the 20. degree of Pisces, his declination, or rather his Meridian altitude, must increase about 6. degrees to make the day an houre longer: and when hee is in the

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beginning of Capricorne, his declination decreaseth scarce 5. degrees to make the day an houre longer.

PROP. XX. To find how many dayes it is ere the day lengthen or shor∣ten an houre.

BRing the foresaid prickes (made in the Colure by the former Proposition) vnto the Meridian, and there make two markes iustly answerable vnto those prickes in the Colure: turne about the Sphaere till the Eclipticke line come iust vnder one of those markes, and there make a pricke in the Eclipticke: then againe turne the Sphaere till the Ecliptick come iust vnder the other marke made in the Meridian, and there make another pricke in the Eclipticke: (But here it is to bee noted, that whereas the Eclipticke may be brought vnder that marke whether way soe∣uer you turne the Sphaere, it must (I say be noted that the Sphaere must be turned that way which may soo∣nest bring the Eclipticke vnder that marke. (Lastly, finde out amongst the signes and degrees described vpon the Horizon, the like arch to this, that is con∣tayned betweene these prickes in the Eclipticke: For the number of dayes answerable to this arch in the Horizon, is the time wherein the day groweth an houre longer or shorter.

Thus shall you finde, that when the Sunne is in the beginning of Aries, it will bee about 18. dayes after, ere the day be one houre longer. But when the Sun is in the beginning of Capricorne, you shall finde that it will be almost twice so much, that is neare 34. dayes before the day will be an houre longer.

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Hereby therefore the error of them manifestly ap∣peareth, which thinke that in euery 15. dayes, the day is lengthened or shortened an houre, whereas indeed the lengthning or shortning of the dayes, keepeth no such rule. For when the Sunne is about the Equi∣noctiall points, the dayes lenghthen or shorten very fast: but when he is neere the Tropicall points, they grow longer or shorter very slowly.

PROP. XXI. To make an Horizontall Diall.

SEt the Sphaere to the eleuation of the place for which you would make the Diall turne about the Sphaere, till the solstitiall Colure be 15. degrees (mea∣sured in the Equinoctiall) from the Meridian; and where the Colure crosseth the Horizon, there make a prick; then turne the Colure yet 15. degr. further, that is 30. degrees from the Meridian; and where the Colure crosseth the Horizon, there make an other prick: againe turne the Colure forwards yet 15. deg. more, (that is 45. degrees from the Meridian) and at the common meeting of the Colure and Horizon, make the third prick in the Horizon; and so proceed with the rest, till you haue made so many pricks on that side of the Horizon as there are houres in halse the longest day. Then looke how many degrees the first, second, third, fourth pricks, &c. are from the Me∣ridian, for so many degrees must the houre lines of 11. a clocke, and one a clocke; of 10. and 2, of 9. and 3. of 8. and 4. &c. be from the 12. a clock line in the Horizontall Dyall.

After this manner in an Horizontall Diall made

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for the Latitude of London, (which is 51. degr. and 32. minutes (you shall finde the distances of all the rest of the Houre-lines from the 12. a clocke line as followeth: Betwixt twelue and 11. and twelue and 1. are conceyned 12. degrees almost: Betweene 12. and 10. and 12. and 2. there are conteyned 14. degr. and an halfe: Betweene 12. and 9. and 12. and 3. 38. degr. Betweene 12. and 8. and 12. and 4. 53. degr. Betweene 12. and 7. and 12. and 5. 70. degrees and an halfe.

Betweene 12. and 6. both before and after noone, 90. degr. The other houre spaces before 6. in the mor∣ning; and after 6. in the euening, are equall to the Houre spaces after sixe in the morning, and before 6. in the afternoone.

PROP. XXII. How to make a direct mural Diall.

SEt the Pole artick of the Sphaere so much vnder the Horizon as is the complement of the Poles eleuation: the Horizon therefore being thus set as it were to the Zenith of the Sphaere, and so representing the verticall Circle of East and West (that is the plaine super fices of a direct mural Diall) you shall finde the distances of all the houre-lines, (both before and after noone) from the 12. a clock line, in such sort as you did before for the Horizontall Dial.

So you shall finde the distances of the houre-lines in an erect direct murall Dial made for the Lati∣tude of London to bee as followeth: Betweene the twelue a clock line and the lines of 11. and 1. 9, degr. and about one third part of a degree: Betweene 12. and 10. and 12. and 2. 19. degrees and one quarter;

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Betweene 12. and 9. and 12. and 3. 32. degr. or little more: betweene 12. and 8. and 12. and 4. 48. degrees: betweene 12. and 7. and 12. and 5. 67. degr. or little more: betweene 12. and 6. both before and after∣noone 90. degrees.

PROP. XXIII. How to make any direct inclining, or direct reclining Dial.

REckon from the Equinoctiall vpwards in the Meridian, so many degrees as the height of the Pole commeth to at that place where you would make your Diall; for there is the verticall point or Zenith of that place: from this Zenith reckon South∣wards in the Meridian, the inclination of south Dials, and the reclination of North Dialls; but contrary∣wise, reckon from the Zenith Northwards the incli∣nation of North Dialls, and the reclination of South Dialls. Then bring that degree of the Meridian, where this reckoning endeth to the Horizon, for so the Horizon representeth vnto you the plaine or the flat superficies of the Diall which you would make. Therefore you shall finde how 〈…〉 euery one of the houre lines should be dist••• from the 12. a clock line, in such sort as you did before in making the Horizontall Diall.

Thus in a South direct Diall inclining 30. degr. or in a North direct reclining 30. degrees made for the Latitude or eleuation of the Pole at London, you may finde the distances of the eleuen a clock line, and of the one a clock line, from the 12. a clock line, to be about 14. degrees.

But the houre lines of 10. in the forenoone, and of

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2. in the afternoon, are distant from the 12. a clock line 28. degr. & one halfe; From 12. to 9. and to 3. you shall find 43. deg. From 12. to 8. in the forenoone, and 4. in the afternoone, you shall haue 58. deg. & an halfe: also from 12. to 7. & to 5. shall be about 74. deg. And from 12. to 6. in the morning, & 6. afternoone 90. degrees.

Likewise in a South direct reclining, or North di∣rect inclining 20. deg. for the eleuation of London; the spaces between 12. & 11. & 12. & 1. shall be about 5. deg. or little lesse: Between 12, & 10. & 12, & •. about 10. deg. & •. third parts. From 12, to 9. in the fore∣noone, & 3. in the afternoon, 18. almost▪ From 12. to 8. & 4. •g. deg. or little more. From the 1•. a clock line; to the line of 7. a clock in the forenoone, & 5. in the af∣ternoone, 50. deg. or thereabouts. From 12. to 6. both before and afternooe▪ 90. deg. as in the former kindes of D•. In all which it is to be noted, that there is al∣waies 〈◊〉 distance betweene the houre lines of 5, & •. & 4, & 6. that there is betweene 7, & 6. and 8, & 6. in the forenoone, and betweene 5, & •. & 4, & •. and 7, & 6. & 8, & 6. in the afternoone. So as the distances of all the houre lines from the 12. a clock line being found from 6. in the morning, till 6. at night, the di∣stances of the other Houre-lines before 6. in the mor∣ning, and after 6. at night shall easily be had.

PROP. XXIIII. To know at what time the Moone, or any other of the Pla∣nets or fixed Stars, that are within the bredth of the Zodiack; rise or set, or come to the Meridian, &c.

FInde the place of the Moone, or any other of the Planets, both in longitude and Latitude, by the

Page 49
Epheme•ides: and finde the place (that is, the Lon∣gitude and Latitude) of any of the fixed Star•es in the Zodiack by some table of the fixed Starres, or o∣therwise; and marke the same place of the Moone; Planet or Starre, in the Zodiack of the Sphaere: and hauing set the Sphaere to the Latitude of the place, bring the place of the Sunne (found by the 2. Propo∣sition) to the Meridian, and the Houre-index to 12. a clock vpon the houre-circle•, then turne the Sphaere till the place of the Moone, Planet or Starre marked in the Zodiack, come to the East semi-circle of the Horizon; for then the Index sheweth the time when the Moone, or that Planet or fixed Starre riseth.

Al•• the number of degree in the Horizon, con∣tayned betweene the point of the Moones, Planets, or Starres rising, and the point of true East, sheweth the bredth, ••denesse, or amplitude of rising; And you may at the same instant, 〈◊〉, what degree of the E∣cliptick riseth with any of them, and what the oblique ascension of any of them is: For if you tell hour ma∣ny degrees of the Equinoctiall are 〈…〉 be∣tweene the beginning of Aries in the Horizon, pro∣ceeding Eastwards, or according to the order of the signes: you shall haue the oblique ascension of the Moone, Planet or Starre, that 〈…〉 for.

But bring the same place of the Moone, Planet, or Starre to the Meridian, and the Index sheweth in the houre circle at what time they come to the Meri∣dian: where you may also see, first what degree of the Zodiath middeth Heauen (that is, 〈◊〉 to the Meridian) with any of them; secondly, you may see how much the declination of any of them is; for

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count how many degrees of the Meridian are contay∣ned betweene the Equinoctiall and the place of the Moone, Planet, or fixed Starre, and so much is the de∣clination. Thirdly, you may there see what the right ascension of any of them is: for the place of any of them being brought to the Meridian and there 〈◊〉, r•ckon Eastwards how many degrees of the Equino∣ctiall are contayned betweene the beginning of Aries and the Meridian, so haue you the right ascension. Lastly, bring the place of the Moone, Planet or Star, to the West semi-circle of the Horizon; for then the Index sheweth the time of their setting; and the number of the degrees of the Horizon betweene the point where any of them setteth, and the Equinocti∣all, or true West point (where the Equinoctiall, and Horizon crosse each other) is the amplitude or bredth of the setting of any of them, shewing how much they set from the true West point.

You may there also see what degree; either of the Ecliptick, or of the Equinoctiall, setteth with any of the• and consequently you may know the oblique descension of any of them, by reckoning how many degr. of the Equinoctiall there are from the begin∣ning of Aries Eastwards, till you come about to the West part of the Horizon.

Take for example the great Starre called the Bulls eye, whose place in longitude is about the 4. degr. of Taurus, and his latitude about 5. degrees and an halfe Southwards.

Following therefore the directions prescribed in this Proposition, you shall finde that vpon the first day of Aprill this present yeare, 1600. the same Starre

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riseth here at London about halfe an houre past 7. of the clock in the morning, and setteth about a quarter of an houre past 10. at night, and commeth to the Meridian about 3. a clock afternoone: Also you shall finde that it riseth with the 15. degree of Gemini, and setteth with the last degr. of Taurus, and commeth to the Meridian, or middeth Heauen, with the 5. deg. of Gemini: Thirdly you shall finde his declination to be about 15. deg. and 2. third parts, his right ascension 63. degr. and a quarter, his oblique asce•sion 43. degr. and his oblique descension about 84. deg. and an halfe: and lastly his amplitude of bredth of rising or letting about 25. degr. and an halfe from the true East and West points towards the North.

PROP. XXV. To know how long the Moone, or any of the Planets of fixed Stars doe shine or continue aboue the Horizon.

THe Sphaere bring set up the latitude of the place, and the place of the Moone, Planet, or fixed Starre, being found and marked in the Zodiack, hoth in Longitude and Latitude, (as in the 〈◊〉 Prop.) bring the place of the Moone, Planet, or Star, 〈◊〉 East semi-circle of the Horizon, and the Index of houres to 12. a clock: Then 〈◊〉 about the Sphaere West-wards, till the same place of the Moone, or 〈◊〉 the same Planet, or Starre, come to the West semi-circle of the Horizon, and marke 〈◊〉 how many houres the Index runneth ouer in the meane time vp∣on the houre circle, for so many houres continueth the Moone, Planet, or Starre aboue the Horizon.

Thus shall you finde that the foresaid 〈…〉

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The Bulls eye 〈…〉 the Ho∣rizon at London, about 14. 〈…〉 and 3. quarters.

PROP. XXVI. To finde which of the Planets or fixed Starres are aboue or vnder the Horizon at any time, &c.

THe place of the Plantes or fixed Starres being marked in the Zodiack of the Sphaere, as in the former propositions, and the place of the Sunne brought to the Meridian, and then the Index to 12. 〈…〉 Sphaere 〈◊〉 the Index 〈◊〉 to that houre vpon the houre 〈◊〉 at which you desire to know what Planets are aboue or vnder the Horizon; and then hold still the Sphaere, and marke what Pla∣nets or Starres are aboue or vnder the Horizon in the Sphaere for the same Planets or Starres are aboue or vnder the Horizon in the Heauens.

As for example: the 1. of Aprill 1600 at 9. of the clocke at night, you may by the Proposition finde; that the most part of the fixed Starres, that are in the constestation of Taurus, Gemini, Cancer, Leo, Virgo, and Libra, together with the three superiour Planets, 〈◊〉, •upiter, & Mars, are at 〈…〉 to be seene a∣boue the Horizon, and that the rest of the Planets and fixed Stars, that are within the compasse of the Zodi∣ack, are vnder the Horizon, and cannot then be seene.

PROP. XXVII. To finde in what time any Signe or part of the Ecliptick riseth or setteth.

BRing the beginning of the Signe, or part of the Ecliptick to the East semi-circle of the Horizon,

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if you would know in how long time it riseth, or to the West part of the Horizon, if you would know in what time it setteth; then set the Index to 12. a clock, and turne forwards the Sphaere, till the whole signe or part of the zodiack be risen, or set: For then the Index sheweth vpon the houre circle in how long time, that signe or part of the Zodiack riseth or setteth.

Thus you may finde (for example) that the whole signe of Aries here at London riseth in one houre or somewhat lesse, and setteth in two houres and three quarters, or something more: And that the whole quarter of the Zodiack, from the beginning of Aries to the beginning of Cancer, riseth in lesse then foure houres, but setteth in more then 8. houres.

PROP. XXVIII. To finde the houre of the night by any of the Planets or fixed Starres in the Zodiack, &c.

THe place (that is to say, the longitude & latitude) of any Planet, or fixed Starre in the Zodiacke, that is aboue the Horizon, being first found, and mar∣ked in the Zodiack of the Sphaere; bring the place of the Sunne (found by the 2. Proposition) to the Me∣ridian, and the Index to 12. a clocke vpon the houre circle: Then hauing found the height of the Starre, or Planet by obseruation, and the Sphaere also being set to the Latitude of the place of obseruation, take be∣tweene the feet of your Compasses, so many degrees of the Ecliptick, or Equinoctiall, as the height of the Planet, or Starre obserued, commeth to; and setting one foote of your Compasses in the place of the Planet, or fixed Starre that you obserued in th Zo∣diack,

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turne the Sphaere forwards or backwards, till you can but onely touch the Horizon with the other foot: for then the Index in the houre circle, shall shew you the houre of the night.

Suppose (for example) I should obserue the height of the foresaid Bulles eye, and should finde the same to be 29. degrees the first day of March at euening: finding therefore the place of that Starre in the Zodi∣ack of the Sphaere, and bringing it (with helpe of the Compasses) to the height obserued (hauing first set the place the Sunne and houre-Index both toge∣ther to the Meridian) the Index of the houres will shew, that when that Starre hath that height of 29. de∣grees, it is about 9. of the clock at night.

PROP. XXIX. To know at any time of the yeare, what Stars in the Zodi∣ack, arise or set, Cosmically, Achronically, or Heliacally.

SVch Stars as rise together with the Sunne, are said to rise cosmically: and such Stars as set when the Sunne riseth, are said to set cosmically; But those Stars which set together with the Sun, set achronycal∣ly; and those Stars that rise when the Sunne setteth, are said to rise achronically. Lastly, those Starres that rise a little before the Sunne, rise heliacally; and those that set a little after the Sunne, set helia∣cally.

All which may thus bee found: Bring the place of the sunne to the East semicircle of the Horizon: for the Stars that are then a little aboue the Horizon rise heliacally; but those that are in the Horizon in the East, rise cosmically; and they that are in the

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West semicircle of the Horizon set cosmically: But bring the place of the Sunne to the West semicircle of the Horizon, for those Starres as are at the West part of the Horizon at the same time, set achrony∣cally; but those that are then in the East semicircle of the Horizon, rise achronycally: and they which are a little aboue the West semicircle of the Horizon set heliacally.

Thus you may know that vpon the 26. or 27. day of May (it our latitude of London) the Bulles eye riseth cosmically, and the Starres in Serpentarius his right foot, set cosmically, you may see also that the same day the Starre in the Bulls South horne setteth achronycally: and the Northermost starre in Serpen∣tarius his right foot, riseth achronycally: and lastly, you may finde that about the same time the Ple•ades and the Starre in the Bulls North home, rise heliacal∣ly, and that the same Starre also, and the former Twinnes feet set heliacally.

PROP. XXX. To finde the foure principall or Cardinall points of Hea∣uen (as the Astrologians call them) at any time.

THese foure Cardinall points are nothing else but foure points of the Ecliptick, whereof one is at the East part of the Horizon, ascending, and is there∣fore called the Ascendent: another is at the vpper part of the Meridian aboue the Horizon, and is cal∣led the midst of Heauen, and the hart of Heauen: the third is at the West part of the Horizon descending, and may be therfore called the descendent: the fourth point is that which is at the nether part of the Meri∣dian

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vnder the Horizon. Which foure points are the beginnings of the first, tenth, seuenth, and fourth Houses. Therefore to finde these points at any time by the Sphaere, bring the place of the Sunne (being found for that time by the 2. Proposition) to the Me∣ridian, and the Index to 12. a clocke: then turne the Sphaere till the Index come to that houre at which you desire to know those foure points, and there hold the Sphaere that it moue not: and looke withall, what points of the Ecliptick are at the East and West se∣micircle of the Horizon; and at the vpper and ne∣ther parts of the Meridian: for those bee the foure principall or Cardinall points you sought for.

Take for example the time of the Sunnes entrance into Aries this present yeare 1600. which was vpon the tenth day of March about eight of the clocke in the morning, or little after with vs here at London, Hauing therefore brought the beginning of Aries to∣gether with the houre Index to the Meridian, and then turned back the whole Sphaere till the Index come to 8. of the clocke vpon the houre circle: you shall finde the ascendent at that time, to be the 27. de∣gree of Taurus; the middest or hart of Heauen, the 27. of Capricorne▪ the descendent, the 27. deg. of Scor∣pio; and the lowest part of Heauen the 27. degree of Cancer.

PROP. XXXI. To finde out the bredth of any climate, &c.

LIft vp, or put downe the pole of the Sphaere, till you finde that there are 7. deg. and an halfe of the Tropick of Cancer, more or lesse aboue the Horizon,

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then there were before; and marke with all how much the pole of the Sphaere is raised, or let fall in the meane time, more then it was before; for so much is the bredth of that climate.

As far example: hauing set the Sphaere to our La∣titude of London of 51. deg. and an halfe, with the point of your Compasses, holding and guiding some point of the Tropick of Cancer right vnder the Hori∣zon; then lifting vp the Pole till you finde 7. degrees and an halfe more aboue the Horizon then were be∣fore, you shall finde the Pole eleuated about 2. degr. and an halfe more then it was before.

Likewise, if you put downe the Pole till there be 7. degrees and an halfe of the Tropicke of Cancer, fewer aboue the Horizon then was before; you shall finde the eleuation of the Pole to be about 3. degrees lesse then before.

PROP. XXXII. The reason of the inequalitie of naturall dayes, &c.

THe reason hereof is shewed partly by the inequa∣lity of the differences of right ascentions answe∣rable to equall arcks of the Zodiack; and partly by the vnequall apparent motion of the Sunne. For the first: the differences of right ascentions answerable to the parts of the Ecliptick, about the Tropicall points of Cancer and Capricorne, are much greater then about the Equinoctiall points of Aries and Libra.

In so much that whereas the difference of right ascension answerable to one signe, or 30. degrees taken about those Tropicall points, is more then 32. degrees and an halfe: about the Equinoctiall points

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it is little more then 27. degrees and an halfe; as it may appeare by the Sphaere. So as you may hereby gather, that the difference of ascention answerable to one degree, which about the beginning of Capricorne is one degree, and about 6. minutes; about the begin∣ning of Aries, or Libra, is onely 55 minutes. Second∣ly, the apparent motion of the Sun is much swifter a∣bout his Parig•••, in the signe of Capricorne, then a∣bout his Apogaeum in Cancer, or in other parts of the Zodiacke: so that whereas the Sunne being in Capri∣corne moueth 61. minutes and something more in a day: in Aries or Libra he moueth but 59. min. or very little more in the same time. Therefore seeing the na∣turall day is nothing else, but the time wherein the Sunne moueth from the Meridian about, till it re∣turne again to the same part of the Meridian; it must needs bee that alwayes in one naturall day, there is made one whole reuolution of the Equinoctiall cir∣cle, and so much more as is the difference of right as∣cention answerable to the apparent motion of the Sun in the meane time: which differences of ascenti∣on because they be vnequall, for the two causes before alledged; the naturall dayes must needs also bee vne∣quall, the motion of the Equinoctiall circle about his owne center being (as it hath beene alwayes supposed to be) equall, that is mouing alwayes an equall space in equall time.

Which by this example may most plainly appeare: The Sunne being in Capricorne moueth 61. minutes in a naturall day: difference of ascention agreea∣ble thereto is 67. minutes, or something more. There∣fore at that time, in the space of one naturall day, the

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Equinoctial circle must make one full reuolution, and 67. minutes more. But when the Sun is in Aries, mo∣uing onely 59. minutes in a day, and the difference of right ascention answerable thereto, scarce 54. minutes more then one reuolution of the Equinoctiall circle; there shall passe onely 54. minutes more in a naturall day; so as here the Equinoctiall circle moueth not a∣bout so much in one day as before by 13. minutes. Seeing then that 15. degr. or little more of the Equi∣noctiall circle doe passe the Meridian in euery houre, and consequently one degree of the Equinoctiall pas∣seth the Meridian in 4. minutes of an houre, and one minute of a degree in 4. seconds of an houre; there∣fore 13. minutes of the Equinoctiall shall passe the Meridian in 52. seconds: that is, almost in one mi∣nute of an houre: Whereby it manifestly appeareth that the naturall day, that is to say, the space of 24. houres, which is the time wherein the Sunne moueth from the Noone-stead to the same noone-stead a∣gaine, is in our age greater almost by one minute of an houre, when the sunne is in Capricorne, then when hee is in Aries or Libra▪

PROP. XXXIII. To finde by the Sphaere how much the naturall dayes are longer at one time of the yeare then at another.

FOr this purpose it will be best to take a good num∣ber of dayes together; as for example, take the whole moneth of December, and the whole moneth of March: both which moneths consist of the same number of 31. naturall dayes: find the place

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of the Sunne for the beginning and ending of both moneths, which you may finde by the second Propo∣sition to be for the beginning of March this present yeare 1600. about 20. degrees and 13. minutes of Pisces; and for the ending about 20. degr. 48. minutes of Aries: Also for the beginning of December the same yeare 18. degr. 46. minutes of S•gitarie; and for the ending, 20. degrees 24. minutes of Capricorne: Then seeke out the right ascensions of the same pla∣ces of the Sunne for the beginnings and endings of both those moneths by the fourth Proposition, and the differences of ascension answerable to the motion of the Sunne in each moneth, by the sixt Proposition; which you may finde by the Sphaere to be about 33. degrees, 24▪ minutes for December, and 28. degrees, 39. minutes for March. Lastly, finde out the diffe∣rence of these differences of ascension by substracting the lesser out of the greater; which in this example is 4. degrees 45. minutes; which resolued into minutes of an houre, by taking for euery degree 4. minutes of an houre, and for euery 15. minutes of a degree, one minute of an houre shall amount to 19. minutes of an houre, that is a quarter of an houre and 4. minutes. And so much is the moneth of December longer then the moneth of March; Notwithstanding both of them consist of the same number of 31. naturall dayes.

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The third Part. (Book 3)
Of the Orbes whereof the SPHAERES of the Sunne and Moone haue beene imagined to bee made, and of their Motions and Vses. (Book 3)

CHAP. I. Of the Orbes whereof the Sphare of the Sunne is made.

WIthin the Sphaere or Orbe contay∣ning all the Circles that wee haue hitherto spoken of, and represen∣ting vnto vs the Primum mobile; that is, the first and highest moue∣able Heauen, that hath been ima∣gined by the Astronomers, to shew the reason of that daily motion, which appeareth to bee in all the Hea∣uens, and of all the apparences that follow there∣upon, are included the Sphaeres and Orbes of the Sunne and Moone.

The sphaere of the Sunne contayneth three Orbes: The vppermost of them (which in this Sphaere is sig∣nified by the yellow Circle that commeth next with∣in the compasse of the Zodiacke) is called Deferens apogaeum Solis; that is, the Orbe which carrieth about that point, wherein the sunne is furthest distant from the earth.

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Next within this Orbe is placed the Eccentrick ca∣rying about the body of the Sunne; which in this Sphaere is represented by the greene coloured circle that commeth next vnder the Deferens apogaeum.

Againe, within this Eccentrick is included the third Orbe of the Sphaere of the Sunne called Deferens Pe∣rigaeum solis; that is, the Orbe carying about that point wherein the Sun is nearest to the Earth. This is the nethermost of the three Orbes of the sunne, and in this Sphaere is represented vnto you by the yellow colou∣red circle next vnder the sunnes Eccentricke.

CHAP. II. Of the vppermost and nethermost Orbes of the Sphaere of the Sunne, more particularly.

IN the vppermost and nethermost of these three Orbes, there be 4. points especially to bee conside∣red: That is, the points where they bee narrowest and where they be broadest, and where they are of a meane bredth betwixt the narrowest and broadest. For at the narrowest part of the vppermost Orbe, where you may see written Aux solis, and the broadest part of the nethermost Orbe, is the place of the sunnes Apogaeum; so that whensoeuer the Sun commeth there, he is fur∣thest distant from the earth. As you may easily try, if (with a payre of Compasses, or otherwise) you take the distance betwixt the Earth and the Sunne, being brought about to that place, and compare the same with the distances that the Sun hath from the Earth in other places. This point is called Aux Solis, and Longitude longior, that is, the point of the sunnes fur∣thest distance from the earth. But vnder the broadest

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part of the vppermost and vttermost Orbe, where you see printed PERIGAEVM, and right aboue the narrowest part of the nethermost Orbe, is the place where the Sun commeth nearest to the Earth, as you may easily find (with your Compasses, or otherwise) in like sort as before was shewed. The point where the Sun commeth nearest to the earth, is called oppo∣situm A•gis, and longitudo propior, that is, the point opposite to the Apogaeum, and the nearest distance. And at those parts of this Orbe, which are in the midst betweene the former; the Sunne hath a meane distance from the earth: a meane (I say) betweene the least, and greatest distance. The very point wherein this meane or middle distance hapneth, is shewed by the points that are iust in the middest betweene the short lines AB, and IK, which are drawne ouer∣thwart on eyther side of this Orbe. These points are called longitudines media; that is, the meane distances of the Sunne, because the sunne comming to these points, hath a meane distance betweene the least and the greatest. About these points also, the true motion of the sun, is as it were in a meane between the slowest, which hapneth the sunne being about the Apogaeum, and the swiftest, which hapneth about his Perigaeum.

Moreouer the lines A, and K, shew the places wher∣in there is the greatest Prosthaphaerisis, or Equation of the sunne: that is, the greatest difference betweene the true, and middle, or meane place of the sunne.

Lastly, the distance betweene the lines I, and K, or A, and B, shew how much the eccentricitie of the sunnes eccentricke is, that is, how farre the Center of the eccentricke is distant from the Center of Earth.

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CHAP. III. To finde how much the Sunne is nearer or further from the earth, at one time then at another.

BY meanes of this Circle, you may easily find with your Compasses, how much the Sunne is nearer to, or further from the earth at one time, then at ano∣ther: for hauing set one foot of the Compasses vpon the vtmost edge of the Deferens Apogaeum, vnder the place of the Sunne in the Zodiacke, found by the se∣cond Prop. stretch out the other foot, to the inner∣most edge of the same Orbe; for then, if you set one foot of your Compasses, vpon the vtmost edge of this Orbe, at the Apogaeum, the other foot turned inwards towards the center of the Sphaere, will shew you how much the Sunne is nearer to the Earth at that time, then when he is in his Apogaeum: for so much as that foot reacheth within the inner edge of the Orbe, so much is the sunne nearer. Likewise if you set one foot of your Compasses, vpon the vttermost edge of this Orbe, at the Perigaeum, and turne the other foot to∣wards the center of the Sphaere, so much as this foot of the Compasse, is from the inner edge of the Defe∣rens Paerigaeum, so much is the Sun further distant from the earth at that time, then when he is in his Paerigaeum.

CHAP. IIII. Of the situation and motion of the uppermost, and ne∣thermost Orbes of the Sunne.

THe vppermost, and nethermost of these three Orbes, called Deferens Apogaeum, & Perigaeum solis, doe alwayes answer each to other, in such sort that the broadest part of the one, is alwayes against the nar∣rowest

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part of the other: And therefore both of them are moued thgether, with one motion about the Ax∣tree and poles of the Ecliptick, making one reuoluti∣on vnder the Zodiack, in the space of 17000. yeares almost. For in Ptolemee his time (that is about the yeare of our Lord 134.) the place of the Sunnes A∣pogaeum, was about the middest of the 6. deg. of Gemi∣ni; as it may appeare by the 4. Chapter of the 3. booke of his Almagest. But in our time we finde that it cannot exceed the 7. degr. of Cancer, although af∣ter the account of Copernicus, and of the Prutenicke tables, it should be in the 9. degr. of Cancer. So as, if the rest of the motion of the Sunnes Apogaeum, that is to come hereafter, be proportionable to that is past, the whole reuolution thereof shalbe finished in 1699. yeares vnder the Zodiack. For in 1463. yeares be∣twixt Ptolemee his time and ours, it hath moued a∣bout 31. degn therefore it shall moue 300. degrees, (that is, the compasse of the whole circle) in 16990. yeares.

Which number of yeares being deuided by 360. it shall appeare that the Apogaeum of the Sunne moueth one degr. in little more then 47. yeares whereby the yearely motion thereof may be sound to be little more then one minute and a quarter.

CHAP. V. How to find the place of the Suns Aux or Apogaeum, &c.

THerefore the place of the Sunnes Apogaeum, be∣ing found for the yeare 1600. to be about 7. degr. in Cancer, the place thereof for any other yeare be∣fore or after, may easely be found in our age, onely

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by subtracting, or adding for euery 4, yeares 5, min. and for euery single yeare 1. minute and a quarter, Al∣though indeed we need not stand so precisely neyther vpon quarters of minutes, neither yet vpon whole mi∣nutes, in the place of the sunnes Apogaeum, which can∣not be by any Art so exactly found, but that the dili∣gentest man that is, may erre many minutes therein.

Take for example the yeare of our Lord 1558. (in which our gracious Q. Elizabeth began her happie reigne, which is now 42. yeares since) taking therefore for euery 4. yeares 5. minutes, that is, for 40. yeares 50. minutes, and for the two yeares remaining 2. minutes and one halfe; that is in all 52. minutes and an halfe, and subtracting the same out of 7, deg of Cancer, there shall remaine the place of the sunnes Apogaeum at the beginning of her Maiesties reigne, in 6. degr. and about 8. min. of Cancer.

The vses of these two Orbes are these.

1. First to make the sphaere of the Sunne concen∣tricall; for these Orbes be framed together, that the narrowest part of the one, answereth alwayes to the broadest part of the other: it commeth to passe by this meanes, that both the out-side, and the in-side of the Sphaere of the sunne, haue alwayes the same center, that the world it selfe hath.

2. The second vse is to shew the reason, and manner of the motion of the Sunnes Apogaeum and Perigaeum.

CHAP. VI. Of the eccentrick of the Sunne, &c.

THe Orbe conteined betweene the two former, and carying about the body of the Sunne it selfe,

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is called the eccentricke of the Sunne; because it hath another center, then the center of the world. The e∣speciall reason, that moued the skilfull in this coelesti∣all science, to make this Orbe (wherein the body of the sunne is carryed) eccentricall, was because they found the apparent motion of the sunne vnder the e∣cliptick line to be vnequall, that is, swifter in the Sou∣therly Signes: and slower in the Northerly.

For Hipparehus, and Ptolemee found in their times, that the sunne continued in the Northerne semicir∣cle of the ecliptick, from Aries to Libra, 187. dayes: and in the other halfe of the Zodiack, that is South∣ward from Libra to Aries, 178. dayes and a quarter onely. But in our time by diligent obseruation it is sound, that the time of the sunnes continuance in the first of those semicircles from Aries to Libra, is 186. dayes 14. houres and an halfe: and consequently in the other semicircle, from Libra to Aries, 178. dayes 15. houres and an halfe. Taking it therefore for a ground, according to the doctrine of Aristotle, that the motion of the coelestiall bodies is circular and e∣qual; it must needs follow, that a greater part of the circle described by the proper motion of the sunne must be conteined vnder the Northerly semicircle of the ecliptick, then vnder the Southerly: and conse∣quently that the circle or Orbe that caryeth about the body of the Sunne vnder the ecliptick, hath ano∣ther center then the center of the Ecliptick.

2. Another reason to proue, that the Sunne is caryed in an eccentricall Circle, is the vnequall ap∣parent, bignes of the Sunnes diameter, the Sunne being of the same height aboue the Horizon and the

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ayre alike affected, and alike cleare; so as if there were any refraction by reason of the thicknes of the ayre, it must needs be the same in both places. For in Som∣mer, when the Sun is at, or neare his Apogaeum, his apparent diameter hath beene found by exquisit ob∣seruation to be 13. minutes 48 seconds. But in win∣ter being about his Perigaeum 33. min. 54. seconds, as it may appeare in Copernicus his reuolutions 4. booke 21. Chapter.

Therefore seeing euery visible obiect appeareth greater when it is neare, and lesse when it is further remoued from vs, it is manifest that the Sun appea∣ring greater in winter, then in sommer, must needes be nearer to the earth in winter, then in sommer.

The reason of which apparance is most easely shew∣ed, by supposing the Sunne to be moued, in an ec∣centricall Orbe.

3. A third reason may bee the vnequall great∣nesse and continuance of the eclipses of the Moone, euen at those times when she hath had the same lati∣tude, or distance from the Ecliptick, and the same distance from the Center of the earth: which argueth that the conicall sharp pointed shadow of the earth, in the place where the Moone in time of the Eclipse passeth through that shadow, at the same distance from the earth, is sometimes greater, and sometimes lesser: wherof there can no cause be shewed more rea∣sonable then this, that the Sun is sometimes further distant from the earth, and the maketh the shadow greater and sometimes nearer, and so maketh it lesser. Whereby it is also manifestly proued, that the Sun is moued about another center then the center of the

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earth, and therefore that the circle or Orbe, wherein the Sunne is moued, is an Eccentricke.

CHAP. VII. Of the vses of the Sunnes eccentricall Orbe.

THerefore the vses of the Sunnes eccentricke may bee these:

1. First to shew the reason of the apparent ine∣qualitie, which seemeth to bee in the motion of the Sunne: for although the Sunne mo•e equally in his owne O•be, and about his owne center; yet to them that are at the center of the world, or vpon the earth, he shall seeme to moue vnequally; that is, swiftly when he is in that part of his eccentricke which is nea∣rest vnto the earth; and slowly when he is farthest from the earth. And therefore in sommer, when the Sunne is about his Apogaeum, and in his greatest distance from the earth, he seemeth to moue little aboue 57. min. in one day. But in winter, being about his Perigaeum and nearest vnto the earth, he seemeth to moue more then 16. minutes: whereas notwithstanding he mou∣eth equally in his Eccentricke, euery day about nine and fifty minutes and 8. seconds; and so finisheth his reuolution in 365. dayes, and six houres almost.

2. The second vse of the Sunnes Eccentricke, may be to shew the reason why the Sun appeareth greater at one time then at another; for the Sun be∣ing in those parts of the eccentrick that are nearest vn∣to vs, seemeth greatest, and when he is in those parts of his eccentrick that are furthest from vs, he appea∣reth to be least.

3. And lastly the inequality of the Sunnes distance

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from the earth, caused by his eccentrick, is one espe∣ciall cause of the inequalitie of the Eclipses, both of the Sunne and Moone.

CHAP. VIII. The definitions of certaine Astronomicall wordes of art, for the better vnderstanding of the Theorick of the Sunne.

1. WHat the Aux or Apogaeum of the Sunne is it hath beene partly shewed already: that ••mely it is that part, or rather point of the Orbe ca∣rying the Sunnes Apogaeum, wherein the said Orbe is thinnest, or narrowest: Or it is that point of the ec∣centrick which is furthest distant from the earth, and is alwayes shewed by a right line vnderstood to be drawn from the center of the world, by the center of the eccentrick, vnto the Orbe carying the Sunnes A∣pogaeum. Which line is therefore called the line of the Sun his Aux or the line of the Sunnes Apogaeum.

2. The motion of the Aux, or of the Apogaeum of the Sunne (which is also called the Sunnes Aux in the second signification) is nothing els but the arch of the Ecliptick, conteyned betweene the beginning of Aries, and the line of the Sunnes Apogaeum, drawne forth to the Zodiack; where this line also sheweth the place of the Sunnes Apogaeum.

3. The middle or meane place of the Sunne in the Zodiack, is shewed by a line drawne from the cen∣ter of the world vnto the Zodiack, equidistant from the center of the Eccentricke, and of the Sunne.

4. This line is therefore called the line of the meane or middle place of the Sun.

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5. The middle or meane motion of the Sunne is the arch of the ecliptick betweene the beginning of Aries, and the middle place of the Sun.

6. The true place of the Sunne is shewed by a streight line drawne from the center of the earth by the center of the Sun vnto the Zodiack, which line is therefore called the line of the true place of the Sun.

7. The true motion of the Sun is the arch of the eclipticke from the beginning of Aries, vnto the true place of the Sun.

8. The argument of the Sun (at the 〈◊〉 •erme it) or the motion of the Sunnes Anomalie (as Copernicus calleth it) is the arch of the ecliptick con∣teyned betweene the place of the Sunnes Apogaeum and the middle place of the Sunne according to the order and succession of the Signes. This arch is called the argument, or motion of the sunnes Anomalie or irregularitie, because that by it is alwayes found how much the suns true motion which (is vnequall and irregular) differeth from his middle motion; which difference they call the Suns equation, or prostha∣pheresis.

9. The equation, or prosthapheresis of the Sun is nothing els but the arch of the ecliptick conteyned betweene the true, and middle places of the sunne.

This arch is called the sunnes equation, be∣cause it maketh the suns middle motion equal to his true motion, being added to it or subtracted from it, as occasion requireth: for which cause it is more significantly and fitly called Prosthaphaeresis, that is as much to say, as that which is to be added to or sub∣tracted from the middle motion, that so we might

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haue the true motion. For so long as the Sunne is in the semicircle of his eccentrick, discending from his Apogaeum to his •••gaeum, so long this Prosthapheresis is to be subtracted from the middle motion: but the Sunne being in the other halfe of his eccentrick ascen∣ding, the Prosthapheresis or equation of the Sun must be added to the middle motion, that 〈…〉 mo∣tion and place of the Sunne may be found, Because that in the first semicircle of the eccentricke descen∣ding, the middle place of the Sunne goeth before the 〈◊〉, and the middle motion is 〈…〉 greater 〈…〉 the Sun, and therefore the difference of these 〈◊〉 motions, (that is to say, the 〈◊〉 or Prosthaphaeresis) must be subtracted, to findeth 〈…〉 for the true place of the Sunne goeth al∣waies 〈…〉 motion and place of the same,

CHAP. IX. Of the vppermost Orbe of the Sphaere of the Moone cary∣ing the Dragons head and tayle.

NExt within the Orbes of the Sun in this Sphaere are conteyned the Orbes of the Sphaere of the Moone: which 〈…〉 in number.

The vppermost of them (which in this Sphaere is next vnder the Orbe that caryeth the Suns Perigaeum and is coloured with red) is called the Caryer of the Dragons head and tayle, or 〈…〉 which is

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as much to say as the Caryer of the knots, that is of the two intersections, or pointes wherein the rest of the Orbes of the Moone, doe crosse ouer-thwart this Orbe. This Orbe is deuided into foure nineties of degree, for the easier reckoning of the motion and place of the Dragons head or tayle in this Sphaere. And it is moued about in 18. Iulian yeares 224. dayes 3. houres and 5. minutes almost, from the East West∣wards, vnder the ecliptick. By reason of this motion it commeth to passe, that the Eclipses, or rather the places wherein the eclipses of the Sunne or Moone doe happen in the Heauens, are remoued continually more backwards in the Zodiack, contrary to the or∣der and succession of the Signes.

As for example; the eclipse of the Moone hapning this present yeare 1600. the 20. of Ianuarie neare vnto the Dragons tayle about the 9. degree and 40. min. of Leo; the next eclipse that shall happen neare the same intersection of the Dragons taile, in the yeare 1601. the 29. of Nouember, shall be in 17. degrees and an halfe of Gemini; And that eclipse which shall be the next yeare after neare the same intersection the 19. of Nouember in the morning, shall be about the 6. de∣gree and 40. minutes of Gemini, &c.

All this remouing of the Eclipses backwards com∣meth to passe, by reason of the motion of this Orbe carying the Dragons head and tayle, contrary to the course and order of the Signes.

This Orbe continueth alwaies right vnder,* 6.1 and euen with the Orbes of the Sphaere of the Sunne which abide alwaies in all parts iust vnder the eclip∣tick line, and hath his center agreeing, and all one

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with the center of the world, and of the ecliptick: And therefore the poles and axtree, about which this Orbe is turned, agree iustly with the axtree of the Ecliptick.

The rest of the Orbes of the Moone,* 6.2 that are con∣teyned within this, haue all theire playnes agreeing in one, and lying euen one with another. But the one halfe of all their playnes, ariseth aboue the playne of the former Orbe, and of the Ecliptick, towards the North pole of the Zodiack: and the other halfe des∣cendeth beneath the playne of the ecliptick, toward the South pole: euen as the one halfe of the Zodiack ariseth aboue the Equinoctiall circle towards the North: and the other halfe descendeth towards the South. And as the angle of intersection, or obliquitie of the ecliptick with the Equinoctiall circle, is 23. degr. and an halfe or little more: so the angle of inter∣section, or obliquity of the playnes of these Orbes of the Moone, from the plaine of the Ecliptick, and of the former Orbe carying the Dragons head and taile, is 5. degrees, or (according to Tig•• Brahe his ob∣seruation) 5. degr. and a quarter almost sometimes, and sometimes lesse then 5. degr.

That point or intersection of these Orbes with the former, from which they begin to arise about the playne of the ecliptick towards the North, procee∣ding East-wards, is called the Dragons head; and is signified by this character ☊: and the other point or intersection diametrally opposite vnto this, is called the Dragons tayle, which is also signified by the for∣mer character turned vp side downe after this man∣ner, ☋.

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The two points of these Orbes that are furthest distant from the plaine of the 〈◊〉, are called the bounds or limites of the Moones latitude, and they are 90. deg. from the Dragons head and tayle, and 5. deg. and a quarter almost from the playne of the E∣cliptick, according to the obliquity, or greatest decli∣nation of the playnes of these Orbes, from the playne of the ecliptick: Of these two points, that which is in the north side of the ecliptick, is called the North li∣mit, or bound of the Moones latitude; and contrari∣wise, the other point opposit to this on the south side of the Ecliptick, is called the South limite of the Moones latitude. And when the Moone commeth to eyther of these two points, she hath her greatest latitude.

CHAP. X. Of the Orbes carying the Moones Apogaeum and Peri∣gaeum.

NExt within the Orbe carying the Dragons head and tayle, is contayned the Orbe called Deferens Apogaeum lunae which is the point wherein the Moone is furthest distant from the earth.

And vnder this Orbe is placed the Moones Eccen∣trick, which is also called Deferens Epiculum Lunae; that is the Orbe carying the Moones Epicycle.

Againe within this eccentrick of the Moone, is conteyned the least and lowest Orbe, of all that are in this Sphaere, Which they call Diferens Perigaeum Lu∣nae; that is, the Orbe carying the Moones Perigaeum, which is the point wherein the Moone commeth nea∣rest to the earth.

The vppermost and nethermost of these three

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Orbes, that is to say, the Orbes carying the Moones Apogaeum and Perigaeum (both which Orbes in this Sphaere are coloured with blew) are alwaies placed in such sort, that the nar••west part of the one, is con∣tinually answerable to the broadest part of the other; whereby it commeth to passe, that the Sphaere of the Moone is made concentricall, that is to say, to haue the same center with the world: which also is one especiall vse, why these Orbes were deuided.

Another vse of these Orbes, is to shew the reason of the motion of the Moones Apogaeum and Perigaeum: Therefore both these Orbes are moued togither with one motion equally, about the center of the world, in the same time from the East Westwards, in the space of 32. dayes 3. houres and 5. minutes al∣most: So mouing in one day 11. deg. 12. min. and 1. third part almost. The axtree, about which these Orbes are moued equally, passeth through the center of the world and of the ecliptick: but the poles of these Orbes differ from the poles of the Ecliptick and of the Orbe carying the Dragons head and tayle, by the space of 5. degr. and a quarter, or thereabouts, which poles are caryed about the poles of the Orbe carying the Dragons head and tayle, with the moti∣on of the same Orbe, in the space of 19. yeares almost. Whereby it commeth to passe, that the poles of the Orbe carying the Apogaeum and Perigaeum of the Moone, describe certaine litle circles about the poles of the Orbe that carieth the Dragons head and taile, euen as the Arctick, and Antarctick circle in the or∣dinary Sphaere, are described by the motion of the poles of the Ecliptick, caryed about dayly with the

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motion of the first and highest moueable Sphaere, in the space of 24. houres almost.

CHAP. XI. Of the eccentricke of the Moone.

THe Eccentrick of the Moone contained be∣tweene the two former Orbes and coloured with a sad yealow colour in this Sphaere, is moued equally about the center of the same Orbes, from the West towards the East, finishing his motion vnder the Zodiack, in the space of 27. dayes, and 8. houres al∣most: and with this motion, it caryeth about the Moones Epicycle equally, vnder the Zodiack.

Therefore the motion of this Orbe, about his owne center, must needs be vnequall, that is to say, swifter in those parts that are about the Apogaeum, and slower in the lower parts about the Perigaeum: Because that greater arches of the Eccentrick, doe answer to equall arches of the Zodiack about the Apogaeum, then about the Perigaeum of the Eccentrick.

The axtree about which this Orbe is moued, is al∣waies in all places equidistant from the axtree of the Orbe carying the Apogaeum of the Moone: and the poles of the axtree of the Moones eccentrick, are fast∣ned in the Orbe carying the Moones Apogaeum, e∣quidistantly from the poles of the same Orbe: there∣fore these poles together with the whole axtree of the eccentrick, are caryed and equally moued about the poles and axtree of the Orbe carying the Apogaeum from the East, towards the West. With this motion therefore, the poles and center of the eccentrick, de∣scribe certaine litle circles of equall bignes, about the

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poles, and center of the Orbe carying the Apogaeum, from the East West-wards. And therefore also the Apogaeum of the eccentrick, is moued about equally, vnder the ecliptick, contrary to the order of Signes from the East West-wards. Whereby it commeth to passe, that both the Apogaeum and center of the eccen∣tricke, are somtimes vnder the Ecliptick, that is, when they are vnder the Dragons head or taile: but for the most part they are beside the plaine of the ecliptick, either towards the North, or else towards the South.

Hereby also it appeareth, that the plaine of the E∣cliptick doth not alwayes deuide the plaine of the ec∣centricke into epqall parts or halfes; but then onely, when the Center and Apogaeum of the Eccentrick, is right vnder the Dragons head or tayle; for then one∣ly the plaine of the Ecliptick deuideth the plaine of the Eccentrick, by the center therof; and consequent∣ly deuideth it precisely into two halfes. Otherwise, if the Apogaeum of the eccentrick, be not vnder the Dragons head or tayle, looke on which side of the plaine of the ecliptick the Apogaeum is, for on the same side of the ecliptick is the greater part of the ec∣centrick.

CHAP. XII. In what proportion the Moones eccentrick, and Orbe, ca∣rying her Apogaeum are moued.

NOw the Eccentrick of the Moone, and the Orbe carying her Apogaeum, are moued in such sort, that the middle place of the Sunne, is alwayes right in the midst betweene the center of the Epicycle cari∣ed in the eccentrick, and the Apogaeum of the Eccen∣trick; except it be when the center of the epicycle is

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in coniunction, or opposition to the middle place of of the Sunne. For in euery middle coniunction and opposition of the Sunne and Moone, the center of the Epicycle, and the Apogaeum of the eccentrick are vnited together; But in the coniunction they are both conioyned with the middle place of the Sun; and in the opposition they are both together opposite to the same. Whereof it followeth, that in the first and last quarters of the Moone, the center of her epicycle is diametrally opposite to the Apogaeum of her eccen∣trick.

Hereof it commeth to passe, that although the Moone haue the same position in her epicycle at the time of the new and full Moone, and of the first and last quarters; yet the equation, or prosthaphaeresis of the Moones Argument (as they call it) that is the difference betweene the true, and middle places of the Moone, is alwayes greater in the first and last quarter, then in the full and new Moone. Hereby likewise it appeareth that in the time contayned be∣tweene new Moone and new Moone (which they call Mensem synodicum, that is the moneth coniunctional, or the time from coniunction to coniunction) the center of the epicycle maketh two complete reuolu∣tions, vnder the Orbe carying the Apogaeum of the Moones eccentrick.

And therefore in euery moneth, the center of the epicycle commeth twise to the Apogaeum and twise to the Perigaeum of the eccentrick; and so the monthly motion of the center of the epicycle, describeth an oual figure: the ends whereof are alwayes towards the place of the full and new Moone, and the •ides to∣wards

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the places of the first and last quarter.

By this that hath beene spoken, it is also manifest, that if the middle motion of the Sunne, be subtracted out of the middle motion of the Moone, there re∣maineth the middle motion of the Moones longi∣tude from the sunne, and that if this longitude againe be doubled, you shall haue the motion of the center of the Moones Epicycle from the Apogaeum of her ec∣centrick, which motion they call the center of the Moone,

CHAP. XIII. Of the Epicycle of the Moone, and how it is moued.

THe little Orbe placed in the Eccentrick, is called the Epicycle of the Moone; in the circumference whereof is also placed the body of the Moone, repre∣sented by the round Beade, set into the Moones Epi∣cycle in this Sphaere.

The plaine superficies of this epicycle agreeth euen with the plaine of the eccentrick: and the axtree a∣bout which it is moued, is perpendicular to the plaine of the eccentrick. This Epicycle is moued equally from his middle Apogaeum, about his owne center and axtree from the East Westwards, contrary to the motion of the eccentrick, carying forwards the body of the Moone with this motion 13. degrees and al∣most 4. min. euery day, and finishing his reuolution in 27. dayes 13. houres and 19. minutes almost.

The middle Apogaeum of the Epicycle is shewed by a right line, imagined to be drawne, from that point of the little circle (described by the motion of the center of the Moones eccentrick) which is opposite

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to the center of the Eccentrick, by the center of the Epicycle vnto the vpper part of the Epicycle.

But the true Apogaeum of the Epicycle, is shewed by a right line, vnderstood to be drawne from the Center of the earth by the center of the Epicycle, vnto the vpper part of the circumference thereof.

By the motion of this Epicycle it may easily be conceiued why the Moone seemeth to moue some∣times swifter and somteimes slower:* 6.3 For seeing that the vpper part of the Epicycle, moueth contrary to the motion of the Eccentrick from the East West∣wards, when the Moone commeth in that part, shee must needs seeme to moue more slowly, to them that are at the center of the world.

But when the Moone commeth in the nether part of the Epicycle, the Eccentrick caryeth the Epicy∣cle and the Epicycle caryeth the body of the Moone both one way: that is, from the West East-wards, and therefore at that time the Moone seemeth to moue more swiftly. According as you may see in Ephemerides, the d•••ne motion of the Moone to be sometimes little more then 11. degrees and some∣times againe little lesse then 15. degrees. The true motion of the Moone seemeth then to be swifter, when the Moone is in the Perigaeum of her Epicycle, and the Epicycle in the Perigaeum of the Eccentrick; because then she is not onely caryed forwards the same way both by her Epicycle and Eccentrick, but she is also at that time nearest vnto vs for which cause her motion shall seeme swifter, then when the Epicy∣cle is in other parts of the Eccentrick. 〈…〉

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CHAP. XIIII. The definitions of certayne Astronomicall wordes of Art, for the better vnderstanding of the Theoricke of the Moone.

1. THe line of the Moones middle motion, is a line vnderstood to be drawne from the cen∣ter of the earth, by the center of the Moones Epicy∣cle, vnto the Zodiack.

2. This line sheweth the middle place of the Moon in the Zodiack.

3. And the middle motion of the Moone, is the arch of the Zodiack, from the beginning of Aries, vnto the same line.

4. So likewise the line of the true motion, or of the true place of the Moone, is drawne from the center of the world, by the center of the Moone, to the Zo∣diack.

5. This line therefore sheweth the true place of the Moone in the Zodiack.

6. And the true motion of the Moone, is the arch of the Zodiack, from the beginning of Aries, vnto the true place of the Moone.

7. The middle longitude of the Moone from the Sunne, is the arch of the Zodiack, from the middle place of the Sunne Eastwards vnto the middle place of the Moone.

8. And this arch doubled, is called the doubled longitude of the Moone from the Sunne, or the center of the Moone (as the Alphonsines call it) which is nothing else but the arch of the Zodiack, betweene the place of the Apogaeum of the Eccentrick and the

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middle place of the Moone. It is called the doubled longitude of the Moone from the Sunne, because it is alwayes twice so much, as is the middle longitude of the Moone from the Sunne.

9. And it is called the center of the Moone, because it sheweth the distance of the center of the Moones Epicycle from the Apogaeum.

10. The equation, or Prosthaphaeresis of the center, is the arch of the Epicycle, betweene the middle and true Apogaeum of the Epicycle.

This equation or Prosthaphaeresis is nothing at all, when the center of the Epicycle is in the Apogaeum, or Perigaeum of the Eccentrick. But the Epicycle be∣ing in any other part of the Eccentricke there is al∣waies some equation of the center; yea in some parts thereof, where it groweth greatest, it is 13. degr. 9. mi∣nutes: and so long as the center of the Epicycle, is in the halfe of the Eccentrick descending from the A∣pogaeum to the Perigaeum, that equation is to be added to the motion of the Epicycle; but in the other halle of the Eccentricke ascending;, it must be subtracted; that so the true Argument 〈…〉 the Epicy∣cle may be had.

11. The Argument, or Anamalie of the Moone is nothing els, but the motion of the Moones Epicycle.

12. The true or middle argument, 〈…〉 is the arch of the Epicycle from the true or middle A∣pogaeum of the Epicycle, vnto the center of the body of the Moone, reckoned that way, which the epicycle moueth.

13. The equation of the argument, or Prostha∣phaeresis of the epicycle, is the arch of the Zodiack,

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〈…〉 the middle, and 〈◊〉 place of the Moone. This equation is 〈◊〉, when the Moone is in the true Apogaeum, or Perigaeum of her epicycle. But it is greatest, when the center of the Moone commeth 〈…〉 of the world, and touching the epicycle, when it is in the Perigaeum of the eccentrick.

And the Moone being in the first, that is in the 〈…〉 of the Epicycle, 〈…〉 from the true Apogaeum thereof, the middle place of the Moone goe 〈◊〉 before the true place, and the equation of the argument must therefore be subtracted: but when the Moone is 〈…〉 semicircle of the epicycle, 〈…〉 before the mid∣dle place, and to that equation must be added to the Moones 〈◊〉 middle motion, that the true motion and place of the 〈…〉 may be found.

CHAP. XV. The reason of the variety of the Moones equation, &c.

THis equation becommeth lesser or greater, accor∣ding as the epicycle 〈…〉 or nearer to the center of the world. The least equations are, when the epicycle is in the Apogaeum of the eccentrick, and con∣trarywise, the greatest must happen, the epicycle be∣ing in the Perigaeum of the eccentrick.

The difference between these greatest, and least Equations, Ptolemee and Copernicus call the excesse: but 〈◊〉, and the Alphonsines call it the di∣uersitie of the Diameter; because that difference of the equations ariseth by reason of the diuerse ap∣parent hignesse of the diameter of the Epicycle, ac∣cording

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as it is nearer to vs, or further from vs.

Therefore in the Astronomicall tables, they vse to set downe those equations onely, which happen when the Epicycle is in the Apogaeum of the eccentrick, which are the least equations, whereto they also ad∣ioyne the excesse, or diuersity of diameter, shewing how much those equations, which happen when the Epicycle is in the Perigaeum of the Eccentrick, exceed those which happen, the epicycle being in the Apogae∣um of the eccentrick. Moreouer, there are annexed certaine min. which they call Scrupula, or minuta proportion•alia: that is, proportionall minutes: where∣by is found, how much of the sayd excesse, is to be added to the foresayd equations, when the epicycle is in any other part of the eccentrick, then in the Apogae∣um: that so the true equation of the argument, for the same part of the eccentrick might at any time be found. For then onely is that whole excesse to be ad∣ded, when the epicycle is in the Perigaeum of the ec∣centrick. But if the epicycle be in any other part of the eccentrick; then looke what proportion 60. hath to the whole excesse, the same proportion haue the proportionall minutes, answerable to that part of the eccentrick, wherein the epicycle is, vnto the part pro∣portional of the excesse, which (part proportionall) being added to the equation before found, shall giue you the true equation.

CHAP. XVI. The reason 〈◊〉 Moones proportionall minutes, &c.

THe reason of those proportionall minutes, may in some sort be shewed, by those concentricall

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arches of circles, which you see drawne vppon the Moones eccentricall Orbe, in this Sphaere: but in∣deed all those arches must bee vnderstood, to haue al∣wayes the same center with the world, and not to be moued about togither with the Eccentrick. The vp∣permost of them is to be drawne by the center of the Epicycle being in the Apogaeum of the Eccentrick, and the nethermost is drawne by the same center when it is in the Perigaeum of the Eccentrick: so as the distance of these two arches, or Peripheryes, is iust twise so much as the eccentricitie; that is the distance of the center of the Eccentrick, from the center of the world, shewed by the distance of the short lines NO, or FF, vppon the Orbe carying the Apogaeum; or of PQ, or GH, vpon the caryer of the Perigaeum of the Moone.

The whole distance, between these two peripheries, from the vttermost to the innermost, is vnderstood to be deuided into 60. equall parts, imagining euery one of these to contayne 10. as may appeare by the fi∣gures set to euery one of them, from the vppermost to the nethermost, in this order: 10. 20. 30. 40. 50. 60.

Now the intersections of these Peripheries with the Eccentrick (that is) with the vppermost of the two deuided Peripheries, which are drawne round about through the midst of the Moones eccentricall Orbe) do shew what proportionable min. answer to any part of the eccentrick,* 6.4 after this manner: In the vppermost of the two foresaid graduated Peripheries, looke that distance of the center of the moones Epicycle from the Apogaeum of the Eccentrick, (that is to say) that doubled longitude of the Moone as the Alphonsines

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call it) which you desire: Then looke which of the consentricall arches before mentioned passeth by the the terme, or end of that distance or doubled longi∣tude: And thirdly, looke about in the same arch, what number is set thereuppon, for that sheweth you the number of the proportionall minut. answerable to the scituation of the Epicycle, at that distance from the Apogaeum of the Eccentrick.

These proportionall min. therefore may be defined to be nothing else,* 6.5 but the sixtieth parts of the diuersity of diameter, or of the excesse wherwith the equations of the argument, or Prostaphaeresis, of the Epicycle are to be augmented when the Epicycle is any other part of the Eccentrick, then in the Apogaeum.

Otherwise also, these proportionall min. may be defi∣ned, to be sixtieth parts of the excesse, wherewith the line drawne from the center of the earth, to the Apo∣gaeum of the Moones Eccentrick, exceedeth the line drawne from the same center to the Perigaeum of the Eccentrick: For these sixtieth parts also may not vn∣fitly be called proportionall min. because that alwaies looke how many of these parts there are left without the circumference of the Eccentrick, or beyond the center of the Epicycle; so many of the former sixtieth parts of the diuersity of diameter, or of the excesse of the Prostaphaerses of the Epicycle, must be added to the Equation of the argument, that the true equation of the argument may bee had, for that position, or scituation of the Epicycle, in the Eccentrick.

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CHAP. XVII. The reason of the Eclipses of the Sunne and Moone, &c.

NOw by this Sphere, it may easily be conceiued, why there is not an Eclipse, in euery coniunction or opposition of the Sunne and Moone. For seeing that the Moone hath for the most part a greater ap∣parent latitude, then the visible or apparent conioy∣ned semediameters of the Sunne and Moone in the coniunction: and because the true latitude of the Moone, is also for the most part greater then the ap∣parent semediameters of the Moone and shadow of the earth (at that place where the Moone should passe through that shadow) in the oppossition, to make an Eclipse: it commeth to passe, that in most coniun∣ctions and oppositions of the Sunne and Moone, there is no Eclipse. And the reason hereof is this, be∣cause that the Moone commeth vnder the way of the Sunne (which wee call the Ecliptick line) onely twise in a moneth, and those 2. points (wherin the wayes of the Sunne and Moone crosse each other) onely twise in a synodicall moneth, which two points wee called the Dragons head and taile; whereof wee haue also spoken before,) Wherfore, seeing the Sunne (going but once only through the compasse of the Ecliptick in a yeare) can come but once in a yeare to eyther of those points; the Moone for the most part, when she cōmeth to bee in opposition, or coniunction with the Sun, must needs be fo farre wide from the Ecliptick line, or way of the Sunne, either towards the North or South: that she can neither come betwixt vs and the Sun in the coniunction, nor yet within the com∣passe of the shadow of the earth in the opposition.

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But when the Sunne commeth neare eyther of those points (which hapneth once in six moneths (there must needs for the most part be some Eclipse, eyther of the Sunne or Moone, or both.

CHAP. XVIII. Of the diuersity of the bounds or spaces, within which an Eclipse may happen: and the reason of that diuersity.

THe bounds or distances from the Dragons head or taile, within which there may happen an E∣clipse of the Moone, are sometimes greater and some∣times lesse, by reason of the diuers distances of the Sunne, or Moone, or both of them, from the earth. For seeing the body of the Sunne is greater then the globe of the whole earth (as it is manifestly demon∣strated by Ptolemee and Copernicus) it must needs be, that the greater distance the Sun hath from the earth, the greater shadow must the earth haue; and the nea∣rer the Sunne is to the earth, the lesse shadow shall the earth haue, at the place of the Moons passage through the shadow, at equall distances from the earth.

Contrariwise, the further that the Moone is from the earth, the lesse shall the shadow of the earth be, and the nearer the Moone is to the earth, the greater shall the shadow be, at the place where the Moone is to passe through the shadow.

The greatest distance therefore from the Dra∣gons head or taile, wherein there can at any time happen any Eclipse of the Moone, is about 13. de∣grees. And the least distance at which it is possible for the Moone to auoid an Eclipse, is about 10. degr. and one third part of a degree; which hapneth when

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the Moone is in the Apogaeum of her Epicycle, in her greatest distance from the earth, and the Sunne in his Perigaeum, in the time of his greatest eccentricity, for then the Sunne commeth nearest to the earth and ma∣keth the least shadow: as contrarywise at the same time of his greatest eccentricity, beeing in his Apogaeum, he hath his greatest distance from the earth, and so maketh the earth cast forth her greatest sha∣dow. At which time, if the Moone also chance to be in the Perigaeum of her Epicycle, and so in her nearest distance from the earth, she may be something Eclip∣sed, although she be full 13. degrees or something more from the Dragons head or taile.

CHAP. XIX. How to find the place of the Dragons head and taile for a∣ny time.

NOw the place, and time of the full Moone, be∣ing easily knowne by some Almanack, or Prog∣nostication; it shall not be hard, to giue a reasonable neare estimate, and to foretell both the time, and quantity of the Eclipse of the Moone, the place of the Dragons head and taile, being first knowne after this manner.

The place of the Dragans head, being first giuen for any time, for euery yeare before the same time, adde to the same place: and for euery yeare after the same time subtract 19. degrees and one third part of a de∣gree and for euery moneth a degree and an halfe and a tenth part of a degree and for euery day 3. minutes and the remainder shall shew you the place of the Dragons head after the same time: or the summe be∣fore

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that time without any great errour.

As for example, The 30. of Iune this present yeare 1600. suppose you would know the place of the Dra∣gons head: The place therefore of the Dragons head being first giuen, for the beginning of the same yeare, in 0. degree 45. minutes, of Aquarius: and six moneths onely of that yeare being passed, I take for those six moneths 6. degrees and 6. halfe degrees that is 9. de∣grees and sixteenth parts of a degree that is 36. min. the summe of all which is 9. degrees and 36. minutes.

Which being subtracted out of 0. degree, 45. mi∣nutes of Aquarius, there remaine 21. degrees 9. min. of Capricorne, for the place of the Dragons head at that time.

CHAP. XX. A table for finding the place of the Dragons head and taile more exactly and the declaration thereof.

BVt if you would haue the place of the Dragons head more exactly, you may find the same most easily, by meanes of the table following, for any time within the space of these 20. yeares, yet to come.

This table conteyneth three principall parts or co∣lumnes, the first part sheweth you in what signe, degr. and min. the Dragons head is, at the beginning of any yeare; from this present yeare 1600. till the yere 1620. The second part sheweth how much the Dragons head moueth, in any number of moneths of the yeare: the third part giueth you the motion of the Dragons head, in any number of dayes of the moneth.

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The place of the Dragons head.
Yeare	Sign.	Deg.	Mt.	Moneths Complete.	De. Mi.	Da.	De. Mi.
1600	Aquarius	0	45	Ianuary	1 38	1	0 3
1601	Capricorn	11	21	February	3 8	2	0 6
1602	Sagittar.	22	2	March	4 46	3	0 10
1603	Sagittar.	2	42	Aprill	6 22	4	0 13
1604	Scorpio	13	22	May	8 0	5	0 16
1605	Libra	23	59	Iune	9 36	6	0 19
1606	Libra	4	39	Iuly	11 14	7	0 22
1607	Virgo	15	19	August	12 53	8	0 25
1608	Leo	25	59	Septemb.	14 28	9	0 29
1609	Leo	6	35	October	16 7	10	0 32
1610	Cancer	17	15	Nouemb.	17 42	11	0 35* 6.6
1611	Gemini	27	55	Decemb.	19 21	12	0 38
1612	Gemini	8	35			13	0 41
1613	Taurus	19	12			14	0 44
1614	Aries	29	52			15	0 48
1615	Aries	10	32			16	0 51
1616	Pisces	21	12			17	0 54
1617	Pisces	1	49			18	0 57
1618	Aquarius	12	29			19	1 0
1619	Capricorn	23	9			20	1 4
1620	Capricorn	3	49			21	1 7
						22	1 10
						23	1 13
						24	1 16
						25	1 19
						26	1 13
						27	1 26
						28	1 29
						29	1 32
						30	1 35

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CHAP. XXI. To finde the place of the Dragons head or tayle, by the former table.

FInde out in the former table, the moneth next go∣ing before the moneth giuen; finde out also the day of the moneth, Adde together the numbers of degrees and minutes answerable to that moneth and day of the moneth, and subtract the same out of the place of the Dragons head at the beginning of the yeare, adding thereto 30. degr. (••at is the whole signe next going before resolued in to degr.) if the Sunne aforesayd be greater then the number of degr. shewing the place of the Dragons head at the be∣ginning of the yeare: so shall you haue the place of the Dragons head for the time giuen. And the point of the Zodiack opposite to this, is the place of the Dragons taile.

Take for example, The 29. of Nouember 1601. I find therefore against October (the moneth going next before Nouember) 16. degrees 7. minutes and against the 29. day 1. degree 32. minutes, the summe of both these added together is 17. degrees 39. min. the place of the Dragons head for the beginning of the yeare 1601. is 11. deg. 21. min. of Capricorne, which because they be lesse then 17. deg. 39. min. I adde vn∣to them 30. deg. that is the whole signe of Sagittarie, and the summe of both is 41. deg. 12. min. out of which subtract 17. deg. 39. min. and there shall re∣maine 23. deg. 42. minutes of Sagittarie; the place of the Dragons head at that time. And the point of the Zodiacke which is opposite hereto (that is the 2•

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〈◊〉 42. minutes of Gemini) is the place of the 〈◊〉 tayle.

CHAP. XXII. To know at what time there shall be an Eclipse of the Moone.

THe place of the Dragons head being thus knowne, finde out the same place vpon the hori∣zon of the Sphaere, and see what day and moneth an∣swereth thereto finde out also the place of the full Moone, which hapneth next before or after that day, which place if it chance to bee within 11. or 12. deg. eyther before or after that point of the Zodiack which is opposite to the Dragons head, there must needs be for the most part in Eclipse of the Moone.

Likewise if you finde what day and moneth is an∣swerable to the place of the Dragons taile vpon the horizon of the Sphaere if the place of the full Moone which hapneth next before or after that day chance to be within 11. or 12. degrees of the Dragons head, for the most part there shall bee an Eclipse of the Moone.

As for example, The 20. of Ianuarie last this present yeare 1600. the place of the Dragons head was found (by the former Chapter) to haue beene in 29. deg. 41. min. of Capricorne; whereto there answereth in the horizon the 10. day of Ianuarie the place of the full Moone hapning next after, vpon the 20. of the same moneth in the morning must needs be in the place opposite to the place of the Sunne the same 20. 〈◊〉 Therefore because 〈◊〉 Sun that day is in 9. deg. 〈◊〉 one halfe of Aquarius, therefore the place

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Notes

* 4.1
Why this Cir∣cle is called the Equinocti∣all or Equator.

* 6.1
The scituati∣on of the Orbe carying the Dragons head and tayle.

* 6.2
The scituati∣on of the rest of the Orbes.

* 6.3
Why the Moone see∣meth some∣times to moue swifter, some∣times slower.

* 6.4
To finde the Moones pro∣portionall mi∣nutes.

* 6.5
What the pro∣portionall mi∣nutes of the Moone are.

* 6.6
•t the begin∣ing of the 〈◊〉 of our ••rd.