called the Houre-circle which is deuided into 24. equall parts signifying and representiâ—â— vnto vs so many equall houres whereof both the 〈◊〉 houres are fixed iust vpon the Meridian becausâ—â—â—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 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 hereafter when we shall speake of the common vse of many circles of the Sphaere together And these two Circles that is the Meridian and Horizon are called immoueable because they keepe themselues alwayes 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 Heauens is made about two Points or Poles represented 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 also the South pole CHAP. VII Of the Equinoctiall Circle THat Circle which compasseth about the midst of the Sphaere and is euery where of equall distance from both Poles is called the Equinoctiall circle or the Equator either because it is equally distant from both Poles of the world or â—â—se because the Sunne comming vnder this Circle maketh equality 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 â— 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 hapneth 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 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 inequalitie 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 Eclipticke and of any other point of Heauen 8. And in this Circle are counted the right ascentions 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 descention is nothing else but the arch of the Equinoctiall contained betweene the beginning of Aries and that 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 ascentionall 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 Latitudes 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 betweene two Meridians whereof one goeth by the canary 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 declining 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 reasonable And this Circle gouerneth the directions whereby things to come are artificially fore-told 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
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 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 lowest in the Meridian and furthest from our Zenith But they that dwell within the Tropicks by a certaine similitude 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 beginnings of Cancer and Capricorne and two low sun-standings 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 Eclipticke which in Ptolomees time was 23. degrees 51. minutes and one third part of a minute But euer since that time it hath beene found by obseruation to decrease so as in this our age it is no more then 23. degrees 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 5. Hereby also the signes are distinguished which doe rise rightly and which rise obliquely in an oblique Sphaere For the descending halfe riseth rightly 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 artificiall 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 bounded 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 againe 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 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 Meridian altitudes or in respect of the motion he hath towards the North or South by reason of the obliquity 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 because it toucheth the Ecliptick in the beginning of Cancer It is also called the Summer Tropick and the Tropick 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 Tropick which toucheth the Ecliptick in the first point of Capricorne It is called the Tropick of Capricorne because it toucheth the Ecliptick in the beginning of Capricorne It is called the winter Tropicke and Tropick of the Winter sun-standing because the Sunne commeth to it in Winter It is also called the circle of the lowest Sunne-standing 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 Solstitiall points of the Eclipticke that is the points wherein the Sunne seemeth to stand and beginneth 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 obliquity 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 separate 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 and are euery where Equidistant from the Equinoctiall 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 Eclipticke 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 described 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 Zodiack and shew their distance from the poles of the Equinoctiall 2. The temperate Zones are bounded by these 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 conteyned 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 betweene the Tropicke of Cancer and the Artick polar circle The South temperate Zone is that which is conteyned 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 vntemperate 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 Torrid 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 conteyned 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 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 likelyhood 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 distant 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 towards 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 Southwards and then make a north shadow For which cause they that inhabite this Zone are called Amphiscij that is such as cast their noone shadowes on both sides But they that dwell in the temperate Zones are 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 inhabit the South temperate Zone hauing the Sunne at noone alwayes Northwards from their Zenith must needs haue their shadowes at noone alwayes towards 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 euery 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 * ⎠* 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. FIrst finde by obseruation or otherwise the height of the Pole or Latitude 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 Horizon 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 PROP. II. To know the place of the Sunne c. LOoke the day of the moneth for which you desire to know the place of the Sunne in the Horizon 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. minutes 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 Meridian is conteyned betweene that point and the Equinoctiall 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
more yeares it returneth againe into Aries The reuolution of one Trigon contayneth 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 beginning 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 aswell 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 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 called 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 measureth 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 quarters 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 Zodiack 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 Circles 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 Planets are obserued The chiefest judgement aswell in casting Figures as in reuolutions and directions is taken from this circle CHAP. X. The description of the two Colures THe two circles crossing each other at right Angles in the poles of the Sphaere are called the Colures whereof the one that passeth by the common 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-standings Vses common to both Colures 1. By meanes of these two Colures all the mouable circles of the materiall Sphaere are framed together 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 Eclipticke 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 into 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 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 oblique 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 Tropicall 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-standings These points are called tropicall which is as much to say as turne-points or points of returne because that when the Sunne going alwayes vnder the Eclipticke commeth to these points which are furthest 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
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. degree and 40. minutes of Gemini c. All this remouing of the Eclipses backwards commeth 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 and euen with the Orbes of the Sphaere of the Sunne which abide alwaies in all parts iust vnder the ecliptick line and hath his center agreeing and all one 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 that are conteyned 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 descendeth 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 intersection 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 Tigâ—â— Brahe his obseruation 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 proceeding 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 former character turned vp side downe after this manner ☋ 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 Ecliptick according to the obliquity or greatest declination 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 limit or bound of the Moones latitude and contrariwise 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 Perigaeum 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 Eccentrick 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 Lunae that is the Orbe carying the Moones Perigaeum which is the point wherein the Moone commeth nearest to the earth The vppermost and nethermost of these three 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 narâ—â—west part of the one is continually 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 almost 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 motion 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 ordinary Sphaere are described by the motion of the poles of the Ecliptick caryed about dayly with the 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 betweene 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 almost 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 alwaies 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 fastned in the Orbe carying the Moones Apogaeum equidistantly from the poles of the same Orbe therefore 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 describe certaine litle circles of equall bignes about the 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
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 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 being in any other part of the Eccentricke there is alwaies some equation of the center yea in some parts thereof where it groweth greatest it is 13. degr 9. minutes and so long as the center of the Epicycle is in the halfe of the Eccentrick descending from the Apogaeum 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 Epicycle 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 Apogaeum 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 Prosthaphaeresis of the epicycle is the arch of the Zodiack 〈…〉 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 middle 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 according 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 contrarywise the greatest must happen the epicycle being 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 diuersitie of the Diameter because that difference of the equations ariseth by reason of the diuerse apparent hignesse of the diameter of the Epicycle according 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 adioyne 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 Apogaeum of the eccentrick Moreouer there are annexed certaine min. which they call Scrupula or minuta proportionâ—alia that is proportionall minutes whereby 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 Apogaeum 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 added when the epicycle is in the Perigaeum of the eccentrick 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 proportional 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 arches of circles which you see drawne vppon the Moones eccentricall Orbe in this Sphaere but indeed all those arches must bee vnderstood to haue alwayes the same center with the world and not to be moued about togither with the Eccentrick The vppermost 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 figures 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 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 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 longitude 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 but