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 of Aries and the Meridian for that is the right ascension of that point So you shall finde the right ascension of the 10. degr of Taurus to be 37. degr 35. min. for if you bring that degree of Taurus to the Meridian 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 minutes of the Equinoctiall circle are conteyned between the East point of the Horizon and the beginning 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 Horizon you shall finde about 19. degrees and an halfe of the Equinoctiall at the same East part of the Horizon 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 together 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 of Taurus being found by the 4. Propo. to be 37. degrees 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 difference 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 contrariwise 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 minute the Sunne riseth and setteth at London Hauing 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 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 artificiall 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 ascension and reduced it into houres and minutes as in the former Proposition double thâ—se houres and minutes 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 subtract 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 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. Proposition 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 Westwards 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 riseth at 4. of the clocke and 48. minutes And bringing the same degree to the West semicircle 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 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 Horizon and set the Index to 12. a clocke as before Then turning forwards the Sphaere from East Westward till the place of the sunne come to
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
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
the East semicircle 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 before in the 10. degree of Taurus bring the same degree 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 Likewise if you bring the same 10. degr of Taurus to the West part of the Horizon and the Index to the Meridian and turne about the Sphaere till that degree come to the East semicircle of the Horizon the number 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 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 dâ—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 degrees 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 Eclipticke which is opposite to the place of the sunne vnto 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 Horizon sheweth how much the sunne is vnder the Horizon 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 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 being duly rectified by the first Proposition shall be about 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 Zodiack 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 Eastwards if it be in the fore-noone or West-wards if 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 being in the 10. degr of Taurus and find him to bee 30. degrees high in the fore-noone you shall find following the directions prescribed in this Proposition that it shall then be about 8. of the clocke in the morning 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 Horizon 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 Northwards 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 thereto vnder the Meridian and turne the Sphaere to or fro till there bee so many degrees and minutes of the 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 Ecliptick come right vnder that degree and minute of declination 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 declination 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 declination 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 betweene the feet of your Compasses 17. degrees of the Eclipticke and setting one foot of the Compasses 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 many 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 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 longer 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 immoueable 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 being 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 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 shorten 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 soeuer you turne the Sphaere it must I say be noted that the Sphaere must be turned that way which may soonest 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 contayned 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 Hereby therefore the error of them manifestly appeareth 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 Equinoctiall 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 measured 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 Meridian 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 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 morning 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
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 Serpentarius his right foot riseth achronycally and lastly you may finde that about the same time the Pleâ—ades and the Starre in the Bulls North home rise heliacally and that the same Starre also and the former Twinnes feet set heliacally PROP. XXX To finde the foure principall or Cardinall points of Heauen 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 therefore called the Ascendent another is at the vpper part of the Meridian aboue the Horizon and is called 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 Meridian 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 Meridian 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 semicircle of the Horizon and at the vpper and nether 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 together 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. degree of Taurus the middest or hart of Heauen the 27. of Capricorne the descendent the 27. deg of Scorpio 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 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 Latitude 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 Horizon then lifting vp the Pole till you finde 7. degrees and an halfe more aboue the Horizon then were before 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 inequality of the differences of right ascentions answerable 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 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 beginning of Aries or Libra is onely 55 minutes Secondly the apparent motion of the Sun is much swifter about his Parigâ—â—â— in the signe of Capricorne then about his Apogaeum in Cancer or in other parts of the Zodiacke so that whereas the Sunne being in Capricorne 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 naturall day is nothing else but the time wherein the Sunne moueth from the Meridian about till it returne 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 circle and so much more as is the difference of right ascention answerable to the apparent motion of the Sun in the meane time which differences of ascention because they be vnequall for the two causes before alledged the naturall dayes must needs also bee vnequall 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 agreeable thereto is 67. minutes or something more Therefore at that time in the space of one naturall day the Equinoctial circle must make one full reuolution and 67. minutes more But when the Sun is in Aries mouing 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 about so much in one day as before by 13. minutes Seeing then that 15. degr or little more of the Equinoctiall circle doe passe the Meridian in euery houre and consequently one degree of the Equinoctiall passeth the Meridian in 4. minutes of an houre and one minute of a degree in 4. seconds of an houre therefore 13. minutes of the Equinoctiall shall passe the Meridian in 52. seconds that is almost in one minute 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 againe is in our age greater almost by one minute of an houre when the sunne is in Capricorne then