center then the center of the 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 inequalitie which seemeth to bee in the motion of the Sunne for although the Sunne moâ—e equally in his owne Oâ—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 nearest 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 moueth 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 being in those parts of the eccentrick that are nearest vnto vs seemeth greatest and when he is in those parts of his eccentrick that are furthest from vs he appeareth to be least 3. And lastly the inequality of the Sunnes distance from the earth caused by his eccentrick is one especiall 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 â—â—mely it is that part or rather point of the Orbe carying the Sunnes Apogaeum wherein the said Orbe is thinnest or narrowest Or it is that point of the eccentrick 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 Apogaeum 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 center 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 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 〈◊〉 â—erme it or the motion of the Sunnes Anomalie as Copernicus calleth it is the arch of the ecliptick conteyned 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 prosthapheresis 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 because 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 subtracted from the middle motion that so we might haue the true motion For so long as the Sunne is in the semicircle of his eccentrick discending from his Apogaeum to his â—â—â—gaeum so long this Prosthapheresis is to be subtracted from the middle motion but the Sunne being in the other halfe of his eccentrick ascending the Prosthapheresis or equation of the Sun must be added to the middle motion that 〈…〉 motion and place of the Sunne may be found Because that in the first semicircle of the eccentricke descending 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 alwaies 〈…〉 motion and place of the same CHAP. IX Of the vppermost Orbe of the Sphaere of the Moone carying 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 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 Westwards 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 order 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
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
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
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
order of Signes from the East West-wards Whereby it commeth to passe that both the Apogaeum and center of the eccentricke 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 Ecliptick doth not alwayes deuide the plaine of the eccentricke 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 onely the plaine of the Ecliptick deuideth the plaine of the Eccentrick by the center therof and consequently 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 eccentrick CHAP. XII In what proportion the Moones eccentrick and Orbe carying 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 caried in the eccentrick and the Apogaeum of the Eccentrick except it be when the center of the epicycle is 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 eccentrick 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 betweene 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 reuolutions 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 â—ides towards 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 remaineth the middle motion of the Moones longitude 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 eccentrick 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 represented by the round Beade set into the Moones Epicycle in this Sphaere The plaine superficies of this epicycle agreeth euen with the plaine of the eccentrick and the axtree about 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 almost 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 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 sometimes swifter and somteimes slower For seeing that the vpper part of the Epicycle moueth contrary to the motion of the Eccentrick from the East Westwards 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 Epicycle 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 dâ—â—â—ne motion of the Moone to be sometimes little more then 11. degrees and sometimes 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 Epicycle is in other parts of the Eccentrick 〈…〉 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 center of the earth by the center of the Moones Epicycle 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 Zodiack 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
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 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 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 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 going 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 â—â—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 beginning 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 vnto 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 remaine 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◠〈◊〉 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 horizon of the Sphaere and see what day and moneth answereth 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 answerable 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 Why this Circle is called the Equinoctiall or Equator The scituation of the Orbe carying the Dragons head and tayle The scituation of the rest of the Orbes Why the Moone seemeth sometimes to moue swifter sometimes slower To finde the Moones proportionall minutes What the proportionall minutes of the Moone are â—t the begining of the 〈◊〉 of our â—â—rd
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
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
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 number 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 of the Sunne for the beginning and ending of both moneths which you may finde by the second Proposition 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 Sâ—gitarie and for the ending 20. degrees 24. minutes of Capricorne Then seeke out the right ascensions of the same places 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 difference 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 The third Part. Of the Orbes whereof the SPHAERES of the Sunne and Moone haue beene imagined to bee made and of their Motions and Vses CHAP. I. Of the Orbes whereof the Sphare of the Sunne is made WIthin the Sphaere or Orbe contayning all the Circles that wee haue hitherto spoken of and representing vnto vs the Primum mobile that is the first and highest moueable Heauen that hath been imagined by the Astronomers to shew the reason of that daily motion which appeareth to bee in all the Heauens and of all the apparences that follow thereupon 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 signified by the yellow Circle that commeth next within 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 Next within this Orbe is placed the Eccentrick carying 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 Perigaeum 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 coloured 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 considered 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 furthest 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 furthest distance from the earth But vnder the broadest 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 oppositum Aâ—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 ouerthwart 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 wherin 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 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 another 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 second Prop. stretch out the other foot to the innermost 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
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 defined to be sixtieth parts of the excesse wherewith the line drawne from the center of the earth to the Apogaeum 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 vnfitly 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 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 apparent latitude then the visible or apparent conioyned 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 apparent 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 coniunctions and oppositions of the Sunne and Moone there is no Eclipse And the reason hereof is this because 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 compasse of the shadow of the earth in the opposition 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 Eclipse of the Moone are sometimes greater and sometimes 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 demonstrated 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 nearer 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 Dragons head or taile wherein there can at any time happen any Eclipse of the Moone is about 13. degrees 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 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 maketh 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 shadow 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 Eclipsed 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 any time NOw the place and time of the full Moone being easily knowne by some Almanack or Prognostication 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 degree 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 before 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 Dragons 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. degrees 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. minutes 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 columnes the first part sheweth you in what signe degr and min. the Dragons head is at the