minutes seconds thirds fourths and fifths into Decimalls and the contrary 10 A Table to convert the hours minutes seconds thirds fourths and fifths of a day into Decimalls and the contrary 14 A Table to convert hours parts into deg parts of the Aequator 20 A perpetual Table for the Equation of Time 21 The Suns mean motions 22 The Aequations of the Suns Excerntrick 26 The Moons mean motions 29 The Aequations of the Moons Excentrick 34 A Table for the finding of the secōd third inequalities of the Moon 37 Bullialdus his Table of Evection 40 A compounded Table of the Moons Evection and Variation 43 A Table of the Aequations of Nodes and Moons latitude 53 A Table of the Reductions to the Ecliptick 56 The difference of the true ☌ or ☠from the middle of the obscuration 57 A Table of the mean Lunations 58 The Horizontall Parallaxes Semidiameters and hourly motions of the Sun and Moon 59 The Declination and Meridian Angles 60 Tycho's Table of Refractions 61 Saturn's mean motions 62 Jupiter's mean motions 66 The mean motions of Mars 70 The mean motions of Venus 74 Mercuries mean motions 78 A Table of Declinations 82 A Table of Right Ascensions 89 A Table of Ascensional Differences 100 A Table of Oblique Ascensions 108 A Table of Positions for the latitude of 51 degrees 53 parts 138 A Table shewing the elevation of the Pole upon the severall circles of Position of the 11 12 2 and 3 houses for 60 degrees of latitude 151 A generall Table of Positions 152 A Catalogue of the more notable fixed Stars with their longitude latitude and magnitude for the yeare 1650 compleat 154 The Preface ALL Propositions Astronomical and Astrological have some dependence on the Sphere or Globe for the better understanding therefore of that which follows it is fit that the Reader be somewhat acquainted with the doctrine thereof that he know at least what a Globe is and what the lines circles and arches usually drawn thereon do represent Now a Globe or Sphere is an Analogical representation either of the Heavens or the Earth And in this Sphere or Globe there are ten imaginary circles whereof there are six great and foure small A great circle is such a one as divideth the body of the Globe into two equal Hemispheres And a small circle is that which divideth the same into two unequal Hemispheres wherof the one is more the other less then half the body of the Globe or Sphere The six great circles are these 1 The Horizon 2 The Meridian 3 The Equinoctial 4 The Zodiack The fifft and sixt are the two colures The four lesser circles are 1 The Tropick of Cancer 2 The Tropique of Capricorn 3 The circle Artick 4 The circle Antarctick And are all exprest in this annexed Diagram 1 The Horizon which is also called the Finitor is a circle which divideth the visible part of the Heavens from the not visible that is the lower Hemisphere from the higher in the figure noted with A B. 2 The Meridian is a circle which passeth by the Poles of the World and through the Zenith and Nadir and is marked with A Z B N. 3 The Equinoctial is a Circle which divideth the whole Sphere into two equal parts and is therefore equally distant from both the Poles to which when the Sun cometh which is twice in the Year the Dayes and Nights are of equal length all the World over this circle is noted with E F. 4 The Zodiack is a great circle which conteineth the 12 Signes cutting in the very middle the Equinoctial in two points which are the beginning of Aries and Libra whereof the one half viz. six Signes decline from the Aequator to the North Pole and are therefore called the Northern Signes as Aries ♈ Taurus ♉ Gemini ♊ Cancer ♋ Leo ♌ Virgo ♠The other six decline towards the South Pole and are therfore caled the Southern Signes as Libra ♎ Scorpio ♠Sagittarius ♠Capricornus ♑ Aquarius ♒ Pisces ♓ 5 The one of the Colures which dividing the Sphere into two parts passeth by the Poles of the World and the two Equinoctial points called the Equinoctial Colure and marked with C D. 6 The other Colure which dividing the Sphere also into two equal parts passeth by the beginning of Cancer and Capricorn and the Poles of the World called the Solstitial Colure and is the same with the Meridian as the Sphere is here projected 7 The Tropick of Cancer is one of the lesser circles distant from the Equinoctial towards the North Pole 23 deg 31 min. 30 seconds or in Decimal Numbers 23 deg 525 to which when the Sun cometh he causeth the longest day and shortest night to all Northern the shortest day and longest night to all Southern inhabitants and is noted with G ♋ 8 The Tropick of Capricorn is a circle distant from the Equinoctial towards the South Pole 23 deg 31 min. 30 seconds or in Decimal numbers 23 deg 525 parts to which when the Sun cometh he maketh the longest day and shortest night to all Southern the shortest day longest night to all Northern Inhabitants and is noted with H ♑ These two circles are called of the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 à convertendo because when the Sun toucheth any of these circles he is at his greatest distance from the Aequator and returneth thither again 9 The Artick circle is distant from the North pole of the world as much as the Tropick of Cancer is distant from the Equinoctial and is noted with K L. 10 The Antartick circle is distant from the South Pole as much as the Tropick of Capricorn is distant from the Aequator and is noted with O M. Besides these circles exprest upon the Globe there are other circles not exprest that are also in familiar use but these being sufficient for our intended matter omitting the rest we will now speak of the several affections of the Sphere or Globe and so proceed to practice According to the diverse habitude of the Aequator to the Horizon which is either Paralel to it or else cutteth it and that either in right or oblique angles there is a threefold position or Situation of Spheres The first is of those that have either Pole for there Zenith or vertical point with these the Aequator and Horizon are Parallel to each other or rather indeed do make but one circle between them and this is called a Parallel Sphere and they which there inhabit if any such be see not the Sun or other Star either rising or setting or higher or lower in their diurnal revolution The third position of the Sphere agreeth to all other places else and is called an oblique Sphere in which the dayes are sometimes longer then the nights sometimes shorter and sometimes of equal length when the Sun is placed in the Equinoctial point the dayes and nights are equal but when he declineth from the Aequator the dayes are observed to
the time of the Suns continuance in every of the 12 signes in their year therefore which is Solar there are alwayes 365 dayes And the Julian yeare which is the account of all Christendome doth differ from the other onely in this that by reason of the Suns excesse in motion above 365 dayes which is about 5 hours 49 minutes it hath a day intercalated once in 4 yeares and by reason of this intercalation it is more agreeable with the motion of the Sun then the former and yet here is a considerable difference between them which hath occasioned the Church of Rome to make some further amendment of the Solar year but hath not brought it to that exactness which is desired nor will as is to be feared be over-hastily brought to that exactnes which it might taking these accounts therefore as they now stand if we will reconcile that discrepancy that is between them there must be some beginning appointed to every of these accounts and that beginning must be referred to some one as to the common measure of the rest The most natural beginning of all accounts is the time of the Worlds Creation but they who could not attain the Worlds beginning have reckoned from their own as the Romanes ab urbe condita or from some great name or notable event so the Greeks account from their Olympicks and the Assyrians from Nabonasser and all Christians from the birth of Christ the beginning of which and all other the most notable Epochaes as others formerly so we now have also ascertained to their correspondent times in the Julian Period which Scaliger contrived by the continual multiplication of three circles all in former times of good use two of them do yet remain the Circles yet in use are those of the Sun and Moon the one to wit the Sun is a Circle of 28 years in which time the Sunday Letter makes all the varieties that it can have by reason of the Bisextile or Leap-year and the Circle of the Moon is the revolution of 19 years in which time though not precisely the Lunations do recur it is called the Golden Number and was made Christian by the Fathers of the Nicene Council as being altogether necessaay to the finding out of the Neomenia Paschalis upon which the Feast of Easter and the rest of the moveable Feasts depend The third Circle which now serves for no other use then the constituting of the Julian Period is the Roman Indiction or a Circle of 15 years for if you multiply 28 the Cycle of the Sun by 19 the Cycle of the Moon the product will be 532 this by 15 the product will be 7980 the number of years in the Julian Period whose admirable condition is to distinguish every year within the whole Circle by a several certain character the year of the Sun Moon and Indiction being never the same again until the revolution of 7980 years be gon about this Period the Authour fixed in the Tohu or eternal Chaos of the World 764 Julian years before the most reputed time of Creation which being premised we will now by example shew you how to reduce the years of Forreigners to our Julian years and the contrary 1 Example I desire to know at what time in the Turkish account the 5 of June 1649 falls The work is this The years compleat are 1648 and are thus turned into Dayes by the table of Dayes and Decimals of Dayes in Julian Years 1000 Julian yeares give dayes 365250 600 years give 219150 40 years give 14610 8 years give 292â— May Compleat 151 Dayes 5 The Summe 602088 Now because the Turkish account began July the 16. Anno Christi 622 convert these yeares into dayes also thus 600 Julian years give 219150 20 years give 7305 1 year gives 365 June Compleat 181 Dayes 15 The Summe subtract 227016 From 602088 There rests 375072 900 Turkish years gives 318930 There rests 56142 150 years gives 53155 There rests 2987 8 years give 2835 There rests 152 Giumadi I. gives 148 There rests 4 Therefore the 5th of June 1649 in our English accompt falls in the Turkish accompt in the year of Mahomet or their Hegira 1058 the 4th day of Giumadi II. 2 Example I desire to know upon what day of our Julian year the 23 day of the moneth Pharmuthi in the 1912 year currant of the Aegyptian accompt from the death of Alexanders fall The beginning of this Epochâ— is from the beginning of the Julian Period in compleat dayes  1603397 1000 Egyptian years give 365000 900 yeares give 328500 10 years give 3650 1 yeare gives 365 Phamenoth compleat 2â—0 Dayes 23 The summe 2301145 6000 Julian yeares 2191500 There rests 109645 300 yeares give 109575 There rests 70 April compleat 59 There rests 11 It therefore fell out in the yeare of the Iulian period 6300 the 11 of March that is subtracting from that period 4712 in the yeare of Christ 1588. He that understands this may by like method convert the yeare of other Epochaes into our Julian yeares and the contrary Next to the tables which concern the reduction of years in general we annexed tables for the perpetual finding of the Sunday letter Golden number and Epact in both the Old Julian and New Gregorian accompt with the fixed and moveable Feasts and a Catalogue of some famous places with their latitude and distance in longitude from the meridian of London whose use is so obvious that it needs but little explanation yet to take away all difficulty we have added these directions The Cycle of Sun Sunday Letter Golden Number and the Epact in both accounts are set against the yeare of our Lord and when those years are out they may be renewed againe as oft as you please thus for the yeare 1656 the Cycle of the Sun 1513 the Sunday letters in the English account are F E in the Gregorian B A the prime or Golden number in both is 4 the Epact in the English accompt is 14 in the Gregorian 4. And now to find the movable Feast seek the English Epact in the first Columne of that Table towards the left hand and the first F that follows will shew you that the 3d. of February is L X X Sunday the 17 of February L Sunday the 20th of February Ashwednesday the first E that follows will shew that Easter day is the 6th of April Ascension day the 15th day of May Whitsunday the 25 of May Corpus Christi the fifth of June Advent Sunday November the 30th But in the Gregorian the Epact and Sunday Letters must be sought in the first Columne towards the right hand so shall the Sunday Letters B A shew the Feast of Easter to be on the 9th of their April and the rest as in that line they are set down The fixed Feasts together with the Week-day Letters are set against their proper dayes in every moneth of the Julian year knowing therefore the Sunday Letter you may easily
know upon what day of the Week any Feast or day of the moneth shall be The Catalogue of places doth serve to shew the height of the Pole in those places and the Difference of the Meridians of any place in the Catalogue from that of London The Letter S notes that the distance is Westward A that it is Eastward the figures under the title of Time are Hours and Decimal parts of an houre the Earth or any Starre comes sooner or later to the Meridian of that place then that of London If the time of a Lunar Eclipse then or other appearance be given at London afternoon 8 hours 23 parts and the time when this happens at Uraniburge be inquired there is found in the Catalogue for Uraniburge 0 hour 83 parts A if therefore according to the letter A 83 parts be added to the time given it makes 9 houres 06 parts for the time at Uraniburge But if the time of another place be to be reduced to the time at London the difference is to be applied with the contrary title And that these Reductions whether in time or motion may be the better compared with those bookes that are written in the old Sexagenary forme we have added tables for the ready converting of Sexagenary parts into Decimall and the contrary the first of these tables is for the converting of the Minutes and Seconds c. of a Degree in motion and the other of the parts of a day in time an example in each will be a sufficient explanation Let it be required to find the Decimall answering to 37′ 25″ 16‴ 5 ' ' ' ' 29 ' ' ' ' ' in motion In the first page of the table I find 37′ 12″ which is the nearest lesse and 62 answering thereunto and in the third columne of the second page in the top of the page I find 12″ in which columne I find 25 seconds and in the sixt and last columne of that page right against 25″ I find this number 36111111 which being annexed to 62. The Decimall of 37 minutes 25 seconds is 6236111111 And the Decimall of 16 thuds 0000740741 The Decimall of 5 fourths 0000003858 The Decimall of 29 fifths 0000000373 Their summe 6236856083 is the Decimall sought 2. Example Again if it be required to find the Decimall of 8 hours 17 minutes 8 seconds 5 thirds 12 fourths 9 fifts In the first columne of the table entituled A Table to convert the hours and minutes of a day into Decimalls I find 7 hours 12 minutes and in the second columne the figure 3 then looking the 12 minutes in the top of the pages I cast mine eye downward in that column till I come to 8 hours 17 minutes and in the last columne of the page against 8 houres 17 minutes I find this number 451388889 and therefore The Decimall of 8 hours 17 minutes is 3451388889 The Decimall of 8 seconds 925926 The Decimall of 5 thirds 009645 The Decimall of 12 fourths 0387 The Decimal of 9 fifths 0005 Their aggregate 3452324852 Is the decimall sought To find the parts of a degree in motion or of a day in time answering to any Decimal given is but the contrary worke to the former Example As if it were required to find the parts of a degree answering to 6236856083 the 2 first figures of this Decimall are 62 which being sought in the first page of the table give me 37′ 12 and 62 being subtract from 6236856083 the remainder will be 36856083 which being sought in the last columne my nearest number is 36111111 and right against that number under 12 in the top of the page I find 25 therefore 37′ 25″ are the parts of a degree answering to the Decimall given but if you would find the thirds fourths and fifths from 36856083 Subtract 36111111 The remainder is 749972 Which being sought amongst the Decimals of the thirds gives me 16 thirds and this number to be subtracted from it 740741 and the remainder 004231 being sought amongst the Decimals of the fourths gives me 5 fourths and this number to be subtracted from it 3858 and the remainder 373 sought amongst the Decimals of the fifths gives me 29 fifths and so the parts of a degree answering to the Decimall given are 37 minutes 25 seconds 16 thirds 11 fourths and 29 fifths Thus may you also find the parts of a day in time answering to any Decimall given The next thing to be done towards the finding of the annuall revolutions of the planets is to find their entrance into any point of the Zodiack desired and that may be done thus Having the place of the planet taken by observation before and after its entrance into the point desired subtract the observed place next before from the observed place next after and the remainder shall shew you the apparent motion answerable to the time between those observation subtract also the former place from the place in the point desired and note their difference for as the former remainder that is the apparent motion between the observations is to the time between those observations so is this difference to the time between the first observation and the planets entrance into the point desired thus we are to deal with those observations that we our selves shall make but one mans age not being distance enough between the observations from whence the middle motions may be rightly stated we must take some observations upon trust and find the middle motions by comparing the observations made in former ages with those of our owne of the Sun or Earth take this Example following The vernal Equinox observed by Hypparchus in the year from the death of Alexander 178 was Mechir the 26 day and 95833333 that is at London 86746111. And the vernal Equinox observed at Uraniburge by Tycho 1588 was March the 9th 86458333 that is at London 82986111. And that the intervall of time between these two vernall Equinoctialls may be known the 9 of March 1588 must be reduced to the correspondent time in Egyptian yeares from the death of Alexander which according to the former directions is thus The Christian Aera began in the 4713 complete yeare of Julian period to which 1587 being added it makes 6â—00 from the beginning of the Julian period therefore to the 11 of March 1588 there are dayes as followeth 6000 Juliaâ— yeares give 2191500 300 years give 109575 February 59 Dayes 08 The Summe 2301142 The Aera Alexandri began in the 12 of November in 4390 yeare of the Julian period in which there are dayes 4000 1461000 300 109575 80 29226 9 3287 October 304 Dayes 11 Which being subtracted 1603397 From 2301142 There rests 697745 1000 Egyptian yeares give 365000 There rests 332745 900 yeares give 328500 There rests 4246 10 years give 3650 There rests 596 1 yeare gives 365 There rests 231 Phamenoth compleate 210 There rests 21 Therefore the 11 of March 2588 in our English account falls in the 1912 yeare of the Aera Alexandri the â—1 day
180. Deduct the Aphelion  95. 39377 There rests in the Ellipsis M H E  84. 60623 And therefore the ½ summe of the angles E M H and M E H  47. 69688 As the summe 203568 co ar 4. 6912904 To the differ 196432 5. 2932122 So tang ½ summe 47. 69688 10. 0409444 To tang ½ differ 46. 67763 10. 0254470 Aggregate 94. 37451 angle E M H  Difference 01. 01925 angle M E H  Differ doubled 2. 03850 angle M B H  Differ subtract 93. 35526 angle B M H  As the sine of M â— H 2. 0385 co ar 1. 4489043 To the side M H 3568 3. 5524248 So is the sine of B M H 86. 64474 9. 9992548 To the side H B 100134 5. 0095839 The side X H 1784  The summe 101918 co ar 4. 9917492 The differ 98â—50 4. 9927743 The tang ½ summe 47. 69688 10. 0409444 Tang. ½ differ 46. 67901 10. 0254679 Difference 01. 01787 X B H which being added to ♎ the place will be 181. 01787 from which subtract B G 5. â—9376 there rests 175 or L B 85. 62411.  The sine of C L 77927  The sine of L B 99707  As the summe 177634 co ar 4. 7504740 Is to K O 3168 3. 5007851 So is A G 10000 5. 0000000 To A G 1783 3. 2512591 which comes so neer to the Excentricity before found that we may without manifest error make use of either CHAP. 6. Of Stating the Earths middle motions by sundry observations TO find the Earths middle motion for any time under a yeare the way already prescribed in the first Chapter as to the use for which it was intended is exact enough but to state the true quantity of the Earths annual motion the apparent Equinoctials must be reduced into the mean which cannot be done unless the Aphelion be first found having found that therefore by the observations of Tycho we will now find it by the observations of Albategnius in the year from the death of Alexander 1206 and the intervall of time then between the Autumne and the Vernal Equinox was dayes 178. 51250 and the middle motion for that time is deg 175. 95083. The true motion is 180. From which subtract 175. 95083 Their difference is 4. 04917 The half difference is K L 2. 02458 Therefore as A E 3568 com ar 6. 4475752 To A E 100000 5. 0000000 So is K L 3533 3. 5481436 To K L 99019 4. 9957188 Half the arch H I L is 87. 97541 whose sine 99938 is the side H L and therefore This Autumne Equinox was observed September the 19th from the death of Alexander 1206 yeares that is in the yeare of our Lord 882. In the beginning therefore of the yeare of Christ 883 the Aphelion was in Gemini 24 d. 25176 And in June 1588 the Aphelion was in Cancer 5. 39377 Their difference is 11. 14201 And betweene both observations there are 706 Egyptian years now then to find the mean motion of the Aphelion for a yeare I say If 706 years give 11. 14201 what shall one yeare or 365 dayes give and the answer is Deg. 0. 0157818838 And againe if 365 dayes give 0157818838 one day shall give o deg 0000432380. In 882 Julian years there are 322150 dayes by which if you multiply 0000432380 the product will be deg 13. 9291217 which being deducted from the aphelion before found Gemini 24. 25176 the aphelion in the beginning of the Christian Aera will be in Gemini 10. 3226383 that is 19 21 29. But from Hypparchus that is from 177 yeare from the death of Alexander to the 1205 yeare compleate in the same account there are 1028 Egyptian years and the meane motion of the Aphelion in that time is Deg. 16. 2237765464 Gemini 24. 2516600000 Gemini 08. 0278834536 which being deducted from there rests for the aphelion at that time And therefore the vernall Equinox observed by Hypparchus in the yeare from the death of Alexander 178 Mechir 26. 95833333 was distant from the Aphelion deg 68. 027883 which being deducted from a Semicircle the angle in the Ellipsis of the next Chapter A M E will be found to be 111. 972117 and this angle is the summe of the angles M E H and M H E and therefore the equation to be subtracted may be thus found The side M E 200000  The side M H 3568 Logarithms The summe 203568 co ar 4. 6912905 The Differ 196432 5. 2932122 The tang ½ summe 55. 98606 10. 1707846 Tang. ½ differ 55. 03186 10. 1552873 Differ 00. 95420 angle M E H  Differ doubled 01. 90840 angle M B H or the Equation sought which may be converted into time thus if the parts of a degree of equal motion 98564 give one day 1. 90840 snall give 1. 93620 and this being added to the true Equinoctial Mechir 26. 95833 the middle will be Mechir 28. 8945â— or deducting 05625 for the difference of meridians between Uraniburge and Alexandria it will be at Uraniburge Mechir 28. 83828. And the vernall Equinox observed by Tycho at Uraniburge 1588 was March the 9. 86458 and the Earths aphelion then was in Cancer 5. 39377 and therefore the arch answering to the excentricity 3568 viz. deg 2. 04529 being converted into time as before will be days 2. 07508 which being added to the former time the middle Equinoctial wil be March the 11. 93966. And in the Egyptian account from the death of Alexander it was 1912 Pharmuthi 23. 93966 from which if you deduct in the same account 178 Mechir 28. 83828 between both observations there will be found 1734 Egyptian years dayes 55. 10138 which being converted into dayes give 632965. 10138. Hence to find the quantity of the Tropicall yeare I say if 1733 Zodiacks give dayes 632965. 10138 that one Zodiack shall give dayes 365. 2418357126. And to find the earths middle motion for a yeare I convert 1733 Zodiacks into degrees and they amount to 623880 degrees then I say if 632965. 10138 give 623880 that 365 days shal give 359. 76106661098 that is in Sexagenary numbers 359 deg 45 minutes 39 seconds 50 thirds 24 fourths And to find the meane motion for a day I say if 365 dayes give 359. 76106661098 that one day shall give 9856467579 that is in Sexagenary numbers 0 degrees 59 minutes 8 seconds 19 thirds 41 fourths 57 fifths And the daily motion of the Aphelion is 0000432380 which being deducted from the diurnall longitude gives the daily motion of the Anomaly 985603599 these things premised we will now determine the Epochaes of the middle motions The middle Equinoctiall Anno Christi 1588 March 11. 9â—966 is from the Aera Nabonassari 2336 Pharmuthiâ—3 â—3 93966. 2335 years being multiplyed by 359. 761067 the product will be 840042. 091445 and the diurnal motion 985647 being multiplied by 232 days the product will be 228. 670104 and the middle motion answering to the parts of a day 93966 is 926173 the which being added togethea do amount to
840â—71 degrees 687722 parts of a degree that is rejecting the whole circles 31 d. 687722 which being deducted from 360 the remainder 328. 312278 or 10 Signes 28 degrees and 312278 parts is the Radix of the earth or Suns mean longitude in the beginning of the Aera Nabonassari To which if you add deg 258. 692408 the middle motion for 424 years the whole circles being rejected the Radix of the earths middle motion to the beginning of the Aera Alexandri shall be 227. 004686 or 7 sines 17 deg 004686 parts And adding to this Epocha deg 51. 944398 which is the middle motion for 323 years 131 dayes the whole circles being rejected the Radix of the earths middle motion in the beginning of the Christian Aera shall be deg 278. 949084 or 9 signes 8 deg 949084 to which if you add 034223 the equal motion belonging to 034722 the difference between the Meridians of Uraniburge and London the Radix of middle motion at London will be 278. 983307 And the Aphelion 70. 322638 And the Mean Anomaly 208. 660669 CHAP. 7. To calculate the Suns true place and distance from the Earth HAving composed tables of the Suns middle motions according to the directions of the last Chapter his true place in the Zodiack and distance from the earth may thus be found 1 Write out the Epocha next before the given time and severally under that set the motions belonging to the years moneths and days compleat and to the houres and scruples current every one under his like onely remember that in the Bissextile year after the end of February the dayes must be increased by an Unite then adding them altogether the summe shall be the Suns meane motion for the time given Example Let the time given be May the 12th houre 11 parts 15 before noon at London in the Bissextile yeare 1656 and the Suns place to be soughts The numbers are thus   Suns Longitude Suns Apogeon   Deg. parts Deg. parts The Epocha 1640 291. 24777 96. 22265 Years comp 15 359. 37294  23686 April 118. 27760  519 Dayes 12 011. 82776  52 Houres 23  94458   Scruples 15  616   Suns Mean Longitude 421. 87681 96. 46522 2 Subtract the Apogaeum from the Mean Longitude there rests the mean Anomaly Example The Suns mean longitude 421. 67681 Apogaeum substract 96. 46522 Rest mean Anomaly 325. 21459 Whos 's complement to a Circle 34. 78541 is the angle A M E in the Ellipsis And the complement of A M E to a semicircle is the angle E M H 145. 21459. The side M E 200000  The side M H 3568  The summe 203568 co ar 4. 6912905 Differ 196432 5. 2932122 Tang. ½ summe of the opposite angles 17. 39270 9. 4958787  17. 39270  Tang. ½ Differ 16. 81799 9. 4803814 Differ 57471 is the angle M E H.  Difference doubled 1. 14942 is the angle M B H  3 The mean Anomaly being above 180 deg the Aequation found must be added to the sunsmeane longitude so have you the Suns true place Example The Suns meane longitude 421. 67681 Aequation adde 1 14942 The Suns true place 422. 82623 or 2 Signes 2 degrees 82623 parts of a degree  Lastly to find his distance from the earth I say As the sine of M B H 1. 14942 co ar 1. 6977118 Is to the side M H 3568 3. 5524249 So is the sine of B M H 34. 78541 9. 7562590 To the side B H  5. 0063957 or distance required 101483  Thus we have found the Suns place by calculation we will now shew how to reduce the Suns mean longitude to his true by the Table of Aequations of the Suns excentrick The Suns Anomaly in this example is 325. 21459 The Aequation of 325 is 1. 15566 326 1. 12648 Difference is 02918 Now then I say if one deg co ar 5. Give 2918 3. 4650853 What shall 21459 4. 3316095 The answer is 6â—6 2. 7966948 Aequation of 325 deg 1. 15566 Part proportional subt 626 Aequation equated 1. 14940 The Snns mean longitude 61. 67681 Aequation adde 1. 14940 Suns true place 62. 82621 And in like manner the Logarithme of the Suns distance from the Earth will be found to be 5. 0063633 which being more necessary then the distance it self in the calculation of the places of the other planets we have as most convenient placed in the table CHAP. 8. Of the Aequation of Civil Dayes SOme there are of late which allow not of any Aequation of Civil Dayes others will have the inequality proceed from two causes First from the unequal motion of the Sun in the Zodiack and the other from the Zodiacks obliquity Tycho whom we shall follow in this particular doth make the difference between the Suns true longitude and his Right Ascension to be the absolute Aequation of naturall dayes the which is also clearly demonstrated according to the Copernican Systeme by Thomas Street in his Ephemeris for the yeare 1655 which being but short is here inserted The Aequation of time demonstrated Let A be the center of the Sun and E of the Earth ♎ E the earths longitude from the Equinoctiall point in the ecliptick ♎ F the like arch projected in the Equator ♎ B the Right Ascension of the Earths or Suns true place G H is a diameter of the Equinoctiall and Meridian of the earths apparent diurnal revolution A B the semidiameter of the true meridian and equinoctial supposed in the heavens and G H parallel to A B though here they appeare as one right line Then let C D parallel to A F be likewise a diameter of the Equinoctial and Meridian of the meane or equal diurnal revolution Hence C E G the angle of the earths libration equal to B A F the difference of longitude and Right Ascension is the true Equation of time or the difference between the equal and apparent time And according to this Demonstration is our Table entituled A perpetual Table for the Equation of time composed In which you must enter with the signe and degree of the Suns place either in the uppermost and left hand columnes descending or in the lowermost and right hand ascending and in the common angle is the Equation according to the titles to be added or subtracted to or from the equal time that it may be made apparent But to reduce the apparent to the equal take the contrary title CHAP. 9. Of the Theory and Motion of the Moon THe Moon according to our Hypothesis is a secondary planet moving about the earth as the earth and other planets doe about the Sun and so not onely the earth but the whole Systeme of the Moone is also carryed about the Sun in a yeare And hence according to Hypparchus there ariseth a twofold but according to Tycho a threefold inequality in the Moons motion The first is periodicall and is to be obtained after the same manner as was the
F the complement of the poles elevation H G the complement of the Suns altitude to find G F H the angle of the Suns distance from the Meridian 1 The side H G 44. 54111  2 The side F H 67. 97090  3 The side G F 38. 46667  Summe 150. 97868  â—alf Summe 75. 48934  â—â—ne of F H 67. 97090 co ar 0. 0329234 â—â—ne of G F 38. 46667 co ar 0. 2061682 Differ G F ½ Summe 37. 02267 9. 7796909 Differ F H ½ Summe 07. 51844 9. 1167578 Quadrat of the sine of half the Angle  19. 1355403 Which bisected is sine of 21. 69295 9. 5677701 And the double therof is 43. 38590. The Suns distance from the Meridian And converted into time gives two houres 89259 parts CHAP. 21. To find the time of the Suns rising and setting with the length of the Day and Night THe Ascensional difference of the Sun being added to the Semidiurnal arch in a Right Sphere that is to 90 degrees in the Northern signes or substracted from it in the Southern there summe or difference will be the Semidiurnal arch which doubled is the day Arch and the Complement to 360 is the night Arch which bisected is the time of the Suns rising and the day Arch bisected is the time of his setting As when the Sun is in ten degrees of Gemini his Ascensional difference is found to be 30. 61613 The Quadrant Add 90. The Semidiurnal Arch 120. 61613 The diurnal arch 241. 23226 Whos 's Complement 118. 76774 Converted into time gives 7 houres 91078 parts which bisected gives the time of the Suns rising 3 hours 95539 parts or a little before 4 of the clock CHAP. 22. To find the distance of a star from the Meridian IF a Starre be between the Mid-heaven and the Horoscope deduct the Right Ascension of the Mid-heaven from the Right Ascension of the Starre what remaineth is the distance from the Meridian If a starre be between the Mid-heaven and the 7 house deduct the Right Ascension of the starre from the Right Ascension of the Mid-heaven and what remaineth is the distance as before IF a starre be between the 7 house and the Imum Coeli or fourth house deduct the Right Ascension of the Imum Coeli from the Right Ascension of the starre and what remaineth is the distance from the Meridan If a star be between the Ascendant and the Imum Coeli deduct the Right Ascension of the star from the Right Ascension of the Imum Coeli and what remaineth is the distance from the Meridian as before For Example In the preceding figure the Right Ascension of the Mid-heaven is 072 deg 82 parts The Sun is in the 12 house and his Right Ascension 155. 97 From which deduct the Right Ascension of the M. C. 72. 82 The distance of the Sun from the Meridian is 83. 15 CHAP. 23. To find the Elevation of the Pole above any circle of position A Circle of position is as it were a certaine Horizon upon which the point or star proposed doth arise passing by the two intersections of the Horizon with the Meridian and may be either above or under the Earth in respect of the place for which the figure is erected A star posited in the 1 2 3 4 5 6 house is Under the earth 7 8 9 10 11 12 house is Above the earth Thus in the annexed Diagram A H C is a circle of position passing by the Horizontal point of the Significator at H and the two intersections of the Horizon of the place at A and C and L M is the elevation of the pole above this Horizon of the star or circle of position To find which there must be known 1. The latitude of the place 2. The Declination of the star or point proposed 3. The distance thereof from the Meridian Hence to find the angle of Inclination of the circle of position with the meridian the proportions are as followeth 1. As the Radius To the tangent of the complement of the stars declination so is the Cosine of the stars distance from the meridian To the tangent of the first-arch To which the pole of the place being added or subtractod from it according to the following direction their summe or difference is the second arch If the distance of the star from the meridian be more then 90 and the declination South under the earth or north above it subtract the first arch from the poles elevation and what remaineth is the second arch If the distance of a star from the meridian be lesse then 90 and the declination south under the earth or north above it adde the poles elevation to the first arch and their aggâ—gate if lesse then 90 is the second arch if more then â—0 the complement thereof If the distance of a star from the meridian be either more or lesse then 90 and the Declination North under the earth or South above it Substract the elevation of the Pole from the first arch and what remaineâ—â—â—s the second arch If the distance of a star from the Meridian be a just quadrant the angle of inclination may be found at one operation as in the fourth example 2 As the sine of the first arch found Is to the cotongent of the Stars distance from the Meridian So is the sine of the second arch found To the cotangent of the angle of inclination Then to find the elevation of the Pole above the circle of position the analogie is 3 As the Radius To the sine of the Pole of the place So is the sine of the angle of inclination to the sine of the Pole of the Circle 1 Example Let the distance of a Star from the Meridian be more then 90 viz. 97 deg And the Declination of the Star 31 deg North above the earth the Pole of the place 45. Then in the oblique Spherical Triangle H M C we have limited 1 The side M C the Poles elevation 45 degrees 2 The side H M the complement of the Stars declination 59 degrees 3 The angle H M C the Stars distance from the Meridian 97 or instead thereof the acue angle I M H 83 the complement of the other to a Semicircle Hence to find I M the proportion is As the Radius 90 10. 000000â— To the tangent of H M 59 10. 2212262 So is the Cosine of I M H 83 9. 085894â— To the tangent of I M 11. 47 9. 3071206 which being substracted from 45 the Poles elevation there resteth 33. 53 the second arch 2 As the sine of I M 11. 47 9. 2985361 To the Cotangent of I M H 83 9. 089143â— So is the sine of I C 33. 53 9. 742232â— To the Cotangent of H C M 71. 17 9. 5328404 The angle of inclination 3 As the Radius 90 10. 0000000 To the sine of C M 45 9. 8494850 So is the sine of H C M. 71. 17 9. 9761116 To the sine of L M.
of Pharmuthi In which space of time There are dayes 697746 And from the death of Alexander to the 26 of Mechir 178 there are 64781 There rests 632965 From days 697746. 829â—6111 Subtract 64781. 86746111 There rests 632964. 96240000 And in this time the Earth or Sun hath gone 1733 circles 〈◊〉 623880 degrees Hence to find the mean motion for a year or 365 days I say If 632964. 9624 d Give 623880 degrees How many degrees shall 365 dayes give And the answer is 359 deg 7611456036. That is in Sexagenary numbers 359 deg 45 minutes 41 seconds 1 third 27 fourths Again to find the mean motion for a day I say If 365 dayes gives 359 degrees 7611456036 what shall one day give And the answer is 0. 9856469743. That is in Sexagenary numbers 0 deg 59 minutes 8 seconds 19 thirds 44 fourths And what is here done for the middle motion of the Earth or Sun may be done for the other planets CHAP. 2. Of the figure which the planets describe in their Motion HAving shewed in the former Chapter by what means the Annuall or Periodicall revolutions of the Planets may be knowne with their mean or equal motion for any part of those revolutions we should now shew you how by those equal motions to find their true or apparent places But we can never hope to find the true and exact Phenomenon of the planets unlesse we first know the figure in which they move And this must be collected from such affections as are by the constant observations of all ages found to be proper and naturall to them or may be rationally collected from them 1 That the planets have one onely motion in one onely line and that those motions are equal constant and perpetual hath been confirmed by the observation of all ages 2 And therefore they must needs be regular their motions must be in a circle or some other line returning into it selfe or else their motions could not be perpetuall 3 Their equall motions must have some place assigned which the planets naturally behold to be the beginning of this equall motion 4 And because the apparent place of a planet taken by observation is generally different from the place reckoned in its middle motion the inequality of this middle and apparent motion must be referred to the center of the Zodiacke â—s to the point of that inequâ—lity 5 And because the center of the Zodiacke and of the world is to out appearance the same the point of this inequality must be referred to the center of the world 6 And because of this difference between the middle and apparent motion the center of the world cannot be the true and exact center of the planets but the center of that figure which the planets describe in their motion must be some other point then the center of the Zodiacke 7 And though the planets to our appearance are observed to be sometimes swifter in motion then at other some yet the cause of this inequality of motion must not be such as shall alter the natural and equal motion of the planet it must be such as shall make the planet to be slower in its furthest distance from the center of the world and swifter at his nearest without transposing the equal motion into any other then the first place assigned whether superficies or circle 8 And further the apparent motions of the planets in their nearest and furthest distances from the center of the world being the same with their middle the way of the planets must be such that when they have gone 90 degrees from their farthest distance in their middle motions their apparent motions must be lesse then 90 by the quantity of that whole inequality between the middle and apparent motion And when the planets have gone a quadrant in their apparent motions their difference between their motions shall be that whole inequality also and therefore the center of that figure which the planets describe in their motions must be in the middle between the points of their equal and apparent motions 9 And because the mean motion from the point of a planets farthest distance from the center of the world to the first quadrant is greater then the apparent therefore the apparent motion must be greater then the mean from the first quadrant to the point of the planets nearest distance and consequently a greater portion of the line in which the planets move must be allowed to the apparent from the first quadrant to the point of nearest distance then from the point of farthest distance to the first quadrant 10 And because the equal motion must not change and that the apparent motion doth increase from the point of the planets farthest distance from the center of the world the angles of the middle motion must be reckoned in the arches of many parallel circles which shall also increase from the points of farthest to the point of their nearest distance to the center of the world and the line of the apparent motion must containe those circles in one and the same superficies and therefore that line must be excentricall from those circles of apparent motion and so placed that all the parts of apparent motion may proportionably answer to all the parts of equal yet so as that the least circles of equal motion shall agree with the point of the planets farthest distance and the greatest circles with the point of the planets nearest distance from the center of the world Seeing now that these circles of middle motion must be parallel succeeding one another in a continued series and are not one within another and that the apparent motion must in the farthest distance answer to the least circles in the nearest distance from the center of the world to the greatest there is none but a solid Superficies that can be capable of those greater and lesser circles And that an unequal sided Cone may be so cut as that the figure upon the plaine of that Section shall truly represent these affections of the planets the learned Bullialldus doth Demonstrate and for a preparation thereunto he sheweth first How two equal right lines may be so drawn in an unequal sided Triangle as that the one shall bisect the other An unequal sided Cone being cut through the Axis by a plaine perpendicular to the plain of the base shall make an unequal sided Triangle and let A B C be such a Triangle whose base B C let be bisected in I and parallel therunto draw the line P S which being within the triangle shall be also bisected in the point R and from a point taken in this line at pleasure suppose at H to the Axis of the Cone A I draw the line H M so as that the angles H M R and M R H may be equal then shall H M and H R be equal also and let the line H M being continued to the sides of the Triangle A B and A C be bisected in the point X and by
39352 656 52 2407407 40123 669 53 2453703 40895 682 54 2500000 41666 694 55 2546296 42438 707 56 2592502 43210 720 57 2638889 43981 733 58 2685185 44753 746 59 2731481 45524 759 60 2777778 46296 772 H. M. P 0 0 2. 24 1 4. 48 2 7. 12 3 9. 36 4 12. 00 5 14. 24 6 16. 48 7 19. 12 8 21. 36 9 A Table to convert the houres and minutes of a day into Decimals and the contrary 0 24 48 12 36 000000000 1 25 49 13 37 006944444 2 26 50 14 38 013888889 3 27 51 15 39 020833333 4 28 52 16 40 027777778 5 29 53 17 41 034722222 6 30 54 18 42 041666667 7 31 55 19 43 048611111 8 32 56 20 44 055555555 9 33 57 21 45 062500000 10 34 58 22 46 069444444 11 35 59 23 47 076388889 12 36 5. 17 24 48 083333333 13 37 1 25 49 090277778 14 38 2 26 50 097222222 15 39 3 27 51 104166667 16 40 4 28 52 111111111 17 41 5 29 53 11805555â— 18 42 6 30 54 125000000 19 43 7 31 55 131944444 20 44 8 32 56 138888889 21 45 9 33 57 145833333 22 46 10 34 58 152777778 23 47 11 35 59 159722222 24 48 12 36 10. 22 166666667 25 49 13 37 1 173611111 26 50 14 38 2 180555555 27 51 15 39 3 187500000 28 52 16 40 4 194444444 29 53 17 41 5 201388889 30 54 18 42 6 208333333 31 55 19 43 7 215277778 32 56 20 44 8 222222222 33 57 21 45 9 229166667 34 58 22 46 10 236111111 35 59 23 47 11 243055555 36 3. 15 24 48 12 250200000 37 1 25 49 13 256944444 38 2 26 50 14 26â—888889 39 3 27 51 15 270833333 40 4 28 52 16 277777778 41 5 29 53 17 284722222 42 6 30 54 18 291666667 43 7 31 55 19 298611111 44 8 32 56 20 305555555 45 9 33 57 21 312500000 46 10 34 58 22 319444444 47 11 35 59 23 326388889 48 12 36 8. 20 24 333333333 49 13 37 1 25 340277778 50 14 38 2 26 347222222 51 15 39 3 27 354166667 52 16 40 4 28 361111111 53 17 41 5 29 368055555 54 18 42 6 30 375000000 55 19 43 7 31 381944444 56 20 44 8 32 388888889 57 21 45 9 33 395833333 58 22 46 10 34 402777778 59 23 47 11 35 409722222 1. 1 24 48 12 36 416666667 1 25 49 13 37 423611111 2 26 50 14 38 430555555 3 27 51 15 39 437500000 4 28 52 16 40 444444444 5 29 53 17 41 451388889 6 30 54 18 42 458333333 7 31 55 19 43 465277778 8 32 56 20 44 472222222 9 33 57 21 45 479166667 10 34 58 22 46 486111111 11 35 59 23 47 493055555 12 36 6. 18 24 48 500000000 13 37 1 25 49 506944444 14 38 2 26 50 513888889 15 39 3 27 51 520833333 16 40 4 28 52 527777778 17 41 5 29 53 534722222 18 42 6 30 54 541666667 19 43 7 31 55 548911111 20 44 8 32 56 555555555 21 45 9 33 57 562500000 22 46 10 34 58 569444444 23 47 11 35 59 576388889 24 48 12 36 11. 23 583333333 25 49 13 37 1 590277778 26 50 14 38 2 597222222 27 51 15 39 3 604166667 28 52 16 40 4 611111111 29 53 17 41 5 618055555 30 54 18 42 6 625000000 31 55 19 43 7 631944444 32 56 20 44 8 638888889 33 57 21 45 9 645833333 34 58 22 46 10 652777778 35 59 23 47 11 659722222 36 4. 16 24 48 12 666666667 37 1 25 49 13 673611111 38 2 26 50 14 680555555 39 3 27 51 15 687500000 40 4 28 52 16 694444444 41 5 29 53 17 701388889 42 6 30 54 18 708333333 43 7 31 55 19 715277778 44 8 32 56 20 722222222 45 9 33 57 21 729166667 46 10 34 58 22 736111111 47 11 35 59 23 743055555 48 12 36 9. 21 24 750000000 49 13 37 1 25 756944444 50 14 38 2 26 763888889 51 15 39 3 27 770833333 52 16 40 4 28 777777778 53 17 41 5 29 784722222 54 18 42 6 30 791666667 55 19 43 7 31 798611111 56 20 44 8 32 805555555 57 21 45 9 33 812500000 58 22 46 10 34 819444444 59 23 47 11 35 826388889 2. 14 24 48 12 36 833333333 1 25 49 13 37 840277778 2 26 50 14 38 847222222 3 27 51 15 39 854166667 4 28 52 16 40 861111111 5 29 53 17 41 868055555 6 30 54 18 42 875000000 7 31 55 19 43 881944444 8 32 56 20 44 888888889 9 33 57 21 45 895833333 10 34 58 22 46 902777778 11 35 59 23 47 909722222 12 36 7. 19 24 48 916666667 13 37 1 25 49 923611111 14 38 2 26 50 930555555 15 39 3 27 51 937500000 16 40 4 28 52 944444444 17 41 5 29 53 951388889 18 42 6 30 54 958333333 19 43 7 31 55 965277778 20 44 8 32 56 972222222 21 45 9 33 57 979166667 22 46 10 34 58 9861â—1111 23 47 11 35 59 993055555 24 48 12 36 00 000000000  Seconds Thirds Fourths Fifths 1 0000115741 0000001929 0000000032 0000000001 2 231481 385â— 64 0000000001 3 347222 5787 96 2 4 463963 7716 0000000129 2 5 578704 9645 161 3 6 694444 0000011574 193 3 7 810185 13503 225 4 8 925926 15432 257 4 9 0001041666 17361 289 5 10 1157407 19290 321 5 11 1273148 21219 354 6 12 1388889 23148 387 7 13 1504630 25077 420 7 14 1620371 27006 453 8 15 1736112 28935 486 8 16 1851853 39864 518 9 17 1967593 32793 559 9 18 2083333 34722 582 10 19 2199074 36651 614 10 20 0002314815 0000038580 0000000643 0000000011 21 2430555 40509 675 11 22 2546296 42438 707 12 23 2662037 44367 739 12 24 2777778 46296 771 13 25 2893518 48225 803 13 26 3009259 50254 836 14 27 3125000 52183 869 14 28 3240741 54112 902 15 29 3356482 56041 934 15 30 0003472222 0000057870 0000000965 0000000016 31 0003587963 00000059799 0000000997 0000000016 32 3703704 61728 1030 17 33 3819444 63657 1062 17 34 3935185 65586 1094 18 35 4050926 67515 1126 18 36 4166667 69444 1157 19 37 4282407 71373 1189 19 38 4398148 73302 1222 20 39 4513889 75231 1254 20 40 4629630 77160 1286 21 41 4745370 79089 1318 22 42 4861111 81018 1350 22 43 4976852 82947 1382 23 44 5092592 84876 1414 23 45 5208333 86805 1446 24 46 5324074 88734 1479 24 47 5439814 90663 1511 25 48 5555555 92592 1544 25 49 5671296 94521 1676 26 50 5787037 96451 1680 27 51 5902778 98380 1641 27 52 6018518 100309 1673 28 53 6134259 102238 1705 28 54 6250000 104167 1737 29 55 6365741 106096 1770 29 56 6481481 108025 1802 30 57 6597222 109954 1834 30 58 6712963 111883 1866 31 59 6828704 113812 1898 31 60 6944444 115741 1929 32 A Table converting Hours and parts into Degrees and parts of the Aequator   IV ‴ ″ ″ ′ 0 Ho. Deg. M D. Parts 1 15 01 00 15000 2 30 02 00 30 3 45 03 00 45 4 60 04 00 60 5
103 283 78 258 04750 102 282 79 259 04389 101 281 80 260 03972 100 280 81 261 03583 99 279 82 262 03194 98 278 83 263 02806 97 277 84 264 02389 96 276 85 265 02000 95 275 86 266 01611 94 274 87 267 01250 93 273 88 268 00833 92 272 89 269 00417 91 271 90 270 00000 90 270   Adde   The difference of the true ☌ or ☠from the middle of the Obscuration Lat. ☽ Differ D. par Parts 0 10 00861 0 20 01722 0 30 02611 0 40 03500 0 50 04361 0 60 05222 0 70 06083 0 80 06972 0 90 07833 1 00 08722 1 10 09583 1 20 10472 1 30 11361 1 40 12222 1 50 13083 1 60 13944 Latitude ☽ North Desc. Adde South Asc. Adde North Asc. Subst South Desc. Subst A Table of the Meane Lunations Yeers Hours Parts Months Common Bissextile Daies Hours 1 255 18944 complea Hours parts Hours Parts 2 510 37889 January 0035 26556 0035 26556 1 24 3 056 83417 Februa 0707 26556 0022 531â—9 2 48 B4 336 02361 March 0043 7972â— 0057 79722 3 72 5 591 21306 April 0045 06306 0069 06306 4 96 6 137 66833 May. 0080 32889 0104 32889 5 120 7 392 85778 June 0091 59472 0115 59472 6 144 B8 673 04722 July 0126 86028 0150 86028 7 168 9 218 50250 August 0162 12611 0186 12611 8 192 10 473 69194 Septem 0173 39194 0197 39194 9 216 11 020 14722 October 0208 65778 0232 65778 10 240 B12 299 33667 Novem 0219 92361 0243 92361 11 264 13 554 52611 Decem. 0255 18944 0279 18944 12 288 14 100 98139    13 312 15 356 17083 Canonion Syzygiarum 14 336 B16 635 36028  ☌ ☠15 360 17 181 81556    16 384 18 437 00500  Hours Parts Hours Parts 17 408 19 692 19444 I 0708 73417 0354 36722 18 432 B20 262 64972 II 1417 46833 1063 10139 19 456 40 525 29944 III 2126 20250 1771 83556 20 480 60 079 21528 IV 2834 03667 2480 56972 21 504 80 341 86500 V 3543 67083 3189 30361 22 528 100 604 51472 VI 4252 40500 3898 03806 23 552 200 500 29556 VII 4961 13944 4606 77222 24 576 300 396 07639 VIII 5669 87361 5315 50667 25 600 400 291 85694    26 624 500 187 63778 Epochae 27 648 600 083 41861 Yeares Compleat Hours Parts 28 672 700 687 93361    29 696 800 583 71417  Christi 0425 70667 30 720 900 479 49500  1600 0176 06694   1000 375 27583  1620 0439 31667   2000 041 81750  1640 0701 96639   3000 417 09333  1660 0255 88194   The Horizontal Parallaxes Semidiameters and Hourly motions of the Sun and Moon Degrees Horiz Paral. ☉ Semidiam ☉ Hourly motion ☉ Semia Cone Shad. HorizoÌ„ Paralax ☽ Semidiam ☽ Hourly motion ☽ Degrees  Parts Parts Parts Parts Parts Parts Parts  0 03855 26936 03972 22948 92692 25964 49444 360 6 03859 26968 03981 22980 92982 26043 49916 354 12 03863 27001 03990 23013 93273 26122 50388 348 18 03868 27033 03999 23046 93564 26201 50860 342 24 03872 27066 04008 23078 93854 26280 51332 336 30 03876 27099 04017 23111 94145 26359 51804 330 36 03881 27131 04026 2â—144 94436 26438 52276 324 42 03885 27164 04035 23176 94727 26517 52748 318 48 03889 27196 04044 23209 95018 26596 53220 312 54 03894 27239 04052 23242 95308 26679 53682 306 60 03898 27271 04061 23274 95599 26754 54164 300 66 03902 27304 04070 23307 95889 26833 54636 294 72 03907 27337 04079 23340 96180 26912 55108 288 78 03911 27369 04088 23372 96471 26991 55581 282 84 03915 27401 04097 23405 96762 27069 55953 276 90 03919 27433 04106 23438 97052 27148 56425 270 96 03924 27466 04115 23470 97343 27227 56897 264 102 03928 27498 04124 23503 97634 27306 57369 258 108 03932 27531 04132 23536 97925 27385 57841 252 114 03937 27564 04141 23568 98215 27464 58313 246 120 03941 â—7596 04150 23601 98506 27543 58785 240 126 03945 27629 04159 23634 98797 27622 59257 234 132 03950 27661 04168 23666 99087 27701 59729 228 138 03954 27694 04177 23699 99378 27780 60201 222 144 03958 27727 04186 23732 99669 27859 60673 216 150 03963 27759 04195 23764 99960 27938 61145 210 156 03967 27792 04204 23797 1 00250 28017 61617 2â—4 162 03971 27824 04213 23830 1 00541 28096 62089 198 168 03976 27857 04222 23863 1 00832 28175 62461 192 174 03981 27889 04231 23896 1 01123 28254 6â—933 186 180 03988 â—7916 04250 23928 1 01414 28333 â—3611 180 Dist 4 32 9 33 291 79 472 ereÌ„c The Declination and Meridian Angles  ♈ ♎ ♉ ♠♊ â™ Â Â Declina Ang. Declina Ang. Declina Ang.   D. parts D. P. D. Parts D. P. D. Parts D. P.  0 0 00000 66. 47 11 51167 69 33 20 22278 77. 70 30 1 0 39889 66. 47 11 86333 69 52 20 43917 78. 07 29 2 0 79806 56. 48 12 21111 69 72 20 63583 78. 43 28 3 1 19694 66. 50 12 55583 69 92 20 83278 78. 80 27 4 1 59528 66. 52 12 89694 70 13 21 02361 79. 18 26 5 1 99361 66. 55 13 23472 70 35 21 20806 79. 57 25 6 2 39111 66. 58 13 56861 70 58 21 38528 79. 95 24 7 2 78778 66. 63 13 89917 70 81 21 55611 80. 33 23 8 3 18444 66. 68 14 22556 71 05 21 72083 80. 72 22 9 3 57972 66. 73 14 54806 71 30 21 87833 81. 12 21 10 3 97444 66. 78 14 86639 71 55 22 02917 81. 51 20 11 4 36778 66. 85 15 18056 71 80 22 17278 81. 92 19 12 4 76028 66. 92 15 49056 72 07 22 30972 82. 31 18 13 5 15139 67. 00 15 79639 72 33 22 43944 82. 73 17 14 5 54139 67. 08 16 09750 72 60 22 56222 83. 15 16 15 5 92972 67 18 16 39417 72 88 22 67750 83. 57 15 16 6 31611 67. 28 16 68861 73 17 22 78611 83. 98 14 17 6 70167 67. 40 16 97278 73 45 22 88694 84. 40 13 18 7 08500 67. 52 17 25500 73 75 22 98083 84. 83 12 19 7 46667 67. 63 17 53167 74 05 23 06750 85. 25 11 20 7 84611 67. 75 17 80389 74 35 23 14639 85. 68 10 21 8 22389 67. 88 18 07056 74 67 23 21806 86. 10 09 22 8 59944 68. 02 18 33250 74 98 23 28222 86. 53 08 23 8 97222 68. 15 18 58833 75 30 23 33889 86. 97 07 24 9 34278 68. 30 18 83917 75 63 23 38833 87. 40 06 25 9 71139 68. 47 19 08444 75 97 23 4300â— 87. 83 05 26 10 07722 68. 63 19 32389 76 30 23 46417 88. 26 04 27 10 44000 68. 80 19 55750 76 65 23 49083 88. 70 03 28 10 80056 68. 97 19 78528 77 00 23 50972 89. 13 02 29 11 15750 69. 15 20 00722 77 35 23 52139 89. 57 01 30 11 51167 69. 33 20 22278 77 70 23
reduced their Epoches to the Meridian of London the most famous City of this our Island of Great Britain For which reason and for the easiness of the calculation which our own Country-man hath invented and we here used the Treatise it selfe doth carry the style of Astronomia Britannica And whether this method of finding the first inequality will agree with observation cannot be known until a Geometrical way of finding the Excentricities Aphelions of the Planets in an Ellipsis be also propounded to us and if at last when all things in this Elliptical Astronomy shall geometrically be demonstrated the places of the Planets thus found shall not agree with observation it will be hard to say in what particular the fault doth lie and therefore we must not then impute it to the first inequality much lesse now when the Geometry of that is demonstrated other parts are defective but a new Hypothesis must be thought of and until this shall be effected as there are no Tables extant by which the places of the Planets can be computed with so much ease so none can be expected by which their places may be computed with more probability of truth then by these which wee must now submit to thy censure and do commend to thy perusal IOHN NEWTON The Contents of the severall Books or parts of Astronomia Britannica The first Book The Preface Page 1. THe Suns greatest declination being given to find his declination in any point of the Eclipticke 9 How to finde the declination of a Planet or fixed Star with latitude 10 How to finde the Right Ascension of any point of the Eclipticke 13 How to finde the Right Ascension of a Planet or other Star with latitude 15 The elevat of the Pole declin of the Sun given to find his amplit 16 The Meridian altitude and declination of the Sun with the Poles elevation given to find his true place in the Zodiacke 17 Having the Meridian altitude of an unknown Star and the distance thereof from a known Starre to find the Right Ascension of the unknown Star Ibid. Having the declin and Right Ascension of a Star given to finde the longitude and latitude thereof 19 How to finde the Ascensionall difference 20 How to finde the Oblique Ascension or Descention of any point of the Eclipticke 21 The Poles elevation and the Suns declination being given to finde his altitude at any time assigned 22 Having the Suns greatest declination with his distance from the next Equinoctional point to finde the Meridian angle or intersection of the Meridian with the Eclipticke 26 To finde the angle of the Meridian with the Horizon Ibid. The Poles elevation with the Suns altitude and declination given to finde his Azimuth Ibid. How to erect a Figure of Heaven 27 To find the angle of the Ecliptick with the horizon or the altitude of the Nonagesime deg together with its distance from the mid-heaven 36 To finde the Parallactical angle or angle of the Ecliptick with the verticall circle â—7 The elevation of the Pole and declination of the Sun given to finde the time when he will be due East and West 39 The elevation of the Pole with the Suns declination and altitude given to finde his distance from the Meridian 40 To finde the time of the Suns rising and setting with the length of the Day and Night Ibid. To finde the distance of a Star from the Meridian 41 To finde the elevation of the Pole above any circle of Position Ibid. Of the Arke of Direction what it is and how to finde it 45 How to direct the Mid-heaven and the Imum Coeli 46 How to direct the Ascendent or Significator posited in the Signes ascending Ibid. How to direct a Significator posited in the Signes descending 47 How to find the Arch of the Equator whereby is made the generall Table of Positions 48 How by the generall Table of Positions to make a particular Table for any latitude there exprest 49 Of the doctrine of the Sphere in Tables 51 The second Book OF the yeare Civill and Astronomical 57 Of the Figure which the Planets describe in their Motion 66 Of the lines and method to be used for the finding of a Planets true longitude from the Aphelion in this Figure 72 Of the proportion by which the motion of the Planets do increase from the Aphelion to the Perihelion 74 Of the inequality of the Earths annuall motion and of the Diameter in which the Aphelion and Perihelion are placed 81 Of stating the Earths middle motions by sundry observations 90 To calculate the Suns true place and distance from the Earth 94 Of the Aequation of Civill Dayes 97 Of the Theory and motion of the Moon 98 To calculate the true motion of the Moon by Tables 109 To find the Moons true latitude and place in the Ecliptick 113 Of the motion of the fixed Starres 115 Of the motion of Saturn 116 Of the motion of Jupiter 121 Of the motion of Mars 124 Of the motion of Venus 128 Of the motion of Mercury 133 Of the Semidiameters of the Sun Moon and shadow of the Earth 136 Of the proportion and magnitude of the three great bodies the Sunne Moon and the Earth 142 Of the proportion between the Orbs of the superiour and inferiour Planets and the Orbe of the Earth 144 To finde the mean Conjunction and Opposition of the Sun Moon 151 To finde the true Opposition and Conjunction of the Sun and Moon 152 To finde whether there will be an Eclipse or not 154 To finde the quantity of a Lunar Eclipse Ibid. To finde the duration of a Lunar Eclipse or the continuance of the totall darknesse where the Eclipse is totall 155 To finde the Moons latitude at the beginning end of the Eclipse 156 To finde the middle of the Eclipse or greatest darknesse 157 Of the calculation of the Suns Eclipse 159 To finde the Parallaxes of longitude and latitude 160 To finde the visible motion of the Moon from the Sun for any time assigned 162 To find the time of the visible Conjunction of the Sun and Moon Ibid. To finde the visible latitude of the Moon at the time of the visible Conjunction 163 To finde the quantity of a Solar Eclipse 164 To finde the beginning and ending of the Suns Eclipse Ibid. To finde the visible latitude of the Moon at the beginning and end of the Suns Eclipse 165 To delineat the Eclipses of the Sun and Moon 166 The use of the Table of Refractions 168 The Index of the Tables A View of the more notable Epochae 2 A Table shewing the Dominical Letter in both accompts 4 A Table shewing the Golden number Epact in both accompts Ibid. The Anticipation of the Gregorian Kallender Ibid. A Table of moveable Feasts in both accompts 5 A Table of fixed Feasts 6 A Catalogue of Places their latitudes and distance in longitude from the Meridian of London 8 A Table to convert Sexagenary