Christi 622. you must convert these years into days also 600 Julian years give days 219150 20 Years give days 7305 1 Year giveth days 365 Iune complete 181 Days 15 The Sum is 227016 Which being substracted from 602088 There resteth days 375072 900 Turkish years give days 318930 There resteth 56142 150 Turkish years give days 53155 There resteth 02987 8 Turkish years give days 2835 There resteth 152 Giumadi 4. 148 There resteth 4 Therefore the fifth of Iune 1649. in our English Account doth fall in the year 1058. of Mahomet or the Turkish Hegira the fourth day of the moneth Giumadi 11 2. Example I desire to know upon what day of our Julian year the 17 day of the moneth in the 1069 year complete of the Persian Account from Ieshagile doth fall The beginning of this Epocha is from the Epocha of Christ in complete days 230639 1000 Persian years give 365000 60 Years give 21900 9 Years give 3285 Chortal complete 90 Days complete 16 The Sum 620930 1000 Julian years Substracted 365250 There rests 255680 700 Julian years 255675 There rests 5 Therefore it falls out in the Julian year from Christ 1700. the fifth day of Ianuary He that understands this may by the like method convert the years of other Epochas into our Julian years and the contrary The Anticipation of the Gregorian Calendar is more easily obtained for if you enter the Table with the years of Christ complete you have the days to be added to the time in the Julian Account to make it answer to the Gregorian which will be but ten days difference till the year 1700. and then the difference will be a day more until the year 1800. and so forward three days difference more in every 400 years to come unless our year shall be reformed as well as theirs CHAP. II. Of the Cycle of the Moon what it is how placed in the Calendar and to what purpose THat the Civil Year in use with us and all Christians doth consist of 365 days and every fourth year of 366 hath been already shewed with the return of the Sunday Letter in 28 years In which time the Moon doth finish her course in the Zodiack no less than twelve times which twelve Moons or 354 days do fall short of the Sun's year eleven days in every common year and twelve in the Bissextile or Leap-year And by Observation of Meton an Athenian it was found out about 432 years before Christ that the Moon in nineteen years did return to be in Conjunction with the Sun on the self same day and this Circle of nineteen years is called the Cycle of the Moon which being written in the Calendar against the day in every Moneth in which the Moon did change in Letters of Gold was also called the Golden Number or from the excellent use thereof which was at first only to find the New Moons in every Moneth for ever but amongst Christians it serveth for another purpose also even the finding of the time when the Feast of Easter is to be observed The New Moons by this Number are thus found In the first year of the Circle or when the Golden Number is 1 where the Number 1 was set in the Calendar in any Moneth that day is New Moon in the second Year where you find the golden Number 2 in the third Year where you find the golden Number 3 and so forward till the whole Circle be expired then you must begin with one again and run through the whole Circle as before 2. And the reason why the Calendar begins with the golden Number 3 not 1 is this The Christians in Alexandria had used this Circle of the Moon two Years before the Nicene Council And in the first of these Years the new Moon next to the Vernal Equinox was upon the 27th Day of the Egyptian month Phamenoth answering to the 23d of our March against that Day therefore they placed the golden Number 1. And because there are 29 Days and a half from one new Moon to another they made the distance between the new Moons to be interchangeably 29 and 30 Days and so they placed the same golden Number against the 26 Day of Phurmuthi the Month following and against the 26 Day of the Month Pachon and so forward and upon this ground by the like progression was the golden Number set in the Roman Calendar and so the golden Number 1 by their example was set against March 23. April 21. Iune 19. Iuly 19. August 17. September 16. October 15. November 14. December 13. But then because in the following Year the golden Number was 2. reckoning 30 Days from the 13th of December the golden Number 2 was set to Innuary 12. February 10. March 12. April 10. May 10. Iune 8. Iuly 8. August 6. September 5. October 4. November 3. December 2. From whence reckoning 13 Days as before the golden Number 3 comes in course for the third Year to be set against the first of Ianuary But that you may know how the golden Number comes to be distributed in the Calendar according to the form in which it now is you must consider that in 19 Solar Years there are not only 228 Lunar Months or 12 times 19 Lunar Months but 235 for the 11 Days which the common Solar Year doth exceed the Lunar do in 19 Years arise to 209 Days out of which there may be appointed 7 Months 6 whereof will contain 30 Days apiece and one Month 29 days and these 7 Months are called Embolismical Months because by a kind of injection or interposition they are reckoned in some of the 19 Years And those Years in which they are reckoned are called Embolismical Years to distinguish them from the common Years which always contain 354 Days whereas 6 of these Embolismical Years do each of them contain 384 Days and the seventh Embolismical Year in which the Month of 29 Days is reckoned doth contain 383 Days 3. The Embolismical Years in the Cycle of the Moon are properly these Seven 3 6 9 11 14 17 19. because in the third Year 11 Days being thrice reckoned do amount to 33 Days that is one Month of 30 Days and 3 Days over Again in the sixth Year the 11 Days which the Solar exceed the Lunar being thrice numbred do amount to 33 Days which with the 3 Days formerly reserved do make 36 Days that is one Month of 30 Days and 6 Days over Again in the Ninth Year there are also 33 Days to which the 6 Days reserved being added there will arise one Month more and 9 Days over But in the Eleventh Year twice 11 Days being added to the 9 Days reserved do make 31 Days that is one Month of 30 days and one day over which being added to the supernumerary days in the fourteenth Year do make another Month of 30 Days and 4 Days over and these being added to the supernumerary Days in the sevententh Year do make another Month of 30 and 7 Days over
because 12 times 30 do make 360 whereas from the first of Ianuary to the twentieth of December inclusively there are but 354 days you must know that to gain the other six days the numbers 25 and 24 are in every other Month both placed against one day namely to February 5 April 5 Iune 3 August 1 September 29 and November 27. But why these two Numbers are chosen rather then any other and why in these 6 Months the number 25 is sometimes writ to XVI sometimes to XXV in a common character and why the number 19 is set to the last day of December in a common Character shall be declared hereafter 7. Here only note that this Asterisk * is set instead of the Epact 30 because the Epact shewing the Number of days which do remain after the Lunation in the Month of December it may sometimes fall out that 2 Lunations may so end that the one may require 30 for the Epact and the other 0 which would if both were written cause some inconveniences and therefore this * Asterisk is there set that it might indifferently serve to both And the Epact 29 is therefore set to the second day of Ianuary because after the compleat Lunation in the second of December there are 29 days and for the like reason the Epact 28 is set against the third of Ianuary because after the compleat Lunation in the third of December there are then 28 days over and so the rest in order till you come to the thirtieth of Ianuary where you find the Epact 1. because after the compleat Lunation on the thirtieth day there is only one day over 8. And besides the shewing of the New Moons in every Month which is and may be done by the Golden Number the Epacts have this advantage that they may be perpetual and keep the same place in the Calendar in all future ages which can hardly be effected with the Golden Number for in little more then 700 years the New Moons do make an anticipation of one day and then it will be necessary to set the Golden Number one degree backward and so the Golden Number which at the time of the Nicene Council was set to the first of Ianuary should in 300 years be set to the last of December and so of the rest but the Epacts being once fixed shall not need any such retraction or commutation For as often as the New Moons do change their day either by Anticipation or by Suppression of the Bissextile year you shall not need to do any more than to take another rank of 19 Epacts insteed of those which were before in use For instance the Epacts which are and have been in use in the Church of Rome since the year of reformation 1582 and will continue till the year 1700 are these 10 following 1. 12. 23. 4. 15. 26. 7. 18. 29. 10. 21. 2. 13. 24. 5. 16. 27. 8. 19. And from the year 1700 the Epacts which will be in use are these * 11. 22. 3. 14. 25. 6. 17. 28. 9. 20. 1. 12. 23. 4. 15. 26. 7. 18. and shall continue not only to the year 1800 but from thence until the year 1900 also and although in the year 1800 the Bissextile is to be suppressed yet is there a compensation for that Suppression by the Moons Anticipation To make this a little more plain the motion of the Moon which doth occasion the change of the Epact must be more fully considered CHAP. V. Of the Moons mean Motion and how the Anticipation of the New Moons may be discovered by the Epacts THe Moon according to her middle motion doth finish her course in the Zodiack in 29 days 12 hours 44 minutes three seconds or thereabout and therefore a common Lunar year doth consist of 354 days 8 hours 48 minutes 38 seconds and some few thirds but an Embolismical year doth consist of 383 days 21 hours 32 minutes 41 seconds and somewhat more and therefore in 19 years it doth exceed the motion of the Sun 1 hour 27 minutes 33 seconds feré 2. Hence it cometh to pass that although the New Moons do after 19 years return to the same days yet is there an Anticipation of 1 hour 27 minutes 33 seconds And in twice 19 years that is in 38 years there is an Anticipation of 2 hours 55 minutes 6 seconds and after 312 years and a half there is an Anticipation of one whole day and some few Minutes And therefore after 312 years no new Moon can happen upon the same day it did 19 years before but a day sooner Hence it comes to pass that in the Julian Calendar in which no regard is had to this Anticipation the New Moons found out by the Golden Number must needs be erroneous and from the time of the Nicene Council 4 days after the New Moons by a regular Computation 3. And hence it follows also that if the Golden Number after 312 were upon due consideration removed a day forwarder or nearer the beginning of the Months they would shew the New Moons for 312 years to come And being again removed after those years a day more would by the like reason do the same again But it was thought more convenient so to dispose 30 Epacts that they keeping their constant places 19 of them should perform the work of the Golden Number until by this means there should be an Anticipation of one day And when such an Anticipation should happen those 19 Epacts being let alone other 19 should be used which do belong to the preceding day without making any alteration in the Calendar 4. And if this Anticipation would do the whole work nothing were more plain then to make that commutation of the 19 Epact once in 312 years but because the detraction of the Bissextile days doth variously interpose and cause the 19 Epacts sometimes to be changed into these that do precede sometimes into these that follow sometimes into neither but to continue still the same therefore some Tables are to be made by which we may know when the commutation was to be made and into what Epacts 4. First therefore there was made a Table called Tabula Epactarum Expansa in this manner First on the top were placed the 19 Golden Numbers in order beginning with the Number 3 which in the old Calendar is placed against the Calends of Ianuary and under every one of these Golden Numbers there are placed 30 Epacts all constituted from the lowest number in the first rank in which the Epact is 1 and in that first rank the Golden Number is 3 the rest from thence towards the right Hand are made by the constant addition of it and the casting away of 30 as often as they shall exceed that number only when you come to the 27 the Epact under the Golden Number 19 there must be added 12 instead of 11 that so the Epact following may be 9 not 8 for the Reasons already given in this Discourse concerning the
T. 72. 195. 10.49327695 t ½ X Cru 69. 306. 10.42281009 2. Operation cs ½ Z 80. 49596. Comp. Arith. 0.78170174 cs ½ X 56. 97096. 9.73628614 Their Sum 10.51798788 t ½ ♈ T. 72. 195. 10.49327695 t ½ Z Cru 84. 34. 11.01126483 1. Arch. 69. 306. Their Sum is 53.740 is the Point of the Ecliptick for the Second House For the Cusp of the Third House In the Oblique angled Spherical Triangle ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 we have 1. ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 174. 39. The half whereof is 87. 195. The Angls ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 are the same with those of the Eleventh House s ½ Z. 72. 85437. Comp. Arith. 0.01977580 s ½ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 49. 32937. 6.88000800 Their Sum 9.89978389 t ½ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 87. 195. 11.30984054 For the Eleventh House For the Cusp of the Twelfth House In the Oblique angled Spherical Triangle ♈ KF we have given 1. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 K. 84. 39. The half whereof is 42. 195. 2. ♈ Kt. 137.46692  3. K ♈ t. 23.525 To find ♈ t. Z. 160.99192 ½ Z. 80.49596 X. 113.94192 ½ X. 56.97096 s ½ Z. 80. 49596. Comp. Arith. 0.00601663 s ½ X. 56. 97096. 9.92351651 t ½ ♈ K. 42. 195. 9.95740882 t ½ X Cru 37. 625. 9.88694196 2. Operation cs ½ Z. 80. 49596. Comp. Arith. 0.78170174 cs ½ X. 56. 97096. 9.73628614 t ½ ♈ K. 42. 195. 9.95740882 t ½ Z Cru 71. 496. 10.47539670 1. Arch. 37. 625. Their Sum 113.6691 is the Point of the Ecliptick for the Twelfth House For the Cusp of the Ascendant In the Oblique angled Spherical Triangle ♈ AG we have 1. ♈ A. 114. 39. The half whereof is 57. 195. 2. ♈ AZ 141. 5333. The Complement of HAAE 38. 46667. 3. A 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 y. 23. 525.  Z. 165.05833 ½ Z. 82.51916 X. 118.00833 ½ X. 59.00416 s. ½ Z. 82. 51916. Comp. Arith. 0 0037162◠s. ½ X. 59. 00416. 9.93313477 t ½ ♈ A. 57. 195. 10.19072348 t ½ X. 53. 296. 10.12757454 2. Operation t ½ X Cru 86. 468. 11.20962043 2. Operation cs ½ Z. 72. 85437. Comp. Arith. 0.53012277 cs ½ X. 49. 32937. 9.81395860 Their Sum 10.34408137 t ½ ♈ 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 87. 195. 11.39984054 t ½ X Cru 88. 729. 11.65392191 1. Arch. 86. 468. Their Sum 175.197 is the Point of the Ecliptick for the Third House And thus we have not only erected a Figure for the Time given but composed a Table for the general erecting of a Figure in that Eatitude for by adding together the first and second Numbers in each Proportion for the first second and third Houses there is composed two Numbers for each House to each of which the Artificial Tangent of half the Ascension of each House being added their Aggregates are the Tangents of two Arches which being added together do give the distance of the Cusp of the House from the first Point of Aries as in the preceding Operations hath been shewed Only note That if the Ascension of any House be more than a Semicircle you must take the Tangent of half the Complement to a whole Circle And to find the Cusp of the House you must also take the Complement of the Sum of the Arches added together The Numbers according to the former Operations which do constitute a Table of Houses for the Latitude of London 51. 53 are as followeth  11 and 3 Houses Ascendant 12 and 2 Houses 1. Oper. 9.89978389 9.93685106 9.92953314 2. Oper. 10.34408137 10.59682651 10.51798788 The Six Oriental Houses by the preceding Operations The opposite Houses are in the opposite Signs and Degrees 10 House ♈ 26.311 11 House ♊ 10.803 12 House ♋ 23.691 Ascendant ♌ 11.693 2 House ♠3.740 3 House ♠25.197 4 House ♎ 26.311 5 House ♠10.803 9 House ♑ 23.691 7 House ♒ 11.693 8 House ♓ 3.740 9 House ♓ 25.197 A Figure of the Twelve Coelestial Houses ASTRONOMY THE Second Part OR AN ACCOUNT OF THE Civil Year With the Reason of the Difference Between the JULIAN GREGORIAN Calendars And the manner of Computing the Places of the SVN and MOON LONDON Printed for Thomas Passinger at the Three Bibles on London-Bridge 1679. AN INTRODUCTION TO Astronomy The Second Book CHAP. I. Of the Year Civil and Astronomical HAving shewed the Motion of the Primum Mobile or Doctrine of the Sphere which I call the Absolute Part of Astronomy I come now unto the Comparative that is to shew the Motion of the Stars in reference to some certain Distinction of Time 2. And the Distinction of Time is to be considered either according to Nature or according to Institution 3. The Distinction of Time according to Nature is that space of Time in which the Planets do finish their Periodical Revolutions from one certain Point in the Zodiack to the same again and this in reference to the Sun is called a Year in reference to the Moon a Month. 4. The Sun doth pass through the Zodiack in 365 Days 5 Hours and 49 Minutes And the Moon doth finish her course in the Zodiack and return into Conjunction with the Sun in 29 Days 12 hours 44 Minutes and 4 Seconds And from the Motion of these two Planets the Civil Year in every Nation doth receive its Institution 5. Twelve Moons or Moneths is the measure of the Common Year in Turkey in every Moneth they have 29 or 30 Days in the whole Year 354 Days and in every third Year 355 Days 6. The Persians and Egyptians do also account 12 Moneths to their Year but their moneths are proportioned to the Time of the Suns continuance in every of the Twelve Signs in their Year therefore which is Solar there are always 365 Days that is eleven Days more than the Lunar Year 7. And the Iulian Year which is the Account of all Christendom doth differ from the other in this that by reason of the Sun's Excess in Motion above 365 Days which is 5 Hours 49 Minutes it hath a Day intercalated once in 4 Years and by this intercalation it is more agreeable to the Motion of the Sun than the former and yet there 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 might be wished 8. This intercalation of one Day once in 4 Years doth occasion the Sunday Letter still to alter till 28 Years be gone about The Days of the Week which use to be signed by the seven first Letters in the Alphabet do not fall alike in every Common Year but because the Year consisteth of 52 Weeks and one Day Sunday this Year will fall out upon the next Year's Monday and so forward for seven years but every fourth year consisting of 52 weeks and two days doth occasion the Sunday Letter to alter till four times seven years that is till 28 years
and these 7 Days being added to the 22 supernumerary Days in the Ninteenth Year of the Moons Cycle do make another Month of 29 Days 4. But because there are 6939 Days and 18 Hours in 19 Solar Years that is 4 Days 18 Hours more then in the common and Embolismical Lunar Years in which the excess between the Lunar and the Solar Year is supposed to be no more then 11 Days in each Year whereas in every fourth Year the excess is one Day more that is 12 Days that is in 16 Years 4 Days and in the remaining 3 Years three fourths of a day more And that the new Moons after 19 Lunar Years or 235 Lunations do not return to the same days again but want almost 5 days it is evident that the civil Lunations do not agree with the Astronomical and that there must be yet some kind of intercalation used 5. Now therefore in distributing the golden Number throughout the Calendar If the new Moons should interchangeably consist of 30 and 29 days and so but 228 Lunations in 19 Years we might proceed in the same order in which we have begun and by which as hath been shewed the third Year of the Golden Number falls upon the Calends of Ianuary But for as much as there are first six Lunations of 30 days apiece and one of 29 days to be interposed therefore there must be 6 times 2 Lunations together consisting of 30 days and once three Lunations of 29 days And that respect may be also had to the Bissextile days although they are not exprest in the Calendar that Lunation which doth contain the Bissertile day if it should have been 29 days it must be 30 if it should have consisted of 30 days it must consist of 31. 6. And because it was thought convenient as hath been shewed to begin with the third Year of the Cycle of the Moon because the Golden Number 3 is set to the Calends of Ianuary therefore in this Cycle the Embolismical Years are 2 5 8 11 13 16 19. But yet that it may appear that these Years are in effect the same as if we had begun with the first Year of the Golden Number save only that the eighth Year instead of the ninth is to be accounted Embolismical I have added the Table follwing in which it is apparent that the former Embolismical years do agree with these last mentioned 7. But as I said before it was thought more convenient to begin the account from the number 3 set to the Calends of Ianuary because by so reckoning 30 and 29 days to each Lunation interchangeably the same Number 3 falls upon Ianuary 31. March 1 and 31. April 29. May 29. Iune 27. Iuly 27. August 25. September 14. October 23. November 22. December 21. As if the Lunar years were compleated upon the 20 of December there remain just 11 Days which the Solar years doth exceed the Lunar 8. And by ranking on and accounting 4 for the Golden Number of the next year you will find it set on Ianuary 20 February 18 March 20 April 18 May 18 Iune 16 Iuly 16 August 14 September 13 Octob. 12 Novemb 11 Decemb. 10. Cycle of the Moon Cycle of the Moon Embolismical Years Number of Days 1 3 Â 354 2 4 Â 354 3 5 Embol 384 4 6 Â 354 5 7 Â 354 6 8 Embol 384 7 9 Â 354 8 10 Â 354 9 11 Embol 384 10 12 Â 354 Â Â Â Â 11 13 Embol 384 12 14 Â 354 13 15 Â 354 14 16 Embol 384 15 17 Â 354 16 18 Â 354 17 19 Embol 384 18 1 Â 354 19 2 Embol 384 9. But in going on and taking 5 for the Golden Number in the third year we must remember that that is an Embolismical Year and therefore that somewhere there must be 2 Months together of 30 days And for this reason the Golden Number 5 is set to Ianuary 9 February 7 March 9 April 7 May 7 Iune 5 Iuly 5 August 3 September 2 as also upon the second day of October and not upon the first that so there may be 2 Lunations together of 30 and the same Number 5 is also set to the thirty first of October to make the Lunation to consist of 29 days and to the thirtieth of November instead of the twenty ninth that so a Lunation of 30 may again succeed as it ought 10. In like manner in the sixth Year having gone through the fourth and fifth as common years you may see the Golden Number 8 set to the fifth of April which should have been upon the fourth and in the ninth Year the Golden Number 11 is set to the second of February which should have been upon the first And there is a particular reason for which these numbers are otherwise placed from the eighth of March to the fifth of April namely that all the paschal Lunations may consist of 29 days For thus from the eighth of March to the sixth of April to both which days the Golden Number is 16 there are but 29 days And from the ninth of March to the seventh of April to both which days the Golden Number is 5 there are also 29 days and so of the rest till you come to the fifth of April which is the last Paschal Lunation as the eighth of March is the first but at any other time of the Year the length of the Month in the Embolismical Year may be fixed as you please 12. And in this manner in the 17 years in which the lunations of the whole Circle are finished and in which the Golden Number is 19 the Month of Iuly is taken at pleasure to the thirtieth day whereof is set the Golden Number 19 which should have been upon the thirty first and the same Number being notwithstanding placed upon the twenty eighth of August that by the two Lunations of 29 days together it might be understood that the seventh Embolismical Month consisting of 29 days is there inserted instead of a Month of 30 days In which place the Embolismical or leaping Year of the Moon may plainly be observed for that year is one day less than the rest which the Moon doth as it were pass over The which one day is again added to the 29 days of the last Month that we may by that means come as in other Years to the Golden Number which sheweth the New Moon in Ianuary following And for this reason the Epact then doth not consist of 11 but of 12 days And thus you see the reason for which the Golden Numbers are thus set in the Calendar as here you see In which we may also observe that every following Number is made by adding 8 to the Number preceding and every preceding Number is also made by adding 11 to the Number next following and casting away 19 when the addition shall exceed it For Example if you add 8 to the Golden Number 3 set against the first of Ianuary it maketh 11
is enough to shew for what reason the letters are so placed in the Table as there you see them for in the year 1600 the Bissextile being neither suppressed nor the Moon aequated the letter D used in the former Centenary or in the latter part thereof from the year 1582 is still the same In the year 1700 because there is a suppression but no aequation the commutation is made to the Letter C descending In the Year 1800 because there is both a suppression and an aequation the same letter C doth still continue In the Year 2400 because there is an aequation and no suppression there is an ascension to the Letter A. And thus you see not only the construction of this Table but how it may be continued to any other Year as long as the World shall last 12. And by these two Tables we may easily know which rank of the 30 Epacts doth belong to or is proper for any particular age for as in our age that is from the Year 1600 to the Year 1700 exclusively that series is proper whose Index is D. Namely 23 4 15 26 c. so in the two Ages following that is from the Year 1700 to the Year 1900 exclusively that series is proper whose Index is C namely these 22 3 14 25. and in the three ages following thence that is from the Year 1900 to the Year 2100 exclusively that series is proper whose Index is B namely these 21 2 13 24 c. And so for any other Hence also it may be known which of the 19 doth belong to any particular Year for which no more is necessary than only to know the Golden Number for the year given which being sought in the head of the Table and the Index of that Age in the side the common Angle or meeting of these two will shew you the Epact desired As in the year 1674 the Golden Number is 3 and the Index D therefore in the common Angle I find 23 for the Epact that year and sheweth the New Moons in every Month thereof And here it will not be unseasonable to give the reason for which the Epact 25 not XXV is written under the Golden Numbers 12 13 14 15 16 17 18 19. namely because the ranks of Epacts which under these greater Numbers hath this Epact 25 hath also XXIV it would follow that in these Ages in which any of these Ranks were in use the New Moon in 19 years will happen twice upon the same days in those six Months in which the Epacts XXV and XXIV are set to the same day Whereas the New Moons do not happen on the same day till 19 years be gone about To avoid this inconvenience the Epact 25 not XXV is set under these great numbers and the Epact 25 is in the Calendar in these Months set with the Epact XXVI but in the other Months with the Epact XXV 14. Hence it cometh to pass 1. That in these Years the Epacts 25 and XXIV do never meet on the same day 2. That there is no danger that the Epacts 25 and XXVI should in these 6 Months cause the same inconvenience seeing that the Epacts 25 and XXVI are never both found in the same Rank 3. That the Epact 25 may in other Months without inconvenience be set to the same day with the Epact XXVI because in these there is no danger of their meeting with the Epact XXIV on the same days 4. That there is no fear that the Epacts XXV and XXIV being set on the same days should in future Ages cause the same inconvenience because the Epacts XXV and XXIV are not found together in any of the other Ranks But that either one or both of them are wanting Besides when one of these Epacts is in use the other is not and that only which is in use is proper to the day As in this our Age until the Year 1700 the Epacts in use are those in the rank whose Index is D. In which these two XXIV and XXV are not both found And in the two following Ages because the rank of Epacts in use is that whose Index is C in which there is the Epact XXV not XXIV the New Moons are shewed by the Epact XXV not by XXIV But because in three following Ages the rank of Epacts in use is that whose Index is B in which 25 and XXIV are both found the New Moons are shewed by the Epact XXIV when the golden Number is 6. And by the Epact 25 when the golden Number is 17 and not by the Epact XXV 15. And if it be asked why the Epact 19 in the common Character is set with the Epact XX against the last day of December know that for the reasons before declared the last Embolismical Month within the space of 19 years ought to be but 29 days and not 30 as the rest are and therefore when the Epact 19 doth concur with the golden Number 19 the last Month or last Lunation beginning the second of December shall end upon the 30 and not upon the 31 of that Month and the New Moon should be supposed to happen upon the 31 under the same Epact 19 that 12 being added to 19 and not 11 you may have one for the Epact of the year following which may be found upon the 30 of Ianuary as if the Lunation of 30 days had been accomplished the Day before CHAP. VI. How to find the Dominical Letter and Feast of Easter according to the Gregorian account HAving shewed for what reason and in what manner the Epacts are substituted in the place of the golden Number and how the New Moons may be by them found in the Calendar for ever I shall now shew you how to find the Feast of Easter and the other moveable Feasts according to the Gregorian or new account and to this purpose I must first shew you how to find the Dominical Letter for that the Cycle of 28 years will not serve the turn because of the suppression of the Bissextile once in a hundred years but doth require 7 Cycles of 28 years apeice The first whereof begins with CB and endeth in D. The second begins with DC and endeth in E. The third begins with ED and endeth in F c. The first of these Cycles began to be in use 1582 in which year the dominical Letter according to the Julian account was G but upon the fifteenth day of October that Year was changed to C for the fifth of October being Friday and then called the fifteenth the Letter A became Friday B Saturday and C Sunday the remaining part of the year in which the Cycle of the Sun was 23 and the second after the Bissextile or leap Year and so making C which answereth to the fifteenth year of that Circle to be 23 the Circle will end at D and consequently CB which in the old account doth belong to the 21 year of the Circle hath ever since been called the first and so shall
continue until the year 1700 in which the Bissextile being suppressed the next Cycle will begin with DC as hath been said already Under the first rank or order of Dominical Letters are written the years 1582 and 1600 under the second 1700 under the third 1800 under the fourth 1900 and 2000 under the fifth 2100 under the sixth 2200 and under the seventh 2300 and 2400. And again under the first Order 2500 under the second 2600 under the third 2700 and 2800 and so forward as far as you please always observing the same order that the 100 Bissextile years may still be joyned with the not Bissextile immediately preceding 1. And hence it appears that the seven orders of Dominical Letters are so many Tables successively serving all future Generations For as the first Order serveth from the year 1582 and 1600 to the year 1700 exclusively and the second Order from thence to the year 1800 exclusively so shall all the rest in like manner which here are set down and to be set down at pleasure And hence the Dominical Letter or Letters may be found for any year propounded as if it were required to find the dominical Letter for the year 1674 because the year given is contained in the centenary 1600. I find the Cycle of the Sun by the Rule already given to be 3. In the first order against the number 3 I find G for the Sunday Letter of that year in like manner because the year 1750 is contained under the Centenary 1700 the Cycle of the Sun being 27 I find in the second rank the Letter D answering to that Number and that is the Dominical Letter for that year and so of the rest 3. Again for as much as the fifth Order is the same with that Table which serves for the old account therefore that order will serve the turn for ever where that Calendar is in use and so this last will be of perpetual use to both the Calendars 4. Now then to find the time in which the Feast of Easter is to be observed there is but little to be added to that which hath been already said concerning the Julian Calendar For the Paschal Limits are the same in both the difference is only in the Epacts which here are used instead of the golden Number 5. For the terms of the Paschal New Moons are always the eighth of March and the fifth of April but whereas there are 11 days within these Limits to which no golden Number is affixed there is now one day to which an Epact is not appointed because there is no day within those Limits on which in process of time a New Moon may not happen And the reason for which the two Epacts XXV and XXIV are both set to the fifth of April is first general which was shewed before namly that by doing the same in 5 other Months the 12 time 30 Epacts might be contracted to the Limits of the lunar Year which consists of 354 days but there is a particular reason also for it that the Antients having appointed that all the Paschal lunations should consist of 29 days it was necessary that some two of the Epacts should be set to one of these days in which the Paschal lunation might happen the Epacts being 30 in number And it was thought convenient to choose the last day to which the Epact XXV belonging the Epact XXIV should also be set and hence by imitation it comes to pass that these and not other Epacts are set to that day in other Months in which two Epacts are to be set to the same days 6. The use of these Epacts in finding the Feast of Easter is the same with that which hath been shewed concerning the golden Numbers For the Epact and the Sunday Letter for that year propounded being given the Feast of Easter may be found in the Calendar after the same manner Thus in the year 1674 the Epact is 23 and the Sunday Letter G and therefore reckoning fourteen days from the eighth of March to which the Epact is set the Sunday following is March 25 which is the day on which the Feast of Easter is observed 7. And hence as hath been shewed in the third Chapter concerning the Julian Calendar a brief table may be made to shew the feast of Easter and the other moveable Feasts for ever in which there is no other difference save only that the Epacts as they are in this new Calendar are to be used as the golden Numbers are which stand in the old Calendar And a Table having the golden Numbers of the old Calendar set in one Column and the Epacts as they are in the new Calendar set in another will indifferently shew the movable Feasts in both accounts as in the Year 1674 the golden Number is 3 and the Sunday Letter according to the Julian account is D according to the Gregorian G and the Epact 23 and therefore according to this Table our Easter is April 19 and the other to wit the Gregorian is March 25. The like may be done for any other year past or to come CHAP. VII How to reduce Sexagenary numbers into Decimal and the Contrary EVery Circle hath antiently and is yet generally supposed to be divided into 300 degrees each degree into 60 Minutes each Minute into 60 Seconds and so forward as far as need shall require But this partition is somewhat troublesom in Addition and Subtraction much more in Multiplication and Division and the Tables hitherto contrived to ease that manner of computation do scarce sufficiently perform the work for which they are intended And although the Canon published by the learned H. Gellibrand in which the Division of the Circle into 360 degrees is retained but every degree is divided into 100 parts is much better than the old Sexagenary Canon yet some are of opinion that if the Antients had divided the whole circle into 100 or 1000 parts it would have proved much better then either only they think Custome such a Tyrant that the alteration of it now will not be perhaps so advantagious leaving them therefore to injoy their own opinions they will not I hope be offended if others be of another mind for their sakes therefore that do rather like the Decimal way of calculation Having made a Canon of artificial Signs and Tangents for the degrees and parts of a Circle divided into 100 parts I shall here also shew you how to reduce sexagenary Numbers into Decimal and the contrary as well in time as motion 2. The parts of a Circle consisting of 360 degrees may be reduced into the parts of a circle divided into 100 degrees or parts by the rule of Three in this manner As 360 is to 100 so is any other Number of degrees in the one to the correspondent degrees and parts in the other But if the sexagenary degrees have Minutes and Seconds joyned with them you must reduce the whole Circle as well as the parts propounded into the
worse of the two yet not so bad but that our Dissenting Brethren have I hope some better Arguments to justifie their Non-conformity than what I see published in a little Book without any name to it concerning two Easters in one Year by the General Table saith this learned man who owneth the Feast of Easter was to be observed Anno 1674. upon the 19 day of April so the Almanacks for that Year as well as the General Table set before the Book of Common Prayer but by the Rule in the said Book of Common Prayer given the Feast of Easter should have been upon the twelfth of April for easter-Easter-Day must always be the first Sunday after the first Full Moon which happeneth next after the one and twentieth day of March and if the Full Moon happen upon a Sunday easter-Easter-Day is the Sunday after Now in the Year 1674. the 19 of April being Friday was Full Moon therefore by this Rule Easter-Day should be the twelfth and by the Table and the Common Almanacks April the tenth but this learned man must know that the mistake is in himself and not in the Rule or Table set down in the Book of Common Prayer for if he please to look into the Calendar he will find that the Golden Number Three which was the Golden Number for that Year is placed against the last day of March and therefore according to the supposed motion of the Moon that Day was New Moon and then the Full Moon will fall upon the fourteenth day of April and not upon the tenth and so by consequence the Sunday following the first Full Moon after the 21 day of March was the nineteenth of April and not the twelfth And thus the Rule and the Table in the Book of Common Prayer for finding the Feast of Easter are reconciled and when Authority shall think sit the Calendar may be corrected and all the moveable Feasts be observed upon the days and times at first appointed but till that be a greater difference than one Week will be found in the Feast of Easter between the Observation thereof according to the Moons true motion and that upon which the Tables are grounded for by the Fathers of the Nicene Council it was appointed that the Feast of Easter should be observed upon the Sunday following the first Full Moon after the Vernal Equinox which then indeed was the 21 of March but now the tenth and in the Year 1674. Wednesday the 11 of March was Full Moon and therefore by this Rule easter-Easter-Day should have been upon March the fifteenth whereas according to the Rules we go by it was not till April the nineteenth The Tables of the Sun and Moons middle motions are neither made according to the usual Sexagenary Forms nor according to the usual Degrees of a Circle and Decimal Parts but according to a Circle divided into 100 Degrees and Parts and this I thought good to do to give the World a taste of the excellency of Decimal Numbers which if a Canon of Sines and Tangents were fitted to it would be found much better as to the computing the Places of the Planets but as to the Primum Mobile by reason of the general dividing a Circle into 360 Degrees I should think such a Canon with the Decimal Parts most convenient and in some cases the common Sexagenary Canon may be very useful and indeed should wish and shall endeavour to have all printed together one Table of Logarithms will serve them all and two such Canons one for the Study and another for the Pocket would be sufficient for all Mathematical Books in that kind and then men may use them all or either of them as they shall have occasion or as every one is perswaded in his own mind What I have done in this particular as it was for mine own satisfaction so I am apt to believe that it will be pleasing to many others and although I shall leave every one to abound in his own sense yet I cannot think that Custom should be such a Tyrant as to force us always to use the Sexagenary form if so I wonder that men did not always use the natural Canon if no alteration may be admitted what reason can be given for the use of Logarithms and if that be found more ready than the natural in things of this kind where none but particular Students are concerned I should think it reasonable to reduce all things hereafter into that form which shall be found most ready and exact now the Part Proportional in the Artificial Sines and Tangents in the three first Degrees cannot be well taken by the common difference and the way of finding them otherwise will not be so easie in the Sexagenary Canon as in either of the other and this me thinks should render that Canon which divides each Degree into 100 Parts more acceptable but thus to retain the use of Sines Degrees and Decimal Parts doth not to me seem convenient and to reckon up a Planets middle motion by whole Circles will sometimes cause a Division of Degrees by 60 which hath some trouble in it also but if a Circle be divided into 100 Degrees this inconvenience is avoided and were there no other reason to be given this me thinks should make such a Canon to be desirable but till I can find an opportunity of publishing such an one I shall forbear to shew any further uses of it and for what is wanting here in this subject I therefore refer thee to Mr. Street's Astronomia Carolina and the several Books written in English by Mr. Wing The fourth Part of this Treatise is an Introduction unto Geography in which I have given general Directions for the understanding how the habitable part of the World is divided in respect of Longitude and Latitude in respect of Climes and Parallels with such other Particulars as will be found useful unto such as shall be willing to understand History in which three things are required The time when and this depends upon Astronomy the place where and this depends upon Geography and the Person by whom any memorable Act was done and this must be had from the Historical narration thereof and he that reads History without some knowledge in Astronomy and Geography will find himself at a loss and be able to give but a lame account of what he reads but after the learning of these Arts of Grammar I mean so much thereof as tends to the understanding of every ones Native Language Arithmetick Geometry and Astronomy a Child may proceed profitably to Rhetorick and Logick the reading of History and the learning of the Tongues and sure there is no studious and ingenious man but will stand in need of some Recreation and therefore if Musick in the Worship and Service of God be not Argument enough to allow that a place among the Arts let that poor end of Delight and Pleasure be her Advocate and although that all men have not Voyces yet I can
to which add 8 more and it maketh 19 to which adding 8 it maketh 27 from which substracting 19 the remainer is 8 to which again adding 8 the sum is 19 to which adding 8 the sum is 24 from which deducting 19 the remainer is 5 and so of the rest In like manner receding backward to the 5 add 11 they make 16 to the 16 add 11 they make 27 from which deducting 19 the remainer is 8 to which 11 being added the same is 19 to which 11 being added the sum is 30 from which deducting 19 the remainer is 11 to which 11 being added the sum is 22 from which deducting 19 the remainer is 3. And by this we may see that every following number will be in use 8 years after the preceding and every preceding Number will be in use 11 years after the following that is the same will return to be in use after 8 Years and 11 and the other after 11 Years and 8 or once in 19 years CHAP. III. Of the Vse of the Golden Number in finding the Feast of Easter THe Cycle of the Moon or Golden Number is a circle of 19 years as hath been said already which being distributed in the Calendar as hath been shewn in the last Chapter doth shew the day of the New Moon for ever though not exactly But the use for which it was chiefly intended was to find the Paschal New Moons that is those new Moons on which the Feast of Easter and other moveable Feasts depend To this purpose we must remember 1. That the vernal Equinox is supposed to be fixed to the twenty first day of March. 2. That the fourteenth day of the Moon on which the Feast of Easter doth depend can never happen before the Equinox though it may fall upon it or upon the day following 3. That the Feast of Easter is never observed upon the fourteenth day of the Moon but upon the Sunday following so that if the fourteenth day of the Moon be Sunday the Sunday following is Easter day 4. That the Feast of Easter may fall upon the fifteenth day of the Moon or upon any other day unto the twenty first inclusively 5. That the Paschal Sunday is discovered by the proper and Dominical Letter for every Year The which may be found as hath been already declared or by the proper Table for that purpose Hence it followeth 1. That the New Moon immediately preceding the Feast of Easter cannot be before the eighth day of March for if you suppose it to be upon March 6 the Moon will be 14 days old March 19 which is before the Equinox contrary to the second Rule before given and upon the seventh day of March there is no Golden Number fixed and therefore the Golden Number 16 which standeth against March 8 is the first by which the Paschal New Moon may be discovered 2. It followeth hence That the last Paschal New Moon cannot happen beyond the fifth day of April because all the 19 Golden Numbers are expressed from the eighth of March to that day And if a New Moon should happen upon the sixth of April there would be two Paschal New Moons that year one upon the eighth of March and another upon the sixth of April the same Golden Number 16 being proper to them both but this is absurd because Easter cannot be observed twice in one year 3. It followeth hence That the Feast of Easter can never happen before the twenty second day of March nor after the twenty fifth day of April For if the first New Moon be upon the eighth of March and that the Feast of Easter must be upon the Sunday following the fourteenth day of the Moon it is plain that the fourteenth day of the Moon must be March 21 at the soonest So that supposing the next day to be Sunday Easter cannot not be before March the twenty second And because the fourteenth day of the last Moon falleth upon the eighteenth day of April if that day be Saturday and the Dominical Letter D Easter shall be upon the nineteenth day but if it be Sunday Easter cannot be till the twenty fifth 4. It followeth hence That although there are but 19 days on which the fourteenth day of the Moon can happen as there are but 19 Golden Numbers yet there are 35 days from the twenty second of March to the twenty fifth of April on which the Feast of Easter may happen because there is no day within those Limits but may be the Sunday following the fourteenth day of the Moon And although the Feast of Easter can never happen upon March 22 but when the fourteenth day of the Moon is upon the twenty first and the Sunday Letter D nor upon the twenty fifth of April but when the fourteenth day of the Moon is upon April 18 and the Dominical Letter C. Yet Easter may fall upon March 23 not only when the fourteenth day of the Moon is upon the twenty second day which is Saturday but also if it fall upon the twenty first which is Friday In like manner Easter may fall upon April 24 not only when the fourteenth day of the Moon is upon the eighteenth day which is Monday but also if it happen upon the seventeenth being Sunday And for the same reason it may fall oftner upon other days that are further distant from the said twenty second of March and twenty fifth of April 5. It followeth hence That the Feast of Easter may be easily found in any Year propounded For the Golden Number in any Year being given if you look the same between the eighth of March and fifth of April both inclusively and reckon 14 days from that day which answereth to the Golden Number given where your account doth end is the fourteenth day of the Moon Then consider which is the Dominical Letter for that Year and that which followeth next after the fourteenth day of the Moon is Easter day Example In the year 1674 the Golden Number is 3 and the Sunday Letter D which being sought in the Calendar between the aforesaid limits the fourteenth day of the Moon is upon April the thirteenth and the D next following is April 19. And therefore Easter day that Year is April 19. Otherwise thus In March after the first C Look the Prime wherever it be The third Sunday after Easter day shall be And if the Prime on Sunday be Reckon that for one of the Three 6. Thus the Feast of Easter may be found in the Calendar and from thence a brief Table shewing the same may be extracted in this manner Write in one Column the several Golden Numbers in the Calendar from the eighth of March to the fifth of April in the same order observing the same distance In the second Column set the Dominical Letters in number 35 so disposed as that no Dominical Letter may stand against the Golden Number 16 but setting the Letter D against the Golden Number 5 write the rest in this
order E F G A B c. and when you come to the Golden Number 8 set the Letter C and there continue the Letters till you come to C again because when the Golden Number is 16 which in the Calendar is set to the eighth day of March is new Moon and the fourteenth day of that Moon doth fall upon the twenty first to which the Dominical Letter is C upon which the Feast of Easter cannot happen and therefore in the third Column containing the day in which the Feast of Easter is to be observed is also void But in the next place immediately following to wit against the letter D is set March 22 because if the fourteenth day of the Moon shall fall upon the twenty first of March being Saturday the next day being Sunday shall be the Feast of Easter To the Letters following E F G A B c. are set 23 24 25 and so orderly to the last of March and so forward till you come to the twenty fifth of April by which Table thus made the Feast of Easter may be found until the Calendar shall be reformed For having found the Golden Number in the first Column the Dominical Letter for the Year next after it doth shew the Feast of Easter as in the former Example the Golden Number is 3 and the Dominicall Letter D therefore Easter day is upon April 19. The other moveable Feasts are thus found Advent Sunday is always the nearest Sunday to St. Andrews whether before or after Septuagesima Sunday is Nine Weeks before Easter Sexagesima Sunday is Eight Weeks before Easter Qainquagesima Sunday is Seven Weeks before Easter Quadragesima Sunday is Six Weeks before Easter Rogation Sunday is five Weeks after Easter Ascension day is Forty Days after Easter Whitsunday is Seven Weeks after Easter Trinity Sunday is Eight Weeks after Easter G. N. D. L. Easter XVI   V D 22 March  E 23 XIII F 24 II G 25  A 26 X B 27  C 28 XVIII D 29 VII E 30  F 31 XV G 1 April IV A 2  B 3 XII C 4 I D 5  E 6 IX F 7  G 8 XVII A 9 VI B 10  C 11 XIV D 12 III E 13  F 14 XI G 15  A 16 XIX B 17 VIII C 18  D 19  E 20  F 21  G 22  A 23  B 24  C 25 CHAP. IV. Of the Reformation of the Calendar by Pope Gregory the Thirteenth and substituting a Cycle of Epacts in the room of the Golden Number HItherto we have spoken of the Calendar which is in use with us we will now shew you for what reasons it is alter'd in the Church of Rome and how the Feast of Easter is by them observed The Year by the appointment of Iulius Caesar consisting of 365 days 6 hours whereas the Sun doth finish his course in the Zodiack in 365 days 5 hours 49 minutes or thereabouts it cometh to pass that in 134 Years or less there is a whole day in the Calendar more than there ought in 268 years 2 days more in 4002 years 3 days and so since Iulius Caesar's time the vernal Equinox hath gone backward 13 or 14 days namely from the 24 of March to the tenth Now because the Equinox was at the time of the Nicene Council upon the twenty first of March when the time for the observing of Easter was first universally established they thought it sufficient to bring the Equinox back to that time by cutting off 10 days in the Calendar as hath been declared and to prevent any anticipation for the time to come have appointed that the Leap-year shall be thrice omitted in every 400 Years to come and for memory sake appointed the first omission to be accounted from the Year 1600 not from 1582 in which the reformation was made because it was not only near the time in which the emendation was begun but also because the Equinox has not fully made an anticipation of 10 days from the place thereof at the time of the Nicene Council which was March 21. The Years then 1700 1800 1900 which should have been Bissextile Years are to he accounted common years but the Year 2000 must be a Bissextile In like manner the Years 2100 2200 2300 shall be common years and the Year 2400 Bissextile and so forward 2. Again because it was supposed that the Cycle of the Moon or Golden Number was so fixed that the new and full Moons would in every 19 years return to the same days again whereas their not returning the same hours but making an anticipation of one hour 27 minutes or thereabouts it must needs be that in 17 Cycles or little more than 300 Years there would be an anticipation of a whole day And hence it is evident that in 1300 Years since the Nicene Council the New and Full Moons do happen more than 4 days sooner than the Cycle of the Moon or Golden Number doth demonstrate Whence also it comes to pass that the fourteenth day of the Moon by the Cycle is in truth the eighteenth day and so the Feast of Easter should be observed not from the fifteenth day of the Moon to the twenty first but from the nineteenth to the twenty fifth 3. That the Moon therefore being once brought into order might not make any anticipation for the time to come it is appointed that a Cycle of 30 Epacts should be placed in the Calendar instead of the Golden Number answering to every day in the Year to shew the New Moons in these days not only for 300 Years or thereabouts but that there might be new Epacts without altering the Calendar to perform the same thing upon other days as need shall require 4. For the better understanding whereof to the Calendar in use with us we have annexed the Gregorian Calendar also In the first Column whereof you have 30 numbers from 1 to 30 save only that in the place of 30 you have this Asterisk * But they begin with the Calends of Ianuary and we continued and repeated after a Retrograde order in this manner * 29 28 27 c. and that for this cause especially that the number being given which sheweth the New Moons in every Month for one Year you might by numbring 11 upwards exclusively find the number which will shew the New Moons the Year following to wit the Number which falleth in the eleventh place 5. And these Numbers are called Epacts because they do in order shew those 11 days which are yearly to be added to the Lunar Year consisting of 354 days that it may be in conformity with the Solar Year consisting of 365 days To this purpose as hath been said concerning the Golden Number these Epacts being repeated 12 times and ending upon the twentieth day of December the same Numbers must be added to the 11 remaining days which were added to the first 11 days in the Month of Ianuary 6. And
Golden Number and Embolismical years And this rank being thus made the other Epacts are disposed in their natural order ascending upwards and the number once again resumed after the Epact 30 or rather this Asterisk * set in the place thereof only observe that under the Golden Number 12. 13. 14. 15. 16. 17. 18. 19. in the place of XX there is yet 25 in the common Character And to the Epacts under the Golden Number 19 12 must still be added to make that Epact under the Golden Number 1. As was said before concerning the lowest Rank 5. And on the left hand of these Epacts before those under the Golden Number 3. are set 30 Letters of the Alphabet 19 in a small Character and 11 in a great in which some are passed by for no other reason save only this that their similitude with some of the small Letters should not occasion any mistake in their use which shall be shewed in its place 6. Besides this Table there was another Table made which is called Tabula AEquationis Epactarum in which there is a series of years in which the Moon by reason of her mentioned anticipation doth need AEquation and in which the number of Epacts signed with the letters of the Alphabet are to be changed being otherwise AEquated where it needeth by the suppression of the Bissextile days 7. But it supposeth that it was convenient to suppress the Bissextiles once only in 100 years and the Moon to be aequated or as far as concerns her self the rank of Epacts to be changed once only in 300 years and the 12 years and a half more to be referred till after the years 2400 they do amount unto 100 years and then an aequation to be made but then it must be made by reason of the interposing this hundred not in the three hundredth but the hundredth year Moreover this aequation is to be made as in referece to the Moon only because as the suppression of the Bissextiles intervene the order of changing the ranks of Epacts is varied as shall be shewed hereafter 8. Again this Table supposeth that seeing the New Moon at the time of the Nicene Council was upon the Calends of Ianuary the golden Number 3 being there placed that it would have been the same if the Epact * had been set to the same Calends that is if the Epacts had been then in use And therefore at that time the highest or last rank of Epacts was to be used whose Index is P and then after 300 years the lowest or first rank should succeed whose Index is a for the letters return in a Circle and after 300 years more the following rank whose Index is b and so forward but that it is conceived that the New Moon in the Calends of Ianuary is more agreeable to the year of Christ 500 than the time of the Nicene Councel and therefore as if the rank of Epacts under the letter l were sutable to the year 500 it seemed good to make use of that rank under the letter a in the year of Christ 800 and those under the letter b in the year 1100 and those under the letter e in the year 1400. 9. Which being granted because in the year 1582 ten days were cut off from the Calendar we must run backward or in an inverted order count 10 series designed suppose by the letters b. a. P. N. M. H. G. F. E. D. so that from the year 1582 the series of Epacts whose literal Index is D is to be used and this is that rank of Epacts which is now used in the Church of Rome 10. And therefore as if this Table had its beginning from that year the first number in the second column is 1582 and then in order under it 1600. 1700. 1800. 1900. 2000. c. And in the third Column every fourth hundred year is marked for a Bissextile that is 1600. 2400. 2800 c. and in the fourth Column to every three hundreth Year is set this Character C to shew in what year the Moon by her Anticipation of one day doth need aequation but in the year 1800 the double character is set CC to signify that then another hundred years are gotten by the 12 years and a half reserved besides and above the other 300 years and this character is also set to the years 4300. 6800 and for the same reason But in the first Column or on the left hand of these years are placed the Letters or Indices of those ranks of Epacts in the former Table which are to be used in those years and when the Letters are charged Thus against the year 1600 the Letter D is continued to shew that from that year to the year 1700 the rank of Epacts is still to be used which do belong to that Letter And for as much as the Letter C is set to the year 1700 it sheweth that that rank of Epacts is then to be used which do belong thereto and so of the rest 11. The reason why these Letters in the first Column are sometimes changed in 100 years sometimes in 200 sometimes not in less then 300 Years and that they are sometimes taken forward sometimes backward according to the order of the Alphabet is because the suppression of the Bissextiles do intervene with the lunar aequation for if the Bissextile were only to be suppressed in these 300 or sometimes 400 years in which the Moon needeth aequation the rank of Epacts in that case would need no commutation but would continue the same for ever and the golden Number would have been sufficient if the suppression of the Bissextile and anticipation of the Moon did by a perpetual compensation cause the new Moons still to return to the same days but because the Bissextile is ofttimes suppressed when the Moon hath no aequation the Moon hath sometimes an aequation when the Bissextile is not suppressed sometimes also both are to be done and sometimes neither all which varieties may yet be reduced to these three Rules 1. As often as the Bissextile is suppressed without any aequation of the Moon then the letter which served to that time shall be changed to the next below it contrary to the order of the Alphabet And the new Moons shall be removed one day towards the end of the Year 2. As often as the Moon needeth aequation without suppression of the Bissextile then the Letter which was in use to that time shall be changed to the next above it according to the order of the Alphabet that the New Moons may again return one day towards the beginning of the year 3. As often as there is a Suppression and an aequation both or when there is neither the Letter is not changed at all but that which served for the former Centenary shall also continue in the succeeding because the compensation so made the New Moons do neither go forward nor backward but happen in the compass of the same days 1. And this
Aphelion for one day viz. 0. 00001. 3014917 by 53245 the product is 0. 69297. 9255665 which being deducted from the place of the Aphelion in the beginning of the Christian AEra before found 18. 97946. 9494841. the remainer 18. 28649. 0239176 is the place of the Aphelion at the time of the observation that is in Sexagenary numbers deg 65. 49′ 53″ 5. The place of the Aphelion at the time of the observation being thus found to be deg 65. 49′ 53″ The Suns mean Longitude at that time may be thus computed In Fig. 8. In the Triangle EMH we have given the side ME 200000 the side MH 3576 the double excentricity before found and the Angle EMH 114. 10′ 07″ the complement of the Aphelion to a Semicircle to find the Angle MEH for which the proportion is As the Summ of the sides is to the difference of the sides so is the Tangent of the half Summ of the opposite Angles to the Tangent of half their difference The side ME. 200000.  The side MH 3576.  Z. Of the sides 203576. Co. ar 4.69127343 X. Of the sides 196424. 5.29321855 Tang. ½ Z Angles 32′ 54′ 56. 9.91111512 Tang. ½ X Angles 31. 59. 21.  Angle MEH 0. 55. 35. 9.79560710 The double whereof is the Angle MBH 1. 51. 10. which being Subtracted from 360 the remainer 358. 08. 50. is the estimate middle motion of the Sun from which subtracting the Aphelion before found 65. 49. 53. the remainer 292. 18. 57. is the mean Anomaly by which the absolute AEquation may be found according to the former operation Z. ME+MH 203576. Co. ar 4.69127343 X. ME-MH 196424 5.29321855 Tang. ½ Anom 56. 09. 28. 10.17359517 Tang. ½ X. 55. 12. 18. 10.15808715 Differ 00. 57. 10.  Doubled 1. 54. 20 which added to the middle motion before found gives the ☉ true place ♈ 00. 3′ 10″ which exceeds the observation 3′ 10″ therefore I deduct the same from the middle motion before found and the remainer 358. 05. 50. is the middle motion at the time of the observation of Hipparchus to which if you add the middle motion of the Sun for 53245 days or for 323 AEgyptian years 131 days 280. 46. 08′ the Summ rejecting the whole Circles is 278. 51. 48 the Suns mean Longitude in the beginning of the Christian AEra 6. But one observation is not sufficient whereby to state the middle motion for any desired Epocha we will therefore examine the same by another observation made by Albategnius at Aracta in the year of Christ 882 March 15. hours 22. 21. but in the Meridian of London at 18 hours 58′ The motion of the Aphelion for 881 years 74 days is 3. 806068653737 which being added to the place thereof in the beginning of the Christian AEra the place at the time of the observation will be found to be 22. 785538148578 that is reduced Deg. 82. 01′ 40″ And hence the AEquation according to the former operations is Deg. 2. 01′ 16″ which being deducted from a whole Circle the remainer 357 d. 58′ 44″ is the estimate middle motion at that time from which deducting the Aphelion deg 82. 01. 40. the remainer 275. 57. 04 is the mean anomaly and the AEquation answering thereto is deg 2. 02′ 18″ which being added to the middle motion before found gives the ☉ place ♈ 00. 01′ 02″ which exceeds the observation 01′ 02″ therefore deduct the same from the middle motion before found the remainer 357. 57′ 22″ is the middle motion of the ☉ at the time of the observation from which deducting the middle motion for 881 years 74 days 18 hours 58 minutes viz. 80d. 06′ 10″ the remainer 277 deg 51′ 12″ is the ☉ mean Longitude in the beginning of the Christian AEra By the first observation it is deg 278. 51′ 48″ By the second 277. 51. 12 Their difference is 1. 00. 36 He that desires the same to this or any other Epocha to more exactness must take the pains to compare the Collection thereof from sundry Observations with one another this is sufficient to shew how it is to be found Here therefore I will only add the measures set down by some of our own Nation and leave it to the Readers choice to make use of that which pleaseth him best The ☉ mean Longitude in the beginning of the Christian AEra according to Vincent Wing is 9. 8d. 00′ 31″ Tho. Street is 9. 7. 55. 56 Iohn Flamsted is 9. 7. 54. 39 By our first Computation 9. 8. 51. 48 By our second 9. 7. 51. 12 In the Ensuing Tables of the ☉ mean Longitude we have made use of that measure given by Mr. Flamsted a little pains will fit the Tables to any other measure CHAP. XI Of the quantity of the Tropical and Sydereal Year THe year Natural or Tropical so called from the Greek word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 which signifies to turn because the year doth still turn or return into it self is that part of time in which the ☉ doth finish his course in the Zodiack by coming to the same point from whence it began 2. That we may determine the true quantity thereof we must first find the time of the ☉ Ingress into the AEquinoctial Points about which there is no small difference amongst Astronomers and therefore an absolute exactness is not to be expected it is well that we are arrived so near the Truth as we are Leaving it therefore to the scrutiny of after Ages to make and compare sundry Observations of the ☉ entrance into the AEquinoctial Points it shall suffice to shew here how the quantity of the Tropical year may be determined from these following observations 3. Albategnius Anno Christi 882 observed the ☉ entrance into the Autumnal AEquinox at Aracta in Syria to be Sept. 19. 1 hour 15′ in the Morning But according to Mr. Wings correction in his Astron. Instaur Page 44 it was at 1 hour 43′ in the Morning and therefore according to the ☉ middle motion the mean time of this Autumnal AEquinox was Sept. 16. 12 h. 14′ 25″ that is at London at 8 h. 54′ 25″ 4. Again by sundry observations made in the year 1650. the second from Bissextile as that of Albategnius was the true time of the ☉ ingress into ♎ was found to be Sept. 12. 14 h. 40′ and therefore his ingress according to his middle motion was Sept. 10. 13 h. 02. 5. Now the interval of these two observations is the time of 768 years in which space by subtracting the lesser from the greater I find an anticipation of 5 days 9 hours 52′ 25″ which divided by 768 giveth in the quotient 10′ 55″ 39 which being subtracted for 365 days 6 hours the quantity of the Julian year the true quantity of the Tropical year will be 365 days 5 hours 49′ 04″ 21‴ Others from other observations have found it somewhat less our worthy countryman Mr. Edward Wright takes it to be 365 d. 5 hours 48′ Mr. Iohn Flamsted
or 146 days 53 revolutions 0 Signes 7 degrees 56 minutes 45 Seconds And the Apogaeon from the AEquinox 5 Signes 12 degrees 46 minutes And hence the daily motion of her mean Anomaly will be found to be 13 d. 03′ 53″ 57‴ 09 iv 58 v. 46 vi Of her Apogaeon 0. 06. 41. 04. 03. 25. 33. And according to these Measures if you deduct the motion of the ☽ mean Anomaly for 1641 years April 4. hours 13. 37′ viz. 8. 22. 02. 00. from 3. 121. 35. 26 The remainer is 6. 201. 33. 26 from which abating 20′ 41″ the ☽ mean Anom AEra Chr. 6. 20. 12. 45.  In like manner the motion of her Apogaeon for the same time is 6. 05. 311. 57 which being deducted from 3. 17. 25. 57 The remainer is 9. 11. 55. 56 To which if you add 21.04 The Sum 91. 121. 15200 is the place of the ☽ Apogaeon in the beginning of the Christian AEra  CHAP. XVI Of the finding of the place and motion of the Moons Nodes ANno Christi 1652 March 28 hour 22. 16′ the Sun and Moon being in conjunction Mr. Street in Page 33 computes the ☽ true place in the Meridian of London to be in ♈ 19. 14. 18 with latitude North 46′ 15″ And Anno Christi 1654 August 1. hour 21. 19′ 30″ was the middle of a Solar Eclipse at London at which time the Moons true place was found to be in ♌ 18. 58′ 12″ with North Latitude 32′ 01″ 1654 August 1. 21. 19′ 30″ ☽ place ♌ 18. 58. 12 1652 March 28. 22. 16. 00 ☽ place ♈ 19. 14. 18 From the first observation to the second there are 27 years 4 months 5 days 23 hours 03′ 30″ Mean motion of the Nodes in that time deg 45. 19. 41 The true motion of the ☽ 119. 43. 54 Their Summ is in Fig. 11. The angle DPB 165. 03. 35 Therefore in the oblique angled Spherical Triangle DPB we have given BP 89. 13. 45 the complement of the Moons Latitude in the first Observation 2. PD 89. 27. 50 the complement of the Moons Latitude in the second observation and the angle DPB 165. 03. 35 whose complement to a Semicircle is DPF 14. 56. 25. The angle PBD is required 1. Proportion As the Cotangent of PD 89. 27. 50 9.97114485 Is to the Radius 10.00000000 So is the Cosine of DPF 14. 56. 25 9.98506483 To the tang of PF 89. 26. 42 12.01191998 BP 89. 13. 45  Their Z is FPB 178. 40. 27. whose complement Is the Arch FG 1. 19. 33. 2. Proportion As the Sine of FP 89. 26. 42. Co. ar 0.00002037 Is to the Cotang of DPF 14. 56. 25 10.57376158 So is the Sine of FG 1. 19. 33 8.36418419 To the Cotang of FGD 85. 02. 56 8.93796614 FGD = PBD inquired  And in the right angled Spherical Triangle BA ☊ right angled at A we have given AB 046′ 15″ the Latitude in the first observation and the Angle AB ☊ = PBD 85. 02. 56. to find A ☊ the Longitude of the Moon from the ascending Node As the Cot. of AB ☊ 85. 02. 56 8.93796614 Is to the Radius 10.00000000 So is the Sine of AB 0 46′ 15″ 8.12882290 To the tang of A ☊ 8. 49. 17 9.19085676 2. To find the Angle A ☊ B. As the tang of AB 0. 46. 15 8.12886212 Is to the Radius 10.00000000 So is the Sine of A ☊ 8. 49. 17 9.18569718 To the Cotang of A ☊ B 5. 0. 41 11.05682506 The angle of the ☽ orbite with the Ecliptick  The first observed place of the ☽ ♈ 19. 14. 18 A ☊ Subtract 8. 49. 17 There rests the true place of the ☊ ♈ 10. 25. 01 The retrograde motion whereof in 4 Julian years or 2461 days is by other observations found to be Sign 2. deg 17. 22′ 06″ and therefore the daily motion deg 0. 03′ 10″ 38‴ 11 iv 35 v. And the motion thereof for 1651 years March 28. h. 22. 16′ viz. Sign 8. deg 18. 26′ 58″ being added to the place of the Node before found Sig. 0. 10. 25 01. Their Sum is the place thereof in the beginning of the Christian AEra Sign 8. deg 28. 51′ 59″ But the Rudolphin Tables as they are corrected by Mr. Horron and reduced to the Meridian of London do differ a little from these measures for according to these Tables the Moons mean motions are AEra Christi The Moons mean Longitude is Sign 04. deg 02. 25. 55 The Moons Apogaeon Sign 09. deg 13. 46. 59 The Moons mean Anomaly Sign 06. deg 18. 38. 56 The Moons Node Retrograde Sign 08. deg 28. 33. 16 And according to these measures the Moons mean motions in decimal Numbers are AEra Christi The Moons mean Longitude deg 34. 00887.345677 The Moons Apogaeon deg 78. 82862.654320 The Moons mean Anomaly deg 55. 18024.691357 The Moons Node Retrograde deg 74. 69845.679010 The ☽ mean motion for one year The Moons mean Longitude deg 35. 94001. 44893. 1 The Moons Apogeaon deg 11. 29551. 126365 The Moons mean Anomaly deg 24. 64450. 322566 The Moons Node Retrograde deg 05. 36900. 781604 The ☽ mean motion for one day The Moons mean Longitude deg 03. 66010. 962873 The Moons Apogaeon deg 00. 03094. 660620 The Moons mean Anomaly deg 03. 62916. 302253 The Moons Node Retrograde deg 00. 01470. 961045 And according to these measures are the Tables made shewing the Moons mean Longitude Apogaeon Anomaly and Node retrograde for Years Months Days and Hours And hence to compute the Moons true place in her Orbit I shall make use of the Method which Mr. Horron in his Posthumas works lastly published by Mr. Flamsted in which from the Rudolphin Tables he sets down these Dimensions The Moons mean Semidiameter deg 00. 15′ 30″ Her mean distance in Semid of the Earth Deg. 11. 47. 22 The half whereof deg 5. 53. 41. he adds 45 the whole is deg 50. 53. 41 Whos 's Artificial cotangent is 9.91000022 And the double thereof makes this standing Numb 9.82000044  Greatest 6685. 44  The Moons Mean 5523. 69 Excentricity  Least 4361. 94  And her greatest variation 00. 36′ 27″ These things premised his directions for computing the Moons place are as followeth CHAP. XVII How to Calculate the Moons true place in her Orbit TO the given time find the true place of the Sun or his Longitude from the Vernal AEquinox as hath been already shewed 2. From the Tables of the Moons mean motions write out the Epocha next before the given time and severally under that set the motions belonging to the years months and days compleat and to the hours and scruples current every one under his like only remember that in the Bissextile years after the end of February the days must be increased by one Unite then adding them all together the Summ shall be the Moons mean motions for the time given But in her Node Retragrade you must leave out the Radix or
according to the title the Sum or difference is the true place of the Node which being deducted from the place of the Moon in her Orb the Remainer shall be the Augment of Latitude or Distance of the Moon from the Node or Leg A ☊ 2. With the Augment of Latitude enter the Table of the Moon 's Latitude and take thence her Simple and Latitude and Increase answering to it Then say as the whole excess of Latitude 18′ or in Decimals 30. is to the Inclination of the Monethly limit So is the increase of Latitude to the Part Proportional which being added to the simple Latitude will give you the true Latitude of the Moon 3. With the same Augment of Latitude enter the Table of Reduction and take thence the Reduction and Inclination answering thereto Then say again as 18′ 00″ or 0. 30. is to the Inclination of the Monethly limit So is the increase of Reduction to the Part Proportional which being added to the simple Reduction shall give the true to be added to or subtracted from the place of the Moon in the Ecliptick Example By the former Chapter we found the mean motion of the Node to be 95. 96094 which reduced to the Degrees and Parts of the common Circle is 345.459384 And the Suns true place to be 345.291334 Their difference is the distance ☉ à ☊ 168050 with which entring the Table Entituled Tabula AEquationis Nodorum Lunae I find the Node to need no Equation and the Inclination limitis menstrui to be deg 00. 30. The place of the ☽ in her Orbit 55.698954 The Nodes true place subtract 345.459384 The Augment of Latitude 70.239570 2. With this Augment of Latitude I enter the Table shewing the Moons simple Latitude and thereby find her simple Latitude to be Degrees 04. 70476. North And the increase 00.28234 And therefore the Moons true Latitude is deg 4.98610 3. With the same Augment of Latitude I enter the Table of Reduction and thereby find the Reduction to be 00.06955 And the increase of Reduction to be deg 00.00855 And therefore the whole Reduction to be sub 00.07810 From the ☽ place in her Orbit 55.69895 The ☽ true place in the Ecliptick 55.62085 That is in Sexagenary Numbers 8. 25. 37′ 15″ CHAP. XIX To find the Mean Conjunction and Opposition of the Sun and Moon TO this purpose we have here exhibited a Table shewing the Moons mean motion from the Sun the construction whereof is this By the Tables of the Moons mean motions her mean Longitude AEra Christi is 34.0088734567 The ☉ mean Anomaly 56.6997085185 Praecession of the AEquinox 20.4976851851 Their Sum is the ☉ mean longit AEra a Christi 77.4973937036 Which being deducted from the ☽ mean longitude the remainer is the Moons mean 56.8114797531 distance from the Sun in the beginning of the Christian AEra  In like manner the Moons mean distance from the Sun in a year or a day is thus found ☉ Anomaly for a year 99.9297857316 Praecession of the AEquinox 0038580246 Their Sum subtract 99.9336437562 From the ☽ mean Longitude 35.9400144893 Moons distance from the ☉ 36.0063707331 Moons distance from the Sun in a days time ☉ mean Anomaly 27378.02348 Praecession of the AEquinox 1.05699 Their Sum subtract 27379.08047 From the ☽ mean Longitude 03. 66010.96287 ☽ Daily motion from the ☉ 03. 38631.88240 And according to these measures are the Tables made shewing the Moons mean motion from the Sun by which the mean conjunction of the ☽ and Moon may be thus computed To the given year and Month gather the middle motions of the Moon from the Sun and take the complement thereof to a whole Circle from which subtracting continually the nearest lesser middle motions the day hour and minute enfuing thereto is the mean time of the Conjunction Example Anno Christi 1676. I would know the time of the mean Conjunction or New Moon in October Epocha 1660 32.697283 Years Compl. 15. 50.254463 Septemb. Compl. 24.465038 1. day for Leap-year 03.386318 Their Sum is the Moons motion from the ☉ 10.803102 Complement to a whole Circle 89.196898 Days 26 Subtract 88.044289 Hours 8. substract 1.152609 1.128772 Minutes 10 Subtract 0.023837 0.023516 The Remainer giveth 8″ .00321 Therefore the mean Conjunction in October 1676. was the 26 day 10 min. 8 seconds after 8 at night And to find the mean opposition To the complement of the middle motion add a semicircle and then subtract the nearest lesser middle motions as before the day hour and minute ensuing thereto shall be the mean opposition required Example Anno Christi 1676. I desire to know the mean opposition in November Epocha 1660 32.697283 Years Compl. 15 50.254463 October Compl. 29.440922 1 day for Leap-year 03.386318 The ☽ mean motion from the ☉ 15.778986 Complement to a whole Circle 84.221014 To which add a Semicircle 50. The Sum is 34.221014 Day 10 subtract 33.863188 Hours 2. .357826 .282193 Minutes 32. .075633 .075251 The Remainer giveth 9 seconds .000382 Therefore the Full Moon or mean Opposition of the Sun and Moon was November the 10th Hours 2 32′ 09″ The like may be done for any other And here I should proceed to shew the manner of finding the true Conjunction or Opposition of the Sun and Moon but there being no decimal Canon yet extant suitable to the Tables of middle motions here exhibited I chuse rather to refer my Reader to Mr. Street's Astronomia Carolina for instructions in that particular and what else shall be found wanting in this Subject AN INTRODUCTION TO Geography OR The Fourth Part of COSMOGRAPHY CHAP. I. Of the Nature and Division of Geography GEOGRAPHY is a Science concerning the measure and distinction of the Earthly Globe as it is a Spherical Body composed of Earth and Water for that both these do together make but one Globe 2. And hence the parts of Geography are two the one concerns the Earthy part and the other the Water 3. The Earthy part of this Globe is commonly divided into Continents and Islands 4. A Continent is a great quantity of Land not separated by any Sea from the rest of the World as the whole Continent of Europe Asia and Africa or the Continents of France Spain and Germany 5. An Island is a part of Earth environed round about with some Sea or other as the Isle of Britain with the Ocean the Isle of Sicily with the Mediterranean and therefore in Latine it is called Insula because it is scituate in Salo in the Sea 6. Both these are subdivided into Peninsula Isthmus Promontorium 7. Peninsula quasi pene insula is a tract of land which being almost encompassed round by water is joyned to the main land by some little part of Earth 8. Isthmus is that narrow neck of Land which joyneth the Peninsula to the Continent 9. Promontorium is a high mountain which shooteth it self into the Sea the outmost end whereof is called a Cape or Foreland as the Cape of Good Hope in Africk 10. The
Earth conteined between three Paralells the middlemo◠whereof divideth it into two equal parts serving for the setting out the length and shortness of the days in every Country 10. These Climates and the Parallels by which they are conteined are none of them of equal quantity for the first Clime as also the Parallel beginning at the AEquator is larger than the second and the second is likewise greater than the third 11. The Antients reckoned but seven Climates at the first to which Number there were afterward added two more so that in the first of these Numbers were comprehended fourteen parallels but in the latter eighteen 12. Ptolemy accounted the Paralells 38 each way from the Equator that is 38 towards the North and as many towards the South 24 of which he reckoned by the difference of one quarter of an hour 4 by the difference of half an hour 4 by an whole hours difference and 6 by a Months difference but now the parallels being reckoned by the difference of a quarter of an hour the Climates are 24 in Number till you come to the Latitude of 66 degrees 31 Minutes to which are afterwards added 6 Climates more unto the Pole it self where the Artificial day is 6 Months in length 13. The distances of all both Climates and Parallels together with their Latitudes from the AEquator and difference of the quantity of the longest days are here fully exprest in the Table following A Table of the Climates belonging to the three sorts of Inhabitants Inhabitants belonging to the several Climes Climes Paralells Length of the Day Poles Elevation Bea of the Clime   0 12.0 0.0   0    4.18   1 12.15 4.18    2 12.30 8.34   1    8.25 Amphiscii  3 12.45 12.43    4 13.0 16.43   2    7.50   5 13.15 20.33    6 13.30 23.10   3    7.3   7 13.45 27.36    8 14.0 30.47   4    6.9   9 14.15 33.45    10 14.30 36.30   5    5.17   11 14.45 39.02    12 15.0 41.22   6    4.30   13 15.15 43.32    14 15.30 45.29   7    3.48   15 15.45 47.20    16 16.0 49.21   8    3.13   17 16.15 50.13    18 16.30 51.58   9    2.44   19 15.45 53.17   Climes Paralells Length of the Days Poles Elevation Breadth of the Clime   20 17.00 54.29   10    2.17 Heteroscii  21 17.15 55.34    22 17.30 56.37   11    2.0   23 17.45 57.34    24 18.00 58.26   12    1.40   25 18.15 59.14    26 18.30 59.59   13    1.26   27 18.45 60.40    28 19.00 61.18   14    1.13   29 19.15 61.53    30 19.30 62.25   15    1.0   31 19.45 62.54    32 20.00 63.22   16    0.52   33 20.15 63.46    34 20.30 64.06   17    0.44   35 20.45 64.30    36 21.00 64.49   18    0.36   37 21.15 65.06    38 21.30 65.21   19    0.29   39 21.45 65.35    40 22.00 65.47   20    0.22   41 22.15 65.57    42 22.30 66.00   21    0.17   43 22.45 66.14  Clime Paralells Length of the Day Poles Elevation Breadth of the Clime   44 23.00 66.20   22    0.11   45 23.15 66.25    46 23.30 66.28   23    0.5   47 23.45 66.30   24 48 24.00 66.31 0.0 Periscii Here the Climates begin to be accounted by Months from 66. 31 where the day is 24 hours long unto the Pole it self where it is 6 Months in length 1 67.15 2 69.30 3 73.20 4 78.20 5 84.0 6 90.0 14. Hitherto we have considered the inhabitants of the Earth in respect of the several Zones and Climes into which the whole Globe is divided there is yet another distinction behind into which the inhabitants of the Earth are divided in respect of their site and position in reference to one another and thus the inhabitants of the Earth are divided into the Perioeci Antoec◠and Antipodes 15. The Perioeci are such as dwell in the same Parallel on the same side of the AEquator how far distant soever they be East and West the season of the year and the length of the days being to both alike only the midnight of the one is the moon to the other 16. The Antoeci are such as dwell under the same Meridian and in the same Latitude or Parallel distance from the AEquator the one Northward and the other Southward the days in both places being of the same length but differ in the Seasons of the year for when it is Summer in the one it is Winter in the other 17. The Antipodes are such as dwell Feet to Feet so as a right Line drawn from the one unto the other passeth from North to South through the Center of the World These are distant 180 degrees or half the compass of the Earth they differ in all things as Seasons of the year length of days rising and setting of the Sun and such like A matter reckoned so ridiculous and impossible in former times that Boniface Arch-Bishop of Mentz seeing a Treatise concerning these Antipodes written by Virgilius Bishop of Salisburg and not knowing what damnable Doctrine might be couched under that strange Name made complaint first to the Duke of Bohemia and after to Pope Zachary Anno 745 by whom the poor Bishop unfortunate only in being learned in such a time of Ignorance was condemned of Heresie but God hath blest this latter age of the World with more understanding whereby we clearly see those things which either were unknown or but blindly guessed at by the Antients 18. The second part of the Terrestial Globe is the Water which is commonly divided into these parts or distinguished by these Names Oceanus Mare Fretum Sinus Lacus and Flumen 19. And first Oceanus or the Ocean is that general Collection of all Waters which encompasseth the Earth on every side 20. Mare the Sea is a part of the main Ocean to which we cannot come but through some Fretum or Strait as Mare
to reduce her place from her Orbit to the Ecliptick Chap. 19. To find the mean Conjunctions and Opposition of the Sun and Moon The Fourth Part or an Introduction to Geography CHap. 1. Of the Nature and Division of Geography Chap. 2. Of the Distinction or Dimension of the Earthly Globe by Zones and Climates Chap. 3. Of Europe Chap. 4. Of Asia Chap. 5. Of Africk Chap. 6. Of America Chap. 7. Of the description of the Terrestrial Globe by Maps Vniversal and Particular A Table of the view of the most notable Epochas The Iulian Calendar Page 461 The Gregorian Calendar 466 A Table to convert Sexagenary Degrees and Minutes into Decimals and the contrary 476 A Table converting hours and minutes into degrees and minutes of the AEquator 480 A Table of the Longitudes and Latitudes of some of the most eminent Cities and Towns in England and Ireland 482 A Table of the Suns mean Longitude and Anomaly in both AEgyptian and Iulian Years Months Days Hours and Minutes 484 Tables of the Moons mean motion 493 A Catalogue of some of the most notable fixed Stars according to the observation of Tycho Brahe rectified to the year 1601. 511 Books Printed for and sold by Thomas Passinger at the Three Bibles on the middle of London-Bridge THe Elements of the Mathematical Art commonly called Algebra expounded in four Books by Iohn Kersey in two Vol. fol. A mirror or Looking-glass for Saints and Sinners shewing the Justice of God on the one and his Mercy towards the other set forth in some thousands of Examples by Sam. Clark in two Vol. fol. The Mariners Magazine by Capt. Sam. Sturmy fol. Military and Maritime Discipline in three Books by Capt. Tho. Kent fol. Dr. Cudworth's universal Systeme The Triumphs of Gods Revenge against the Crying and Execrable sin of wilful and premeditated Murther by Iohn Reynolds fol. Royal and Practical Chymistry by Oswaldus Crollius and Iohn Hartman faithfully rendred into English fol. 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Calvert twelves Pilgrims Port or the weary mans rest in the Grave twelves Christian Devotion or a manual of Prayers twelves The Mariners divine Mate twelves At Cherry Garden Stairs on Rotherhith Wall are taught these Mathematical Sciences viz. Arithmetick Algebra Geometry Trigonometry Surveying Navigation Dyalling Astronomy Gauging Gunnery and Fortification The use of the Globes and other Mathematical Instruments the projection of the Sphere on any circle c. He maketh and selleth all sorts of Mathematical Instruments in Wood and Brass for Sea and Land with Books to shew the use of them Where you may have all sorts of Maps Plats Sea-Charts in Plain and Mercator on reasonable Terms By Iames Atkinson FINIS