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ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A37608	Mēno-Ezeologia, or, A treatise of moneths and years comprehending a survey of the solar and lunar moneths and years, a description of the moneths and years heretofore in use among the Hebrews, Babylonians, Persians, Egyptians, Grecians, Arabians, and ancient Latines : an accommodation of all the said moneths and years to the present Julian and Gregorian : together with a new and easie directory for the finding out of the golden number, cycle of the sun ... : to which is also adjoyned, an abridgement of the history of the world from the creation unto Christ, and a continuation of the British history from Christ to this present : with a reduction of the era's of Nabonaffer, of the Olympiads, of Rome ab urbe condita, and of Seleucus, unto Scriptural accounts, and an adjustment of them vvith one another, very necessary for the understanding of the writings of the ancients : with many other chronological and mathematical observations, no less useful than delightful / composed by Nathaniel Eaton.	Eaton, Nathaniel, 1609?-1674.	1657 (1657)	Wing E117; ESTC R872	44,898	112

even ones that is to the 2. 4. 6. and others of that kind they only assigned 29. from whence it also proceeded that they called the one 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 full and entire moneths and the other 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or months that were maimed and defective because they wanted a day of that was allotted to the other 5. The second Lunar moneth that I may also say somthing to the rest though they have little to do with our account of times is that which Galen calls 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 The time of the Moons proper circuit by later Astrologers it is called the moneth of Peragration comprehending the time wherein the Moon passeth through the Zodiacque not regarding whether she have overtaken or be in conjunction with the Sun or not which is absolv'd in 27. days and 8. hours saith Galen or if you examine the matter more exactly in 27 days 7. hours and 20. minutes So that this moneth cometh short of the former well near the space of a whole Sign that is two days 4. hours and about 40. minutes Yet doth not the Moon as she passeth through the Zodiacque move at all times with an equal quickness for when she is in apogaeo or in the higher part of his Orb she moveth slowly by reason that that part of his epicycle is carried against or contrary to the succession of the Signs from the East unto the West and then in 24. hours she moveth but through 11. degrees 37. minutes and 10. seconds and continueth in a Signe about 64. hours but when she is in perigaeo or the lowest part of her Orb she moveth swiftly by reason that that part of her epicycle is carried along or together with the succession of the Signs from the West unto the East and then in 24. hours she moveth through 15. degrees 19. minutes and 50. seconds and continueth little more then 47. hours in a Sign In her mean motion that is when she participates of neither of these extreams she moveth in 24. hours through 13. degr 10 min. and 36. sec and continueth in a Signe almost 55. hours and by this motion not heeding either of the extreams which ballance one another we may calculate her progress and determine very near what Sign she is in every day of the year for ever allowing her at the time of her change to be not above 15 degr at the most nor less then 6 degr at the least distant from the Sun whether she precede or follow him For this is to be noted that the Moon is not alwaies in the same Sign with the Sun when she is in conjunction with him but somtimes in the Sign before him and somtimes in the Sign behind him but still within the distances before mentioned And here because we are treating of this subject it will not be amiss to subjoyn what Plin. l. 1. c. 17. and with him Macrobius l. 1. Somnii have observed upon it viz. that somtime during the whole time that the Sun is in Sagittarius the Moon hath no conjunction at all with him and somtimes again before he go out of Gemini she changeth twice or hath two conjunctions with him which things are peculiar unto these Signs and happen not when the Sun is in any of the other Unto this proper circuit of the Moon it is that Galen refers those particular and proper changes which happen unto every singular and individual person as preferments honours and the like together with those diseases which proceed from the particular either natural or self-acquired indisposition of every mans body and upon the successive weeks of this moneth every one of which consisteth of 9 days 19 hours and about 50 minutes would he have a critical or decretory judgement to be made upon them unto life or death either good or evil 6. The third Lunar moneth is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the moneth of Illumination or Apparition comprehending the time wherein the Moon demiseth his beams upon the earth and is conspicuous unto men and that saith Galen de dieb decret l. 3. c. 9. is 26 days and 12 hours so that this moneth is 3 days shorter then the moneth of Consecution Which though it be not alwaies true for somtimes the Moon recovereth the light within 1 or 3 days and somtimes again not until 4 days after her conjunction be compseated yet 3 days is the middle betwixt both the extreams and falleth out more frequently to be the time of the Moons recovering his light then either of the other Now the causes say Astrologers why the Moon recovereth her light somtimes earlier and somtimes later after her conjunction with the Sun are these three 1. The swiftness of her motion when she is in the lower part of her epicycle 2. Her septentrional latitude when her conjunction is in the head of the Dragon as it is from the beginning of Capricorn to the beginning of Cancer 3. Her conjunction in Signs by reason of her greater elevation from the Horizon directly occidental that is when the degrees of the Circle of the Moons elevation above the Horizon be more then the degrees of the Zodiaque which she hath passed Now as often say they as all these causes do concur which can only be as Pliny and Macrobius in the before-mentioned places do affirm when the Sun is in Aries and at no time else then the same day may we see both the old Moon and the new but this happens exceeding rarely When two of these causes meet together then she is seen the second day after her conjunction when but one of these causes onely is existent then she appeareth the third day after her coition but when there is none of these causes at all in being then it is the fourth day after her conjunction before she become perspicuous This third Lunar moneth is called by Galen 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the common circuit of the Moon because indeed as it hath nothing proper of its own but is compacted and results out of the common stock of both the other so also it hath a common and universal efficacy upon all men and in that respect is elsewhere termed by him 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the circuit wherein she putteth out her efficacy upon us for as Galen conceiveth those days wherein the Moon is deprived of her light she is also deprived of this common efficacy but as she recovereth her light so she recovereth her virtue which together with her light she imprints upon the Elements the Ayr the Water and the Earth whereof because all men do partake therefore this efficacy takes hold of all men and doth as he saith 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 equally conduce unto us all So that if there be a Pestilence a Famine Inundations Storms Hail or any disease which runneth almost over all a Country proceeding from the extraordinary immutation or putrefaction of the Ayr or other elements it is from this efficacy of the Moon that they

arise and by the critical weeks of this moneth which consist of 6. days and 15 hours that the events and issues of them must be judged 7. Out of a mixture of these 2 last moneths joyning first the sum of both their circuits into one and then retaining the half of the result Galen raiseth a fourth moneth which he calls 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the middle circuit consisting of 26 days and 22 hours and this he conceiveth to be more valid in the judgement of diseases then either of the other out of which it is compacted because the Moon in this hath a double influence both that which she deriveth from the Signs and that which she receiveth and draweth from the Sun By later Writers this moneth is called mensis medicinalis the medicinal month and mensis Galeni Galen's moneth because it is a moneth of his invention Johannes Picus Mirandula and Johannes Franciscus his Nephew Agerus Ferrus Fernelius and many others cavil at it and call it a fictitious imaginary moneth a moneth that hath none of Natures stamp and impress on it But whether they blame him justly for it I leave it to others to determine Of the Solar and Lunar years 1. THe Solar year is that space of time wherein the Sun by his own proper motion runneth through all his Sphaere for that other motion whereby he is every day carried about the Earth from one point of the heavens to the same point again is effected by the rapture or turning round of the Primum mobile and is not his own and this proper circuit of his saith Alphonsus to whom all the late Astrologers do agree is absolved in 365 days 5 hours 49 min. and 15 seconds Ptolomy in the beginning l. 3. Almagest makes it to be 365 days 5 hours 55 min. and 12 sec Julius Caesar as Suetonius delivers l. 2. c. 2. accounts it to be full 6 hours more then 365 days although Ovid in his 3. book de Fastis speaking of the same Caesar saith that he added to the 365 days 5 hours only he calls them e pleno tempora quinta die The Astrologers which were before Hipparchus extend the circuit of the year yet more then this account of Caesars some besides the 6 hours add 7 min. and 9 sec Thebit adds 9 min. and 12 sec and Galen l. 3. progn cap. 4. sticks not to affirm that it contains 365 days 6 hours and about the hundreth part of a day besides which amounts to 14 min. and 26 sec so that according to this computation Galens account of the year exceedeth that of Alphonsus 25 m. 11 sec The bits account exceedeth 19 57 The other Astrologers exceed 17 54 Caesars account exceedeth 10 45 Ptolomy's account exceedeth 5 57 But we rather in this case chuse to desert the authority of the Ancients how famous soever in their times they were then to disavow the experience of all both the present and modern Astrologers in the world 2. The Lunar year not to speak of those curtal computations which Macrobius mentions l. 1. Saturn c. 8. viz. that of the Arcadians who terminated their year at three moneths end or that of the Acarnanians who allowed but six moneths unto theirs is generally received to be that space of time wherein the Moon after her conjunction with the Sun in any of the Signs compleateth 12 moneths of consecution and at the end thereof meeteth with the Sun again in the same Signe or near unto it in which at the beginning of the said moneths she closed with him which annual circuit of hers she absolveth in the space of 354 days that is 11 days sooner then the Sun absolveth his 3. Now though the true reason of the discrepancy of the annual circuits of the Sun and Moon be the difference of their Monethly motions the moon in every moneth of her consecution coming short of the Sun 22 hours and about 30 min. which in 12 months time amounts to the 11 days before specified and some odd hours which the Grecians also as I shall show hereafter made an allowance for yet it is an ingenious observation and worth our noting which Severianus a Greek Author makes upon that question as you may find it Centur. 1. c 94. of Angelus Politianus his Miscellanies It is not to be doubted saith he but God having made the Sun to rule the day and the Moon to rule the night did also place them in the first moment of their Creation in such stations of the heavens as were most convenient for the functions unto which they were designed that is the Sun in the East and the Moon in the West diametrically opposite unto one another Neither indeed was it fitting as he conceiveth that the Moon at her entrance into the world should be imperfect in her light as she is in both her quarters and a little before and after her conjunction but rather shining with a full and ample Orb for those changes and various faces of hers those waxings and waynings which we since have seen were to be the distinctions of ensuing times and were no ways congruous to her first position She was therefore at her Creation at the Full in all her luster and when the Sun had dispatched his first diurnal race and was now setting in the West she had also in the interim run through her Hemisphere and was come about unto the East But saith he the Moon could not be opposite to the Sun and at his full unless you allow her to be 15 days old that is 11 days elder then the world for it was upon the fourth day of the world that the Sun and the Moon were made So that to bring the Moon into that position in which in all probability she was set at her Creation we must borrow for her 11 days more then she could any other ways pretend unto for the utmost that in reason could be granted to her without this borrowing was to bear the figure of the fourth day which was the day of her Creation but upon the fourth day she could not have filled up the light of all her Orb nor be in the Eastern limits of the heavens when the Sun was in the West to remove therefore these impediments and fit her the better to discharge her office she took up as we may say 11 days upon lone or interest appearing to the world as 15 days old when indeed she had not right to any more then 4. which 11 days as she had borrowed at the first and by this means gotten the start of the Sun for such a time so it was meet she should pay them back again and come so much short of the Sun at the end of his annual course as she was before him at the beginning of it which hath been and still is every year 11 days from the Creation to this present Of the Hebrew Moneths and Years 1. THe Names and Order of the Hebrew moneths as they are gathered

the Solstitial year by interposing intercalar moneths be so ordered it that every 24 year he made it equal with the Solar Liv. lib. 1 primae decadis ab Vrb condit 5. Macrobius in the before mentioned place lib. 1. Saturn cap. 15. affirms that Numa Pompilius in his intercalations conformed himself unto the manner of the Graecians which if he did it seemeth strange why it was every 24th year only as Livy saith that his year agreed with the Solar whereas the Graecian years agreed with the Solar every 8th year immediately upon the interposition of their Embolim or intercalar moneths Lalamanti●s in answer hereunto affirms that Numa Pompilius being led by a Pythagorical superstition rather then any Astrological reason in honour of the odd numbers added every year a day unto January by means whereof notwithstanding his intercalation of 90 days at the end of his first and second octennium after the Graecian manner he found still that his years exceeded the Graecian years so many days as there were years elapsed to salve which incongruity at the end of his third octennium or 24th year he took away 24 dayes out of the 3 embolim or intercalar moneths which were then to follow in lieu of so many days wherein in that interim his January had made his years exceed the Graecian years and inserted only 66 days that is 22 in every intercalar moneth and by this means at the end of the said 24 years a perfect agreement was made up betwixt his years and the Graecian and betwixt both of them as Livy will have it with the Solar Of the Julian and Gregorian Years 1. JVlius Caesar finding the intercalations of Numa Pompilius to be full of trouble and accompanied withal with much confusion the aestival months within the circuit of 8 years becoming vernal and the vernal hiemal reduced the year unto the Solar course dividing the moneths as we now have them and assigning to the year 365 days and 6 hours and accordingly for the odd six hours he appointed every 4th year a day more to be inserted into February which day hecause it was immediately placed after the 6th of their Calends which is our 24th day and they that they might not vary their usual forms for 2 days together wrote sexto calendarum Martii The Leap year therefore or the year wherein that Writing was so repeated was called Annus Bissextilis 2. But Augustus Caesar who succeeded Julius as Macrobius witnesseth lib. 1. Saturn cap. 17. finding the intercalations of Julius to be greater then they ought as indeed they were commanded that the Bissextile should be taken in every 5th year only and not every 4th as Julius had appointed but succeeding times perceiving the account of Julius though not so exact as might be wished yet to be neerer unto Truth then that of Augustus was laid aside his computation as the more erroneous and kept themselves firmly to the former 3. And in this manner things continued especially in Europe and those other parts of the world that professed Christ for 1600 years together though with some confusion in the computations of the Church for by reason of those few minutes wherein the Julian account exceedeth the true circuit of the Sun the Festivals of the Church had anticipated already about 12 days and were still certain to anticipate more and more from time to time if no remedy were provided to the contrary 4. For proof of this there is a place alledged out of St Augustine wherein he affirms that Christmass day or the 25 of December at such time as Christ was born was the shortest day of the year and John the Baptists day or the 24 of June was at that time the longest day in the year as they were both indeed within the two Solstitia's no manifest increase or diminution of the days being as yet to be discerned in either of the seasons and this was not without a mystery saith the Father for Christ was to increase but John was to decrease John 3. 20. which was intimated saith he in the very times of their Nativity the one being born when the days were at the shortest but began to receive an augmentation the other when the days were at the longest but began to suffer a diminution But with us that adhere unto the Julian account neither of these Festivals answer unto this Position the Sun being entred into Capricorn 14 days before our Christmass day and the like time into Cancer before the Feast of John the Baptist 5. At last about 90 years ago the Councel of Trent took into their consideration this difference of time which was hapned in the keeping of our Christian Festivals by reason of the few minutes before mentioned and that they might come a little nearer to the primitive observation of these Feasts they brought the year ten days backward causing that to be called the 25 day of the month which before was but the 15th which was not so much indeed as they ought to have done for the Solstices had anticipated 12 days already as hath been said from the time of Julius but it sufficed them as they thought to bring things into that condition which they were in at the Councel of Nice which was much about the State whereunto they now reduced them for they had the Acts and Decrees of that Councel in so much veneration that they believed they could not without great impiety make any addition or alteration in them And from Gregory the 13. who then sate in the Papal chair when the year was thus brought back this computation hath since been called the Gregorian computation and it is received at this day in all Countries that profess a subjection to the See of Rome but we in England who a little before had cast off our obedience to that See made no alteration in our Calendar but still followed the Julian account though so erroneous as was said before that if the world should last so long our Christmass day that should be in the Solstice would in time fall into the aequinoctial nay Christ and John would shift their Tropicks and when the Sun comes into Cancer we should keep the Feast of Christs Nativity and when he enters into Capricorn we should keep the Nativity of the Baptist 6. This Gregorian account which is ten days before our English their 11th day being the first of ours and our last day of every moneth the 10th of theirs will continue in the same state that now it is without any alteration till the year 1700. at which time being Leap year letting fall only the intercalar day which should have been inserted into February in recompence of the 10 min. and 45 see which for 134 years together since the reduction of their year have been advanced their year will afterwards run on again as it did before till the year 1834 and then or at least the next Leap year after that they must again cast away another day

Μηνο-Εξεολοία OR A Treatise of Moneths and Years Comprehending A Survey of the Solar and Lunar Moneths and Years A description of the Moneths and Years heretofore in use among the Hebrews Babylonians Persians Egyptians Grecians Arabians and ancient Latines An accommodation of all the said Moneths and Years to the present Julian and Gregorian Together with A new and easie Directory for the finding out of the Golden Number Cycle of the Sun Dominical letters Leap-years Easter with the Moveable Feasts Epact with the Changes of the Moon for both the last Computations for ever All which are delineated according unto both Accounts for thirty years ensuing and particularly exemplified in two distinct Calendars for this present year 16●7 To which is also adjoyned An Abridgement of the History of the World from the Creation unto Christ and a continuation of the Brittish History from Christ to this present With A Reduction of the Era's of Nabonasser of the Olympiads of Rome ab Urbe condita and of Seleucus unto Scriptural accounts and an adjustment of them vvith one another very necessary for the understanding of the writings of the Ancients With many other Chronological and Mathematical Observations no less useful then delightful Composed by NATHANAEL EATON Doctor of Philosophy and Medicine London Printed by J. Macock for the Company of Stationers 1657. Authors made use of in this Treatise A Gerus Ferrus Alphonsus Angelus Politianus Aratus Augustinus Bucholzer Bunting Chald. Paraphrast Clemens Alexandrinus Codoman Diodorus Siculus Diegenes Laertius Eusebius Eratosthenes Fernelius Galen Gauricus Halicarnassaeus Hector Boetius Herodotus Heylin Johan Picus Mirand Johan Francisc Nep. Josephus Julius Scaliger Justin Lactantius Firmianus Lalamantius Libanius Livius Macrobius Mercator Nicephorus Calistus Ovid. Plinius Plutarch Ptolomy Raleigh Solinus Antiochenus Speed Strabo Suetonius Suidas Tullius Varro Virgilius To his ever honoured Mother and her no less venerable Sister the two famous Universities of this Land Cambridge and Oxford This his Μηνο-εξεο-λοια most humbly Dedicates P. M. D. TImes ancient Records whilst I here unfold And those great things that have been done of old At whose feet else should I my Labours lay But at the daughters of Mnemosyna And when I track the Circuits of the Sun The Poets Father and how times have run From his first Fabrick to these days to whom But you fair Sisters should my Travels come Who are their Parent too and have a share As well as he in what they have or are Take therefore these my Works but take them wel As Mothers do the tales their children tell Syllabus Libri Ad LECTOREM LUnar and Solar th'Hebrew months and years How Persians and Egyptians ordered theirs How Greeks Arabians Latines theirs and when The Julian and Gregorian Counts began How th'aequinoctial periods still ensu'd And when the Moon her waining light renew'd Through times dark mists what lights the Scripture yeild How Judah and Israels Kings are paralleld When Shemer's walls and Zions Towers were burn'd When the two Tribes from Babels bonds return'd What Kings the second Temple did adorn When Daniel's weeks commenc'd and Christ was born When Troys rich Empire Greeks did over-run When the Olympiad Aera was begun Carthage foundations and when Romes were laid When Nabonasser and Seleucus sway'd To the Reader Th'Eclipses which did in that space betide When Philip and great Alexander dy'd What Kings in Egypt what in Persia sate The wars and rising of the Roman State When Julius conquer'd when Augustus reign'd How long their Legions in this Land remain'd When Hengist with his Saxon Troops came in And when their several Kingdoms did begin When Danes usurp'd what Kings of them did reign And when the English thrust them out again When Norman William entred with his men What Princes of his Line have rul'd since then When Scots the Isles North limits first assail'd When they ore Dousken King of Picts prevail'd What Kings from Kenneth held that Throne what fate The Welsh and Irish Crowns did subjugate Would'st thou know this and more this Book alone Reader will give thee satisfaction Of the Solar and Lunar Moneths 1. THough it be certain that the circuits and variations of times may be as well computed by the motions and errors of the other Planets as by those of the Sun and Moon yet because the most of men neither know those limits nor are able to observe their periods some of them extending unto two some of them to twelve and some to thirty years it is therefore according to the circulation of these two Planets only that the distinction of moneths and years is generally measured and accounted 2. The Solar moneth to begin with that is the time wherein the Sun moveth from one signe unto another as from the first degree of Aries to the first degree of Taurus or the like But of these moneths we find not any Nation that ever did or yet doth retain a true account For neither do we in Europe who from Julius Caesars time have been the most exact in this particular of all the world much less do other Nations begin our moneths at the very time that the Sun makes his entrance into these Signes neither do we alot to every moneth that just extent wherein he continueth in a Signe but many times exceed and somtimes are under the proportion 3. Next unto the Solar are the Lunar moneths by which indeed the general mensuration of times hath been alwaies made especially until Caesar's time in all Nations of the world except the Persians and Egyptians of whose moneths we shall speak hereafter as being more obvious to vulgar apprehensions then the others are 4. Of these Lunar moneths we find in Galen a fourfold division or partition of which it was the first only that was taken into the ordinary or common dimension of the year which he therefore calls 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the exact monthly time because how ever th' other have the name of months yet not so properly as this which is as it were by nature squared and fisted to that end And this is it which our late Writers call the moneth of Consecution or Conjunction comprehending the time wherein the Moon overtaketh the Sun after his departure from him or the interim that is from one change unto another which is 29 days and 12 hours In consideration of which 12 hours the ancient Grecians at the end of every other moneth took in a whole day which they called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Varro dere rustica lib. 1. cap. 37. calls it extremam primam Others have called it veterem nova●am because it was the end of the old Moon and the beginning of the New Solon as Diogenes Laertius mentions in his life was the first that caused it to be called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the 30 day and from his time downwards to the odd moneths viz to the 1. 3. 5. and the like they always assigned 30 days and to the

you shall find the golden Number for the said year being 9 and the Epact for the Julian account being also 9 which two are the stars that must guide you in the finding of the changes of the Moon to be upon the 4. day of April that is 5 days after the aequinoctial by which you may conclude that the Hebrews began their year upon the 20 day of March being the new Moon went before the aequinoctial The like course you may take for any other year and at your pleasure by the help of the following Calendar reduce the Julian account to the Gregorian 13. Only this you must observe that the Jews following of this course before mentioned in the beginning of their year and having a regard that their Passeover according to the Law might be celebrated either on or after the vernal aequinoctial were often forced to make an intercalation of a whole moneth betwixt the end of one year and the beginning of another and this they did not by any certain rule but somtimes every second and somtimes every third year as they found themselves necessitated by the falling of their Passeover but when they made no intercalation then the ensuing year began where the former ended and anticipated yearly 11 days according to the manner of the ordinary Lunar years 14. This will be evident if you observe the following Ephemeris for the Hebrew year beginning at the year of the world above-mentioned and continuing for 11 years that is from the year 2994 to the year 3004. in which you may see how the following years somtimes anticipated one another 11 days and how somtimes again a whole moneth was interserted betwixt the conclusion of one year and the beginning of another and all that the Passeover as hath been said might be kept either on or after the vernal aequinoctial by which president you may make any other Ephemeris for what number of years you do desire from the Israelites coming out of Egypt to this present A. M. Aeq G. N. Ep. Nisan Pascha 2998 M30 9 9 Mr. 20 Apr. 4 2995 30 10 20 Ap. 7 22 2996 30 11 1 Mr. 28 12 2997 30 12 12 17 1 2998 30 1 23 Ap. 4 19 2●99 30 14 4 Mr. 25 9 3000 30 15 15 Ap. 12 27 3001 30 16 26 1 16 3002 30 17 7 Mr. 22 6 3003 30 18 1● Ap. 9 24 3004 30 19 29 M● 30 14 15. As for the Hebrew years before Moses it is believed that they took their beginning with the full Moon next adjoyning to the Autumnal aequinoctial whether it did precede or follow it the moneth Thisri or Ethanim being the first moneth of the year and the other months succeeding in their order till you come to Nisan and end in Elul 16. Now to find the Autumnal aequinoctial you have no more to do but to seek out the vernal aequinoctial in the former table and having found it to add thereunto 186 days which is the time the Sun spends betwixt the one aequinoctial and the other and that will bring you to the Autumnal So that if at the Creation the vernal aequinoctial were upon the 21 day of April the Autumnal must be upon the 24 of October 17. The intercalations must be as they were in the Mosaical years viz of a whole moneth every second or third year according as you are necessitated to begin you year with the full Moon either preceding or following the aequinoctial Take a view thereof in the first te● first yeare after the Creation allowing according to Julius Scaligers computation of which more hereafter the golden number for the first year to be 17 and the Epact to be 7. and s● every year after in proportion and then you will have the anticipations and intercalations o● the said years as followeth A. M. Equinoct G. N. Ep. Thrisi A. M. 1 Octob. 24 17 7 Octob. 29 1 2 24 18 18 18 2 3 24 19 29 Nov. 6 3 4 24 1 11 Octob 25 4 5 24 2 22 16 5 6 24 3 3 Nov. 2 6 7 24 4 14 Octob. 22 7 8 24 5 25 13 8 9 24 6 6 30 9 10 24 7 17 Octob. 19 10 Of the Aegyptian Moneths and Years 1. NExt unto the Hebrews we may justly place the Egyptians amongst whom saith Macrobius lib. 1. Saturn cap. 8. there hath alwaies been a certain measure and equability of the Year 2. The names of their moneths are 1. Thoth 2. Phaothy 3. Athyr 4. Choiac 5. Tybi 6. Mecheir 7. Phalmenoth 8. Pharmouti 9. Pacon 10. Paini 11. ●p●phi 12. Mesori 3. To every one of these moneths they assigned thirty days so that they were neither absolutely Lunar nor Solar moneths but of a mixed nature betwixt both And to the end of Mesori or their last moneth they superadded five days more making their whole year 365 days 4. The odd hours or quadrant of a day wherein the year exceedeth 365 days they made no reckoning of until the time of Dioclesian the Emperour and then they were compelled to take in a Bissextile and to conform their Calendar to the Romans 5. From the deficiency of this Bissextile every fourth year their first moneth Thoth did anticipate a day so that their year which in Pliny's time began the 18 of July in the time of Lactantius Firmianus de fals Relig. lib. 1. cap. 6. took its beginning in September 6. Lalamantius in his commentary upon Galen de diebus decretoriis contends that Anno 1540. 41 42 and 43. their moneth Thoth began the third day of August according to which computation the last year 1656 this present year 1657 and the two following years viz. 58 and 59 must begin the 5. day of July 7. And thus if we should allow this Egyptian account to have continued from the Creation to this present their moneth Thoth in this interval of time would have shifted well neer four times through the Calendar falling out somtimes in the Spring somtimes in the Summer somtimes in Autumn and somtimes in Winter varying in every 120 years a moneth or thereabouts Of the Babylonian and Persian moneths and years 1. THe Babylonians and Persians in all things agreed with the Egyptians both in the quantity of their year the beginning of it and the partition of their moneths Diador Sicul. lib. 2. cap. 1. Strab. lib. Geograph 17. 2. The names of the Persian moneths are 1. Formidech 2. Ardaimech 3. Cardaimech 4. Zirmech 5. Mardan 6. Sarenbemech 7. Machiramech 8. Ebemnich 9. Ydramech 10. Dim●ch 11. Bechmem●ch 12. Azsirda●ith Of the Grecian or Attick Moneths and Years 1. THe Attick moneths like the Hebrews were moneths of consecution every two whereof contained 59 days that is the odd moneths 30 days and the even but 29. 2. The names of their moneths were 1. Ἑκατομβαίων 2. Μεταγειτνίων 3. Βοηδρομίων 4. Μαιμακτηριων 5. Πυανεψίων 6. Ἀνθεστηρίων 7. Ποσειδέων 8. Γαμηλίων 9. Ἐλαφηβολίων 10. Μουνηχίων 11. Θαργηλίων 12. Σκιρῥοφορίων 3. These moneths they

divided into 3 decads the first whereof was 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 of the moneth beginning the second decad was 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 of the middle of the moneth and the last was 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 of the moneth expiring The two former of these Decads they numbred in a regular forward order calling the first day of the moneth 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the first day of the moneth beginning the second 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the second day of the moneth beginning and so unto the tenth In like manner they called the 11 day 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the first after the tenth of the middle of the moneth the 12 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the second of the tenth of the middle of the moneth and so unto the 20 which was called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 But in the last Decad they used a retrograde or backward order calling the 21 of the odd moneths 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the tenth day before the ending of the moneth the 22 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the ninth day before the ending and so unto the last which saith Suidas was promiscuously called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 because it was the end of one moneth and the beginning of another standing as it were in the middle betwixt them both and borrowing half a day from either But in the even moneths the 21 day was not called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 but 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the ninth of the moneth expiring for unto these moneths there was no tenth at all assigned but was as it were cut off and lopped from them and this was the reason why they were called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that is moneths that had but nine days in this last part or section whereas the other called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 had 10 allotted to them Neither was the 29 day of these moneths called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 for they had already as hath been said passed over their odd 12 hours unto the former moneths and had no common tie with those that followed but simply 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the last day of the moneth or first before the end thereof 4. And as the moneths of the Atticks were Lunar moneths so were their years also Lunar years consisting only of 354 days that is being 11 days and some odd hours shorter then the Solar to make up which deficiency at the first as Plutarch mentions in the life of Numa they took in every second year a moneth of 22 days and afterwards as Herodotus and Libanius in his argument upon Demosthenes his Oration against Andro●ion do affirm they made an intercalation every third year of 33 days but finding still that they came not up unto the Solar year because the odd quadrant of a day was every year omitted the year before the first Olympiad they moulded up their years into an octennial chain or circuit at the end whereof they inserted three moneths which they called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 containing 30. days apiece or 90 days in all that is 88 days for the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or several elevens and 2 days for the Bissextiles or quadrants of a day which in that interim of time they had lost from the Solar reckoning Mac. l. 1. Saturn cap. 15. 5. The beginning of this octennial circuit or chain of years they alwaies made at the first new Moon after the Summer Solstice beginning their day at Noon which was also common to the Babylonians Persians and Egyptians as the Romans did theirs at midnight and the Hebrews theirs according to the Law at Even But after the first year all the other years of the octennium anticipated one another 11 days until the end of the 8 or Embolim year when the intercalar moneths came in and then they returned to the same point where they began before 6. Hence we collect numbring the year from the first Olympiad to this present according to the Chronology hereafter following that from the first institution of this octennial chain to this instant year 1657. there have intervened 304 embolims or intercalar years and that this present year is the first of a new circuit or revolution and consequently that their moneth Hecatombaeon beginneth this year June 30 being the first New Moon after the Summer solstice Of the Arabian moneths and Years 1. THe Arabians in the ordination of their year followed partly the Attick and partly the Egyptian customs 2. With the Egyptians they agreed in this that they made no allowance for the quadrant or excurrent particulars of a day as Strabo calls them wherein the year exceeds 365 days and hence it is that the beginning of their year is fleeting and uncertain and every fourth year as the Egyptians did anticipates a day being somtimes in Winter somtimes in Summer somtimes in the Spring and somtimes in Autumn running from one solstice and one aequinoctial to another 3. With the Atticks they agreed in this that their year consisted of 12 Lunations or months of consecution every one of which began with the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or conjunction of the Luminaries and that at every three years end though the Athenians upon better grounds reformed that practise they made an intercalation of 33 days for the so many elevens wherein annually the Lunar year is exceeded by the Solar 4. The Names of the Arabian moneths are 1. Almuharaz 2. Saphar 3. Rabe 1 4. Rabe 2 5. Gemedy 1 6. Gemedy 2 7 Rage 8. Sahaben 9 Ramaden 10 S●nel 11 Dulc●ida 12 Dulcheya 5. If you would make an Ephemeris for this account set but the first day of Almularaz in the same place with the Egyptian Thoth and at the end of every three yeers you shall find both the Calendars exactly agreeing with one an other Of the Latine Moneths and Years 1. BEfore Romulus what moneths and years were received amongst the Latines is somthing doubtful yet Ovid in l. 3. de Fastis makes it more then probable that they were Lunar moneths they used 2. By Romulus the year was altered and 10 moneths only taken into the account thereof unto 4 of which he assigned 31 days and to the rest but 30 making it in the whole to consist of 304 days Macrob. lib. 1. Saturn cap. 13. 14. 3. The names and order of his moneths you have in these four verses of Ovid. Martis erat primus Mensis Venerisque secundus Haec generis Princeps conditur ille fuit Tertius a senibus Juvenum de nomine quartus Caetera de numero turba notato suo est Which are the same which we yet retain save only that in honour of the Caesars July and August were afterwards inserted instead of Quintilis and Sextilis 4. Numa Pompilius added January and February and brought his year to the course of the Moon which yet because he found that it came short of

satisfaction I have adjoyned this following Table by which observing only the Golden Number they may know when the Moon changeth in February for ever in both accounts both Julian and Gregorian 2. Yet it is to be noted in this Table that we reckon the day according to the custom of Astronomers to begin at Noon and therefore we conclude that when the Golden Number is 8. then there is nothing of the Moon in the Julian February which accounting the days otherwise doth not hold for whensoever the Golden Number is 8. and the Dominical Letter B as it was in the year 1603. and will be again in the year 1698. then the Moon changeth the first of February in the forenoon which changes notwithstanding we repute to be in New Moons Feb. Jul. Golden Number New Moons Feb. G. 17 1 27 07 2 17 25 3 05 15 4 25 03 5 13 22 6 02 10 7 20 00 8 10 19 9 00 08 10 18 26 11 06 16 12 26 05 13 15 24 14 04 13 15 23 02 16 12 21 17 01 09 18 19 28 1● 08 N. Moons Feb. Jul Golden Number N. Moons Feb. G. January and therefore quinquagesima or Shrove-sunday in both those years and all others of the same kind falls not until the 6th day of March following which is five weeks after The like may be observed in the Gregorian February when the Golden Number is 9. for then beginning the day astronomically there is no change which beginning it otherwise would somtimes happen The Epact 1. AS the annual circuit of the Moon every year cometh short of the Sun 11 days as hath been said before so by adding these elevens yearly unto one another and casting away 30 which is the limits of a moneth as often as the Sun exceeds that period we make an estimate of the proportion that the Moon keepeth in her course for ever 2. These elevens that are yearly added unto one another or unto the remaining surplusage after the rejection of the aforesaid thirthys are called the Epact and this addition or change of the Epact is made every year upon the first day of March. 3. Every 19 years which is the Cycle of the Moon the Moon in that interim as hath been said returning to the same point of the Sun the Epact also is the same that it was before and hath alwaies a necessary dependance upon the Golden Number 4. When the Cycle of the Moon or Golden Number is 1 the Epact in the Gregorian year is also 1 but in the Julian year it is 11. 5. All other Epacts whether Julian or Gregorian are formed by the additions and substractions before mentioned that is by adding 11. and substracting 30. as often as occasion doth require 6. In the following Table you may see all the Epacts both Julian and Gregorian with their dependancies upon the Golden Number every year from the beginning of the Cycle to the end thereof 7. To know the age of the Moon by the Epact or the proportion that she keepeth in her course every moneth you must do as followeth 1. Take the number of the moneths to that time that you desire reckoning March to be the first April the second and so in order till you come to February which is the 13th 2. Take also the number of the days of the moneth how many of it are past to that instant day that you enquire for 3. Unto both these numbers add the number of the Epact which account soever you desire it for for that year present and if the total Jul. Ep. Gol. N. Gr. Ep. 11 1 01 22 2 12 ●3 3 23 14 4 04 25 5 15 06 6 26 17 7 07 28 8 18 09 9 29 20 10 10 01 11 21 12 12 02 23 13 13 04 14 24 15 15 05 26 16 16 07 17 27 18 18 08 29 19 19 sum be under thirty it shews you the age of the Moon for that present time but if it exceed thirty the overplus only is her age 4. But in such moneths as have under one and thirty days you must cast away only nine and twenty from the Sum and account the residue for the age of the Moon The Moons coming to the South After change or full 0 12 00 0 0 06 00 0 After either quarter 1 12 48 1 1 06 48 1 2 01 36 2 2 07 36 2 3 02 24 3 3 08 24 3 4 3 12 4 4 09 12 4 5 04 00 5 5 10 ●0 5 6 04 48 6 6 10 48 6 7 05 36 7 7 11 36 7 Between the two Quarters the Moon Southeth in the night before and after them she Southeth in the day The hour of the Night 1. OBserve her shaddow on a Sun-dyal and if it be past the 12th hour line add there unto the Moons southing and the aggregate is the hour of the night but what hours and minutes the shadow wants of the said 12th hour-line substract it from the Moons southing and the remainder is the hour of the night 2. Yet you must remember that so many half hours as the shadow is past the hour of 12. you must substract so many minutes but for so many half hours as the shadow wants of the hour of 12. you must add so many minutes The time of the Tides 1. AT Quinborough South-hampton Portsmouth and Wellins it is full Sea the same hour and minute that the Moon cometh to the South 2. In all other Havens or Ports where the hours and quarters stand before the same there it is high water so many hours and quarters before the Moons coming to the South but where the hours and quarters stand after the same there it is high water so long after the Moons southing as in the following Table 0. 3. Rye Callice Calshot Winchelsea Gorend 1. 2. Yarmouth Bulloign Dover Harwich Wight 2. 1. Needles Diep Casket Lux Lenow Orford Laisto 3. 0. Orkney Pool Orwell St Hellen Vlie Eames Embden 3. 3. Portland Peterport Hareflew Hague Blanchy 4. 2. Milford Bridgewater Northwast Exwater Taxel 5. 1. Bristol Lanion Foulnes Mousbray Antwerp Hanb Lin Humber Weymouth Plimouth Dartmouth Lime Sale 6. 0 Aberden Redbane Rochester Maldon West end of the Nore 0. 3 Gravesend Downs Romny Tenet Romkins 1. 2 Dondee St Andrews Lisbon Silly Maze St Lucar 2. 1 London Tinmouth Hartlepool Amsterdum Gascoigne 3. 0 Berwick Ostend Scarborough Hamborough Flushing 3 3 Frith Lieth Dunbar Laur Bloy Egmon Monsh 4. 2 Falmouth Foy Garnsey Severn Mouth Waterford Youghall Kinsale 5. 1 A delineation of the Julian year for 30 years an ☉ D. ☾ ep Quin Pasc Trin. Adv           f. m. m. a. m. A.   n. d 57 14 d 5 25 28   29   24   26 29   58 15 c 6 6 21     11   6 24 28   59 16 b 7 17 13     3 29   25 27   ●0 17 a g 8 28   4   22   17 23   2 61 18 f 9 9 24

    14   9 24   1 62 19 c 10 20 9   30   25   26 30   63 20 d 11 1   1   19   14 23 29   64 21 c b 12 12 21     10   5 24 27   65 22 a 13 23 5   26   21   27   3 66 23 g 14 4 25     15   10 24   2 67 24 f 15 15 17     7   2 25   1 68 25 e d 16 26 2   22   17   27 29   69 26 c 17 7 21     11   6 24 28   70 27 b 18 18 13     3 29   25 27   71 28 a 19 29   5   23   18 23   3 72 1 g f 1 11 18     7   2 25   1 73 2 e 2 22 9   30   25   26 30   74 3 d 3 3   1   19   14 23 29   75 4 c 4 14 14     4 30   25 28   76 5 b a 5 25 6   26   21   27   3 77 6 g 6 6 25     15   10 24   2 78 7 f 7 17 10   31   26   26   1 79 8 e 8 28   2   20   15 23 30   80 9 d c 9 9 22     11   6 24 28   81 10 b 10 20 13     3 29   25 27   82 11 a 11 1 26     16   11 24   3 83 12 g 12 12 18     8   3 25   2 84 13 f e 13 23 10   30   25   26 30   85 14   d 14 4   1   19   14 23 29   86 15 c 15 15 14     4 30   25 28   A delineation of the Gregorian year for 30 years an ☉ D. ☾ ep Quin Pasc Trin. Adv           f. m. m. a. m. F.   n. d. 57 14 g 5 15 11     1 27   26   2 58 15 f 6 26   3   21   16 23   1 59 16 e 7 7 23     13   8 24 30   60 17 d c 8 18 8   28   23   26 28   61 18 b 9 29 27     17   12 23 27   62 19 a 10 10 19     9   4 25   3 63 20 g 11 21 4   25   20   27   2 64 21 f e 12 2 24     13   8 24 30   65 22 d 13 13 15     5 31   25 29   66 23 c 14 24   7   25   20 22 28   67 24 b 15 5 2●     10   5 24 27   68 25 a g 16 16 12     1 27   26   2 69 26 f 17 27   3   21   16 23   1 70 27 e 18 8 23     13   8 24 30   71 28 d 19 19 8   29   24   26 29   72 1 c b 1 1 28     17   12 23 2●   73 2 a 2 12 19     9   4 25   3 74 3 g 3 23 4   25   20   27   2 75 4 f 4 4 24     14   9 24   1 76 5 e d 5 15 16     5 31   25 29   77 6 c 6 26   7   25   20 22 28   78 7 b 7 7 20     10   5 24 27   79 8 a 8 18 5   26   21   27   3 80 9 g f 9 29   4   21   16 23   1 81 10 e 10 10 16     6   1 25 30   82 11 d 11 21 8   29   24   26 29   83 12 c 12 2 21     11   6 24 28   84 13 b a 13 13 13     2 28   26   3 85 14 g 14 24   4   22   17 23   2 86 15 f 15 5 24     14   9 24   1 Of the Eclipses which will happen this present Year 1657. 1. THere will be this year two Eclipses of the Sun the former upon the tenth day of June the other upon the 25th of November but neither of them conspicuous to us at London and therefore not material to our present Treatise 2. Of the Moon there will be also two Eclipses the first of which will happen upon the 15th day of June the beginning thereof will not be seen at London the Sun being then above and the Moon below the Horizon but the middle and the end will be conspicuous it begins about 40 minutes after 6 of the Clock at night and ends about 11 minutes after 10. The time of the greatest obscuration is 8 of the clock and 26 min. The whole continuance 3 h. 30 min. and 18 seconds 3. The other Eclipse of the Moon will happen upon the 10th day of December and will be visible at London from the beginning to the end thereof the beginning will be at 5 hours 41 min. 11 sec the end at 7 h. 57. m. 3. sec the total duration will be 2 h. 15 min. 52 sec The greatest obscuration at 6 of the clock 49 min. and 7 seconds January hath XXXI Days Julian account     Gregor account M. D. W. D   Sun set Sign       1 a Circumcis 3 55 ♐   11 d 2 b   3 57     12 e 3 c   3 58 ♑ Hilary 13 f 4 D ● 1. n. 3 59   ● 1 n 14 G 5 e   4 00 ♒   15 a 6 f Epiphany 4 02     16 b 7 g   4 03 ♓   17 c 8 a   4 05     18 d 9 b Sol in Aquario 4 06   ☉ in ♒ 19 e 10 c   4 07 ♈   20 f 11 D   4 09   Agnes 21 G 12 e ☾ 5 17 n 4 11 ♉ ☾ 5 17 n 22 a 13 f Hilary 4 12     23 b 14 g   4 13     24 c 15 a   4 15 ♊ Convers Paul 25 d 16 b   4 17     26 e 17 c   4 18 ♋   27 f 18 D   4 20     28 G 19 e ❍ 10 55 n 4 22 ♌ ❍ 10 55 n 29 a 20 f   4 23     30 b 21 g Agnes 4 225 ♍   31 c 22 a   4 27     1 d 23 b Term begins 4 28 ♎ Purif Mary 2 e 24 c   4 30     3 f 25 D Conver. Paul 4 32 ♏   4 G 26 e ☽ 2 8 4 35   Agathe ☽ 2 8 5 a 27 f   4 36     6 b 28 g   4 38 ♐   7 c 29 a   4 39     8 d 30 b   4 41 ♑   9 e 31 c   4 43