is as for the use of it Certain and not liable to any Error or Mistake It was stiled Aera Dionysiana or Aera Christiana and afterwards Vulgaris was added to it to distinguish it from Aera Christiana Vera as contended for though never in use Till then the Accounts in use were the Olympiads the Consuls Urbs Condita Indictions The Olympiads were a small Cycle but of four Years still repeated and numbring withall the Repetitions But Iphitus made them an Aera by accompting a continual Series of Expanded Years from the first Olympick and they were used both ways but chiefly the Olympiads by Quaternions CHAP. III. Of Epocha's Cycles or Periods § Of the Dionysian Period § Of the Cycle of the Sun and Changes of the Dominical Letter Containing also an Account of the Week and Bissextile With a Table of the Dominical-letter c. § Some other Periods particularly that called the Julian § The Indiction § Some Principal Aera's and Periods with a Table reducing them to the Year of our Lord. HERE if I may have leave to Digress and take in Notions though not so Pertinent to our present Design yet equally Profitable and Usefull to Young Students for whom this Discourse is intended I would in this Place say something more of Epocha's and Periods And first I take Epocha to be the Head or Beginning the Pause 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Stop if you reckon up or backwards as far as you can And Aera the Continuation or Series of any Account of Years which is or may be supposed to be Extended and Numbred onwards as long as Time shall have a Being Secondly a Cycle or Period is an Account of Years that has a Beginning and an End too And then begins again and again as often as it ends and so obtains a Perpetuity The Aera has but one Beginning which is the Epocha if we speak strictly though the Words are often Promiscuously used And from thence a Continual Extension The Cycle or Period has its Continuation by beginning again as oft as it ends going as it were in a Circle and thence it has its Name Thus the Cycle of the Moon after every Space of 19 Years begins again toties quoties in infinitum I think we do more commonly use these words so as to stile a lesser Space a Cycle and a greater by the Name of Period and you may not improperly call the Beginning of a large Period the Epocha thereof For the Derivation of these Words Epocha and Aera I refer you to the Etymologists The aforesaid Dionysius or as some affirm Victorius Aquitanus about 70 Years before him considering that a small Cycle of Years by reason of its often Revolution cannot give so certain a Character of Time as a large Period contrived a Period usefull for Computation consisting of 532 years by applying the Cycle of the Sun 28 to that of the Moon 19 which multiplied together give the Number of 532 beginning as oft as those two Cycles take their Rise together at 1 as they did lately in the Year 1672. Dionysius however gave it a new Beginning by applying it to the Year of our Lord and therefore it was generally stiled the Dionysian Period This Period has had but 4 Beginnings since Christ viz. A. D. 76 608 1140 1672 and this present Year 1693 is the 22d year of this Period As the Cycle of the Moon serves to shew the Epacts and that of the Sun the Dominical Letter throughout all their Variations So this Dionysian Period serves to shew these two Cycles both together and how they proceed and vary all along till at last they accomplish their Period and both together take their Beginning again after every 532d year And it serves farther also which was the chief Design of it for more Certain Computation by how much it is a Larger and more Comprehensive Period and under a more Undeceivable Calculation The two Cycles which make this Period are or ought to be very well known to all One of them that of the Moon or Golden Number is at large explicated in the following Discourse The other that of the Sun so called because it shews the Sunday Letter being a Table or Cycle of the Changes of the Dominical Letter I shall briefly here explain Instead of the ancient Roman division of the Month into Nones Ides and Calends we reckon the Days of the Month in Order And instead of their accompting by their Nundinae quasi Novendinae their Mercates or Fayrs for the Country-People to come to Town every 9th Day for Commerce and Trade and to receive their Laws as the Greeks reckoned by Ten 's dividing their Month into 3 Parts we as the Hebrews number our Days by Weeks and their Returns after every 7 Days which the Jews did in relation to their Sabbath and possibly the Assyrians c. in relation to the Quarters of the Moon consisting each of about 7 days and we as Christians for our Lord's day We describe the Days of the Week by seven several Names as Sunday Monday Tuesday c. And to distinguish them in the Calendar there are 7 Letters appropriated and set in Alphabetical order before them and so repeated throughout the whole Year viz. A B C D E F G and some one of these is the Dominical Letter or the Letter for Sunday and the Letters following for the other Days as they follow But the Sunday Letter is not constantly the same but is changed once in every Common Year and in every Fourth or Leap-year twice And the reason is First because the Common Year does not consist of just Weeks but of 52 Weeks and one Day So that as the Year begins with A set before New-year's-day So it ends with A set before the last Day And the Year beginning again at A there will be two A A falling together Dec. 31 and Jan. 1. and if one of them the former happen to be Sunday the other in course must stand for Monday and then reckoning onward Sunday must fall upon the first following G and G will be the Dominical that ensuing Year Thus the odd Day shifts back the Dominical Letter every Year by one Letter And this Revolution would be terminated in 7 Years But secondly there comes in another odd Day every 4th Year being Leap-year And in that Year there are consequently two such Shifts the Sunday Letter being changed twice Once at the beginning of the Year and the 2d time towards the latter end of February by Interposition of the Bissextile or Intercalar Day called Bissextile because the 6th of the Calends of March is twice repeated And the reason why this was done in that Month and not rather at the end of the Year seems to be because by Numa's Institution for the better regulating the Year in imitation of what the Greeks had done before there had been an Intercalation of several Days at that very time in February To take a more easie
carried round the World backward the daily Motion compared with the Annual 365 times and almost a Quarter while he makes his own Round forwards of 360 Degrees of the Ecliptic So no Circle of Even Days can make a Year which as was said creates difficulty in keeping account of Years And the very Steps which the Sun appears to us to make through the Ecliptic are Unequal as also the Days if one be compared to another successively throughout the Year are found not to be Equal and will not justly correspond with any Artificial or Mechanic Equal Measures of Time as by Watch Clock c. So that we are to find out the Extremities on both Sides and from and between them the Midle dayly Motions of the Sun along the Ecliptic and to frame Tables of Equation of Natural days to be applied to the mean Motion by Addition or Subtraction as the Case shall require which are styled Prosthaphaereses The Greek word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 being fitted to comprehend both addition and subtraction The Day is limited to us by the Interchanges of Light and Darkness and the Year by the successive Seasons of Winter Spring Summer and Autumn And these are Signal and Certain tho' not Original Measures of Time constituted by the Revolutions and manifested to us by the Light of the Sun And we have no other Measure save one of the Moon but are as we say Artificially made out of these by Compounding or Dividing them No other Measure of Time deduced from any other Original than the Motion of the Sun can be so evident to us For these are apparent at least after a gross manner to all Mankind and to almost all Living Creatures others only to the Learned in Astronomy or else derived from these by Institution for Civil Use And from these Constituted Measures and Denominations of Time viz. Day and Year not excluding the Lunar Month all other Measures of Duration or Successive Motion are Artificially contrived for Civil Use by dividing these into less parts or Collecting and Compounding them The Day for Small Measures chiefly by Partition and the Year for Great by Collection of Numbers of Years Or we may measure by Numbers of Days and Parts of a Year Some divided the Natural day comprizing Day and Night into four Parts or Quarters for the Day and four for the Night and each of these Quarters consisted of three Planetary Hours The Artificial day from Sun-rise to Sunset be it longer or shorter being divided into 12 Equal Hours and the Night likewise into 12 Three of which Hours made one Part or Quarter But the Hours of the Day were always unequal to the Hours of the Night according to the Increase or Decrease of the Lengths of Days and Nights Only if the Sun were in the Equinoctial or the Inhabitants under the same then the Days and Nights being Equal so would the Hours be also But the General Usage is to divide the whole Natural day into 24 Equal Hours an Hour into 60 I Minutes a Minute into 60 II Second Minutes a Second Minute into 60 III Thirds and so on And by thus dividing the Day we compute the smallest Measures of Time and by Compounding Years we measure the Greater Spaces of Duration But we must observe that the Day is not thus divided by Nature as it is into Light and Darkness and by the Meridian into Noon and Midnight But this Division as most others are is Artificial and at our pleasure by Consent of Nations We may observe likewise that the common Division of a Circle into 360 Degrees or Parts is also Artificial and Arbitrary But it is well chosen and pitched upon as being a Number that abounds with Integer Aliquot Parts and therefore most apt for Partition and being as near as may be suited to the number of Days which the Sun makes in a Year in compassing his whole Circle of the Ecliptic viz. 360 to 365. And in both respects it is best fitted for Astronomical Uses Of the former of these the Aliquot Parts of the Number 360 take a short View as follows 1 360 2 180 3 120 4 90 5 72 6 60 8 45 9 40 10 36 12 30 15 24 18 20 In toto 23 several Aliquot parts The Number 6 is celebrated for having all Aliquot Parts viz. 3 2 and 1 and for being composed of the Aggregate of them all and therefore is stiled The Perfect Number And 10 is the first of the Saracenical Characters or Figures with Cypher that great Friend to Calculation or rather which changeth Calculation strictly so called into easie Computation Now the Number 360 consists of the Square of 6 viz. 36 multiplied by 10 or having a Cypher added to it Of these 360 Degrees or Parts of a Circle every one may be supposed to be subdivided into Minutes Seconds Thirds c. And these Parts are marked alike with the Parts of an Hour ex gr For Hours 3 H 2 I 5 II 4 III and so onwards For Degrees 3 Gr or 3° 2 I 5 II 4 III c. i. e. 3 Hours or 3 Degrees 2 Minutes 5 Seconds 4 Thirds and so forwards A Minute being 1 60 of an Hour or of a Degree a Second 1 60 of a Minute a Third 1 60 of a Second c. So that one Hour or Degree contains 60 I 3600 II 216000 III and as many Fourths IIII as is the last Number multiplied by 60 viz. 12960000 IIII almost 13 Millions By Composition or Joint Number of Days besides such as have been formerly in use we have now chiefly the Week made of seven Days and a Month made of 4 Weeks or 28 Days By Partition or Gross Dividing of the Year we have the 4 Quarters or Seasons of the Year we have 12 Calendar Months intended however now Unequaly constituted at Pleasure to measure the Movement or Passage of the Sun through every of the 12 Signs of the Zodiac Lastly by Compounding or Numbring Years we keep Account of Ages and Publick Transactions and Memorable Accidents we make Cycles and Periods of Years as Decads Centuries Chiliads c. chiefly for the use of Computations in History Chronology Astronomy c. The Numbers of Years by which we measure the Spaces of Time having their several Epocha's or Beginnings as from the Creation of the World from the Floud from the first Olympiad from the Building of Rome or from any remarkable Passage or Accident giving us a pleasant Prospect into the Histories of Antiquity and of former Ages We Christians make the Reputed Year of the Nativity of our Blessed Saviour our chief Epocha from which to make our Dates brought in use first by Dionysius Exiguus Abbas who lived in Justinian's Reign about the Year of our Lord 528 And tho' his Computation may perhaps differ two Years from Truth as Helvicus or more Years as others are of opinion yet since it is and has been universally received over all Christendom our Compute by it
Account of these Changes there is appropriated a Cycle which comprehends in order all the Variations of the Sunday Letter and is therefore called the Cycle of the Sun composed of 4 which makes the Leap-year and 7 the change of the one odd Day throughout the Septimana or Week 4 times 7 gives 28. This Cycle begins at that Leap-year wherein G and F are the Sunday Letters and is terminated at 28. By the Table annexed you may see how it proceeds I have added to it the Cycle of the Moon or Golden Number that you may view their Progress from their being joined and beginning together in the Year 1672. A. D. Cyc ☉ D. Letter Cyc ☽ 1672 1 G. F 1 73 2 E 2 74 3 D 3 75 4 C 4 76 5 B. A 5 77 6 G 6 78 7 F 7 79 8 E 8 1680 9 D. C 9 81 10 B 10 82 11 A 11 83 12 G 12 84 13 F. E 13 85 14 D 14 86 15 C 15 87 16 B 16 88 17 A. G 17 89 18 F 18 1690 19 E 19 91 20 D 1 92 21 C. B 2 93 22 A 3 94 23 G 4 95 24 F 5 96 25 E. D 6 97 26 C 7 98 27 B 8 99 28 A 9 1700 1 G. F 10 701 2 E 11 702 3 D 12 703 4 C 13 704 5 B. A 14 c. It is likely the aforesaid Period was made by Dionysius or whoever else first attempted it in imitation of Calippus who many Ages before in like manner and for the like reason joined four of Meton's Lunary Decennoval Cycles what they are you will see hereafter out of which he made a Period of 76 Years which had its beginning at the New-moon next after the Summer Solstice after the Victory of Alexander the Great over Darius And in the same manner after the third Revolution of this Period Hipparchus enlarged it by adding together four of these Calippic Periods and so obtain'd a greater Period of 304 years containing 16 Metonic Cycles Upon the same Principle but with a greater and nobler Design and Event Joseph Scaliger formed a Period which is become as it were a Standard to all others including and comprehending them all and excells them all for Certainty because we can when we please by Calculation of the Course of the Cycles of which it consists trace up to the Head or Beginning of it and so infallibly determine in what year of this Period any given year is to be placed which by him was thus contrived Upon the Dionysian Period formed as I have shewn out of two Cycles viz. of the Sun and Moon he grafted another most excellent one for Largeness and Certainty beyond all other commencing 764 years before the reputed Epocha of the Creation in use with us serving for many thousand years And it was by joining the Roman Indiction a Cycle of 15 to the other two Cycles i. e. to the Period of Dionysius The Indiction instituted by Constantine the Great is properly a Cycle of Tributes orderly disposed for 15 years And by it Accounts of that kind were kept Afterwards in memory of the great Victory obtained by Constantine over Maxentius 8. Cal. Octob. 312 by which an entire Freedom and as it were a new Life was given to Christianity the Council of Nice for the Honour of Constantine ordain'd that the Accounts of years should be no longer kept by the Olympiads which till that time had been done but that instead thereof the Indiction should be made use of by which to reckon and date their years which hath its Epocha Anno Dom. 313. Jan. 1. Now this Cycle as was said was by Scaliger joined to the other two making the Epocha or Beginning when all three Cycles begin together at 1 which comprehends a Period of 7980 years having its Epocha 764 years before that of the Creation now in use And this is stiled the Julian Period The Golden Number has its Period in 19 years the Cycle of the Sun in 28 the Indiction in 15 The two former as before multiplied one by the other give 532 which multiplied by 15 gives 7980. This Period is of great use in Chronology and they apply all other Periods and Epocha's to it Chronologers differ amongst themselves about most other Great Epocha's as particularly that most principal Epocha of the Creation which is accounted by Arch-bishop Usher to have been 4003 years compleat before the Vulgar Aera of Christ by Scaliger 3949 by Petavius 3983 c. So that when I read of an Action said to be done in such a year of the Creation I am in uncertainty whose Opinion amongst them my Author follows and consequently know not what year he means But the Julian Period is so fixed by Certain Calculation of the Revolutions of those Cycles which make it that it can lie under no Mistake or Doubt but is an Infallible Character of that one year to which therefore all other Aera's must be reduced as well as we can It is necessary to know the different Periods and Epocha's as they were in use amongst several Nations and to know how to reduce them to our way of Accounting else we cannot understand their Historians as to the true Date and Time of Occurrences which they Relate and Account after their own way The Greeks accounted by the Olympiads chiefly the Romans from the Building of Rome and by their Fasti Consulares as the Athenians did by their Archontes The Astronomers from Nabonassar The Aera of Dioclesian or of the Coptites or Martyrs in many places was used until the Christian Aera took place and is still in use as Helvicus relates amongst Arabian and Aethiopic Christians The Arabians and Turks account from the Hegira or Flight of Mahomet The Persians from Jezdagird c. I have for this cause in the following Tables endeavoured to reduce the principal Aera's and Periods to the Year of our Lord Some having their Epocha's before the Nativity and some after Scaliger An. Do. 1 1600 1695 1700 Julian Period 4714 6313 6408 6413 Creation 3950 5549 5644 5649 Judaic Period 3761 5360 5455 5460 Deluge 2294 3893 3988 3993 Exodus Aegypt 1498 3097 3192 3197 Troy Destr 1183 2782 2877 2882 Solomon's Temple 1018 2617 2712 2717 Olympiad 1.195 4.594 3.618 4.619 Iphitus 777 2376 2471 2476 V. C. 753 2352 2447 2452 Nabonassar 749 2349 2444 2449 Julian Calendar 46 1645 1740 1745 Heads of some Aera's after Christ A. D. Years expanded since to the year of our lord 1600 1695 1700 Destruction of Jerusalem 70 1530 1625 1630 Dioclesian's Aera 284 1316 1411 1416 Indiction 313 13. 1287 3. 1382 8. 1387 Hegira 622 978 1073 1078 Jezdagird 632 968 1063 1068 Conquest 1066 534 629 634 Calendar reformed 1582 18 113 118 As to these Tables the Reader may observe that Authors differ about fixing some of the principal Aera's as I said before especially that of the Creation about which many Learned Men dissent from one another But chiefly the