CHAP. I. Concerning some-Terms in Chronology, and those the most common, viz. Mi­nutes, Scruples and Moments.

• 1. A Minute is usually the least Part of time, which is commonly called a Scruple.
• 2. A Scruple is one thing as it is taken in the u­sual and Mathematical sense, and another as it is receiv'd in the Jewish.
• 3. The Vulgar and Mathematical Scruple is the 60th part of an Hour, divisible into 60 other Parts, and so on; whence they are called 1′ 2″ 3‴ 4'''', &c.
• 4 A Jewish Scruple is the 1080th part of an Hour, divided usually farther into Moments.
• 5. A Jewish Moment is the 76th part of a Scruple.

§. 1. FAbricius Paduanus ^(a) hath observ'd that the ancient Chronologers divided the Hours into Points, Moments, Ʋncias and Atomes: So that the Point was the 4th part of The Ancients Division of in Hour. [Page 9] an Hour, a Moment the 10th part of a Point, an Uncia the 12th part of a Moment, and an Atome the 47th part of an Uncia; so that a whole Hour contains 4 Points, 40 Moments, 480 Uncia's, 22560 Atomes; but this Division is now grown obsolete.

§. 2. Yet Chronologers as well as Mathematici­ans, Mathematical Division, do not only divide the Hours and its Parts, but also every Total, or any thing that is like it, into 60 Scruples: For although the Division of the whole into Points may be free, yet, to avoid the Trouble of computing which Fractions cause, except the 10 (which is still better) a more fit than this can't be found out, especially if it be observed that those 60 Parts may be used as In­tegers, as it may be more at large shewn in Arithmetick.

§. 3. But the Author of the New Moons The Jewish Division. gives this account why the Jews divided the Hour into 1080 Scruples, viz. that because there is no Number more easily divisible into so many Parts as is the 1080, being that it can be divided by 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, &c.

§. 4. And this the Jews, according to their Institution of it Divine. wonted Superstition and Boastings of Revelati­ons, will not have of any Humane Invention, but assert it to be Divine. Concerning which, R. Samuel saith, Isachar ascended into Heaven, and brought from thence 1080 Parts.

§. 5. Neither would they have this to have been By others used. used by any others besides themselves, since that from Aben Ezra to the 12th Chapter of Exodus these Portions are called the Parts of Israel, tho' very falsely, Scaliger having observed ^(b) that both the Samaritans, Arabians and Persians, as well as other Eastern Nations have made use of this Division as well as they.

§. 6. However to reduce those Jewish Scru­ples How to reduce Mathemati­cal to Jewish Scruples. to the Mathematical, and these again to the Jewish, you may say, If 60 Mathematical Scruples give 1080 Jewish, how many will the aforesaid Mathematical Scruples give? And again, if 1080 Jewish Scruples be equal to 60 Mathematical Scruples, how many of them will be equal to the aforesaid Number of these? And it will appear when the Operation is fi­nished, that one Mathematical Scruple contains 18 Jewish, and one Jewish 3″ 20‴ of the Ma­thematical; and on this Accounts are the fol­lowing Tables calculated.

§. 7. Epiphanius reports, that divers of the Mar­cosians (so called from one Marcus a celebrated [Page 11] Wise Man who espoused the Valentinian Here­sie) Of some that divide the Hours other­wise. divided the Hour into 30 Parts, which Division was not peculiar to them, but com­prehended the two Equinoctial Hours; whence undoubtedly it came to pass, that whereas 30 Degrees were equal to that time, the Marcosians divided their compounded Hour into so many Parts. So likewise the Inhabitants of Cataja (which the Ancients called Serica) and the Sub­jects of the great Cham of Tartary divide the Year into 24 equal Parts; so that every Part contains 15 Days and 2814 Particles, and ten thousand of these Particles (every one of which they call a Fenack) answer to one Day amongst them; Of which more hereafter.

CHAP. II. Concerning Hours.

• 1. An Hour is commonly called the 24th part of a Day.
• 2. There are two sorts of Hours; some are called equal, others unequal.
• 3. Equal Hours, which the Greeks call [...], are those in which the Night and Day are divi­ded into 24 equal Parts.
• 4. Ʋnequal Hours, which the Greeks call [...], are those wherein the time of the natural Day is divided into 12 Parts, and the Night into as many.

§. 1. ALthough some will have the Word Hour in Latin, Hora, divided from the Greek The Derivati­on [...]f the Word Hour. Word [...], which signifies to limit or bound; because it is the Measure of time; yet the most [Page 12] common Opinion is, that its Original is owing to the Egyptians; because Macrobius Saturn. l. 1. c. 21., and from him many others observe, that the Sun with them was called Horum; of which Opinion Pausanias was also long since.

§. 2. But the Word Hour has not always What it sig­nifi'd formerly. been of the same signification; but in ancient times an Hour did indefinitely express a short space of time; in which sense the LXX In­terpreters have sometimes translated it, and Ʋl­pian in Athenaeus (not without Reason) doubt­eth whether it may be used as for a Definite, or set part of the Day in the Writings of the Ancient Greeks. Certain it is in St. Luke [...], St Luke ch. 14. v. 17. is used for Supper-time. Besides, Homer calls [...] the Coeli janitrices; to which Ovid alludes, bringing in Janus.

Praesideo foribus coeli cum mitibus Horis.

Some believe that heretofore the four Seasons of the Year, wherein the Sun finished its Course, had the Name of HOƲRS, as ancient Wri­tings do testifie. Others there are would have the Reason hereof to be, that because an Horus instituted a certain three-monthly Year; therefore the Ancients called Spring, Sum­mer, Autumn and Winter Years; nay the Year it self Horus; of which thing some Footsteps appear in this, that the Greek Annals called them their Hori, and their Writers Horographici. And others there are also who in a particular Accep­tation of the Word, think that the Greeks call that Part of Time an Hour wherein the Dog-Star arises; whence Galen in his Book de Ali­mentis calls those Horean Fruits which sprung up at that time wherein the Dog-Star arose; and Horace says,

Flagrantis atrox hora Caniculae, &c. Lib. 3. O. 13▪

So that in general the Ancients by an Hour have signify'd an Age; by the 12th Hour, Old Age, as in that Dialogue of M. Crassus, and the King of Galatia. What mean you? says he, art not thou now arrived at the 12th Hour, and yet talkest of building a new City?

§. 3. Herodotus relates, ^(a) that the Graecians Why the An­cients divided the Day into 12 Parts. received from the Aegyptians the Use of the Pole, the Gnomon, and the twelve Parts of the Day: and Pierius Valerianus ^(b) says, that the O­riginal of that Use among the Aegyptians was, because their Priests were wont twelve times a Day to cry aloud with a howling Noise to their Cynocephalus; and both Cicero and Marius Vi­ctorinus have taken notice of such a Ceremony to Serapis.

Galen remarks other things of this Number, viz. that the Romans used it not only for their Hours, but also in Weights, Measures, &c. as being a Number divisible into many aliquot Parts.

§. 4. And doubtless Astronomers according What Hours the Ancients had. to the Motion of the Aequator, have constituted equal Hours, yet it is apparent that the Anci­ents used the unequal more than the equal Hours. St. John says ^(c), are there not 12 Hours of the Day? which must be false, if Equinoctial: As likewise St. Matthew ^(d) in the Parable of the Vineyard; where those that came at 11, staid but one Hour; and that place of Plautus in Pseudolus ^(e), must mean the same Hours, as well as this of Martial:

§. 5. It is not known at what time the Cu­stom of dividing the Days into Hours began a­mong The dividing Days into Hours the most ancient Way. the Aegyptians, yet undoubtedly it is but of short standing amongst other Nations, and chiefly the Romans, which Censorinus ^(f) ob­serves as an Argument that the Word Hour was not known amongst the Romans 300 Years after the Building of the City, by reason there is not any mention made of 'em in the 12 Ta­bles, as the other Laws after that time do; before which the Divisions were only before and after Noon,

§. 6. The Turks not having Clocks as we have, The Turks divided theirs. the Priests in their stead stopping their Ears with their Fingers, proclaim from the Top of their Mosks the Cock-crow, the Break of Day, Noon-tide, Three of the Clock and Twi-light, with a very high Voice: The same Custom the old Romans used, as appears by Martial.

And in Athenaeus mention is made of [...], a mercenary Hour-teller; and also of [...], a Parasite that declared Supper-time.

§. 7. But amongst the many Instruments the The Ancients manner of no­ting the Hours of the Day. Ancients made use of to distinguish their Hours, the Sun-Dial or Heliotropia is certainly the most ancient. For, in the Holy Scripture we read ^(g) of Ahaz's Dial, where that great Miracle was wrought of the Sun's going back [Page 15] ten Degrees; about which not only R. Solomon, but other Interpreters agree that those Degrees were the Indices of such parts of the Day: Nor do we believe that this so publick a Ma­chine was only in use amongst Mathe­maticians, as Salmasius fancies, against whom Dion. Petavius very well urgeth, that then it would not be the Custom to erect them so publickly in the Market-places; and much more from hence the Falsity of a contrary O­pinion doth appear, that the Use of Fortune-tellers and Astrologers were very severely for­bidden by the Jews. However, the Use of Dials was not only long since known to the Jews but to other Nations, as the Greeks, as Diogenes Laertius reports; and the Romans, as Pliny ^(h) relateth. Pomponius also gives an Account of a famous Dial in the Field of Mars, which Persius speaks of when he says,

§. 8. And since we cannot at all times be A Descripti­on of the Ro­man Clepsy­dra. so happy as to enjoy the Light of the Sun, the ancient Romans or rather the Greeks, to make some amends for the frequency of Storms, &c. found out, according to the Inge­nuity of that Age, an artificial Invention. The Author, as Pliny ⁽ⁱ⁾ writes, was Scipio Nasica; which Pancirollus gives the following Descripti­on of; They took says he, a Vessel made of Glass, in the bottom of which was a narrow Hole done about with Gold, lest the Water should wear it away. On the other part of the Vessel was drawn a right Line, having the twelve Hours set upon it; after which they filled the Vessel with [Page 16] Water which issued Drop by Drop out of the little Hole; they thrust a Cork into the Water, fastned to a little Wand, the end of which pointed at the 1st Hour, and as the Water fell down more at the 2 d, 3 d, &c. Hours. This in the Greek was cal­led a Clepsydra, and with us an Hour-Glass.

§. 9. Natural Hours are not every where Natural Hours not e­very where unequal. unequal, since that there cannot be any diffe­rence of Hours Artificial and Natural, as to the Quantity, with those that live under the mid­dle of the Torrid Zone, or under the Aequator, where the Signs of the Zodiack ascend directly: Yet is it otherwise with those that live under the Temperate Zone, if the Sun be in the Equinocti­al Points.

§. 10. And it is commonly thought, that all the Hours of the Day, which they call [...], [...], Equal one with another. are equal one with another; not considering, that the very Days from Noon to Noon are unequal; and then their Parts can never be equal; but since the Inequality is but little, a Mathematician ought to know it; but 'tis but of little moment in ordinary Uses.

§. 11. Unequal Hours are called Planetary; because Astrologers have taught with greater Va­nity Why artificial are called Planetary. and Superstition than Certitude, that the several Planets rule in several Hours, beginning this Order from the first Hour on Sunday, and continuing of it, as you may see in the Table annext; in which it is supposed against all A­stronomick Reason, that Venus, Mercury. and the Sun were the Inferiour Planets; Mars, Jupiter, and Saturn Superiour ones. All which were the Dreams of an unhappy Age.

§. 12. Unequal Hours may be reduced to How to re­duce the une­ [...]u [...] to equal. equal, by knowing first the Quantity of the Natural Day: of which the time, of the Year and Place being given and known; say, as 12 Hours is to the Quantity of the Natural Day, so is one equal Hour to the unequal Hour that answers it; by this means the Proportion between equal and unequal Hours will be so well known, that it will be very easie to reduce them. For Example, sup­pose here at Wittebergh, That the greatest Na­tural Day is 16 Hours and an half; then one equal Hour 22′ 30″ will answer to an unequal Hour, or the twelfth Part of the Natural Day.

§. 13. There are several Computations of Of the Deno­minations of Hours. an Hour amongst several Nations in their De­nominations and setting of them in order. The Graecians commonly began theirs from the Rising of the Sun, the Italians from its Setting, the Europeans generally from Midnight; but the Ʋnequal Hours, some do term them the Jewish, as also Ancient.

§. 14. The Custom of the Romans in their The Ancients Division of Hours for La­bour. Division of their several Hours of the Day for their ordinary Concerns, Martial gives us the following Account of, viz.

But the Greeks used six Hours only for the dispatching their Affairs, spending the rest in the Refreshment of the Body and Mind; whence these Verses,

As also,

CHAP. III. Of Vigils and Watches.

• 1. A Vigil is a certain space of Time, wherein the Natural Day and the following Night was for­merly divided into certain Parts, so called from the changings of Centinels or Watch-men.
• 2. There are two Vigils, one of the Day, and the other of the Night.
• 3. Those of the Day, or rather Centries, Watch and Wards, were most commonly four equal Parts of a Natural Day, each of which contained three Hours.
• 4. And those of the Night, with some Nations were four equal Parts of the Night, of the same Continuance with the former.

1. THE Ancient Division of the Night and The Ancient Division of the [...]. Day, were into Evening and Morning; of which the History of the Creation often [Page 20] makes mention; and although the Lights were not created till the third Day, yet the Motion of the first Light resembling the Sun that fol­low'd after, might make a distinction of Even­ing and Morning.

§. 2. The Name of Vigils or Watches arose The Names of the Vigil. from the Watchmen changing their Posts every three Hours, lest they might either fail, and be over-wearied for want of Sleep, or that too much time might be given to the Enemy to exe­cute their treacherous Practices against the Ci­ty; whence it's plain, that it had its first Rise from a Military Custom; and this Flavius Va­getius (a) confirms, giving this Account of the same; namely, That out of every Century four Horse, and as many Footmen were drawn forth to keep the Watch, and that because it was difficult for the same to keep Guard all Night: Therefore was it thought necessary to divide it into four Parts, according to the Order describ'd before: The Watch was set by Sound of Trumpet, and call'd off by that of the Cornet: Besides which the Tribunes appointed some of the chiefest to go about the Watch to see if any were remiss in, or left their Posts.

§. 3. But since we can find little about the Days Watches, we shall only speak of those of [...]. Jews [...]. the Night. Some think that the Jews divided the Night at least into three Watches, the first of which began at Sun-set, and lasted till Midnight; whence in Job ^(b) it is called the Time when deep Sleep falleth on Men. The second is sup­posed to begin at Midnight, and end at the Cock-crow, where the third commences, lasting until the Sun begins to rise. And indeed the Jews themselves do frequently make mention of three Watches: For in their Thalmud ^(a) [Page 21] Book of Prayers and Thanksgivings) R. Isaac the Son of Samuel saith, There are three Watches of the Night, in every one of which the Holy and Blessed God sitteth roaring like a Lyon; and saith, Woe unto you Children; for I have devou­red my House by reason of your Sins, and burnt my Temple, &c. and the like you may find in R. Salom ^(c): But in the time of the New Te­stament it is plain, that the Night was divided into four Watches, a Custom probably introdu­ced by the Romans; as in those Places of Mat. 14. v. 25. Mark 6. v. 48. c. 13. v. 35. in which sense Suidas interpreteth [...], calling it the fourth Part of the Night.

§. 4. Some think that the Jews received this Received from the Romans. Custom of dividing the Night into Watches, from the Romans, yet without much Ground: For as much as mention is made of the Jew [...]sh Vi­gils before ever the Name o [...] Empire of the Romans was known to the Jews: But it cannot be denied but that the Jews followed the Roman Custom when the Jewish Policy began to de­cline.

§. 5. Yet the famous Scaliger ^(d) is of opini­on Another sort of V [...]g [...]ls. that the Jews as well as the Romans and Greeks divided their Night and Day into four Parts, and called those Quarters the Vigils; the first of which (as he says) was from Sun-set to Midnight: The second also called the Middle, as being betwixt the two Suns, viz. the Set­ting of the one, and Rising of the other, was from Midnight to the Sun-rise. After these was the Morning-Watch, which began at Sun-rise, and continued till Noon: The last continued from Noon till Sun-set.

§. 6. But the Romans distinguished their Night How the Ro­mans divided the [...]. and Day by various Names; some of which we [Page 22] find in the twelve Tables and others elsewhere, the Beginning and End was Midnight; after followed the Night, after this the Cock-crow, after this the Dead of the Night, after this before Day, after this Day-break, after this the Morning, after this the Forenoon, then Noon; after this the Af­ternoon, then late; after this the Evening, then Twilight; after this Candle-light, after that Bed-time, after that far in the Night, then to Midnight, and so Midnight again.

§. 7. However we are yet in the dark as to How they and the Greeks agreed in this matter. the Greeks agreeing with the Romans, although it is no doubt, but that in the time of War the Romans divided their Night into four Parts; and some think, that the Greeks imitated them herein; tho' many Places in ancient Writings seem to contradict it: From which it appears, that the Greeks divided their Day and Night ra­ther into three than four Parts; as appears by Seneca in Thyeste, where the Chorus is intro­duced thus: Quo terrarum, &c. And in Andro­mache thus:

And the Scholiast very clearly on the 10th Iliad of Homer: For as the Poet divided the Day into three Parts, viz. into Morning, Noon and E­vening, so does he the Night: [...]: For he would have the Hom. Ili [...]d. Night to consist of Three Vigils.

CHAP. IV. Of the Days.

• 1. A Day is that Space of time wherein the Sun in its rising and setting, performs either an entire Course, or a certain Part of the Globe.
• 2. It is commonly divided into Natural and Civil.
• 3. That Space of time is called the Natural Day, which passeth betwixt Sun-rise and Sun-set.
• 4. The Civil Day is that which contains one Revolution of the Heavens, and so including also the Night, distinct from the Natural Day, whence the Greeks call it [...].
• 5. Days also are either Holy-Days or not.
• 6. Holy-Days are those wherein Business is laid aside; which the Romans formerly called Nefasti.
• 7. And those are made holy, either by Divine or Humane Authority.
• 8. Some People by Divine Right observe Sundays and other Holy-Days.
• 9. But many Nations by Humane Imposition did heretofore vainly observe several Days, and do at this time; as may appear in the ensuing Dis­course, and the various ways of chusing them.
• 10. Those that are not Holy-Days, but Work-Days, are also called Fasti, being those where­in the solemn Offices are not performed either to the true God, or the false Gods of the Gentiles.

§. 1. THose that call that Space of time a The reason of the Natural and Civil Day. Natural Day wherein the Sun is upon the Horizon, are chiefly moved thereto, be­cause [Page 24] Nature and not Art effects that Day, but those that would have it an entire Revolution of the Sun, alledge that Nature intends a per­fect Circulation, likewise [...] is called a civil Day, because that the Citizens were wont to use it in dating their Contracts and other Civil Actions; and again they call the Suns stay­ing upon the Horizon an Artificial Day, since that it's then convenient for Artificers to do their Work; and as some will add, because the Dif­ferences of such days cannot be made, but by the Workmanship of Almighty God, and may be understood by the use of an Artificial Sphere.

§. 2. But an Artificial Day is not taken in the same Not the same with all Au­thors. Sence by all Authors, for what in Chronology we call a Natural Day, the same the Astronomers usually term an Artificial, and what we call a Civil, they call Natural.

§. 3. The measure of the Civil Day (according to The measure of a Civil day. Chronologers) and the Natural (according to A­stronomers) is by the daily Motion of the Sun round the Earth, or as Astronomers do otherwise speak, it is an entire Revolution of the Aequator, with so much over as answereth to the Suns own Motion, receding in the mean time on the Ecliptick, whence the Complements are unequal. The mean ones are 59′. 8″. in time 3′. 57″, by which part of time the Solar days exceed the day of the Primum Mobile.

§. 4. The difference of a Natural day from The difference [...]. the Civil, consisteth in their equality and ine­quality, some calling those that are unequal Natural days, and those that are equal Civil, though very absurdly; for those that dwell un­der the Aequator, have all Natural days equal, and if we should speak truly, Civil days are not equal, by reason of the inequality of what is added; so if a Country just under the Pole was habitable, its Inhabitants would have their [Page 25] Natural day neither equal nor unequal; for it is called equal or unequal, in respect of each other; however they would know no other day till the year was past. Yet it is true in an Oblique Sphere, for its Inhabitants would have their Natural days unequal, whence Ovid when he would describe an impossibility, says,

And heretofore also Boetius.

§. 5. Yet all Civil days are equal and precise­ly All Civil days precisely 24 hours. 24 hours, for in that time an entire Revolution of the Aequator from rising to setting is perform­ed; but because the Sun like other Stars whilst it turns round so quickly upon the Aequator, hastens towards its rise, performing its mean daily course in 59′. 8″. but the space is une­qual and hence the former degree of the E­cliptick, together with a degree of the Aequator being come to the Meridian, the Sun wants some little space; to compleat which, a little part of time should be added, besides 24 hours which by reason of the Suns apparent unequal Motion, will be unequal as above, but this is fully rectified by the Famous Astronomer Mr. Flamsted, in his Calculation of the following Table of Aequation of Time. viz.

§. 6. That the Distinction of the Day into The Ancient Distinction between Civil and Natural days. Natural and Civil is very ancient, plainly ap­pears by that Stratagem the Thracians formerly made use of, which as Strabo relates ^(a) was thus. Ephorus says he, Writes that the Thraci­ans making Truce with the Boetians (so that then they might have less regard to their Camps) fell upon 'em by Night and destroyed them, whereby they broke the Truce; but the Thracians denied they did any such thing, since that the Truce was made for the days, and they fell upon them by Night; whence is the Proverb, Thracicum Com­mentum: The like Story Plutarch relates in's Laconick Apophthegms.

§. 7. The Variety of several Nations in their Of the various beginnings of days. fixing the beginning of their days is very great, as well as that of their Months and Years; but as to several of the Ancients this following Memorable Distich, gives some small account of, viz.

§. 8. Those People indeed that have computed Those that be­gin their day from Sun-set. their days from Sun-set, are such as have ob­served the course of the Moon; for in that time the Rule of the Lunar Seasons appear in the Starry Orb, this they may perhaps have prefer­red to all others in imitation of Moses, which there is no question but by the Jews, Arabians Athenians, and other Eastern Countries as well as in Africa, was made use of.

§. 9. And this also was used by the Babyloni­ans, From Sun-r [...]se. Chaldaeans, Syrians and Persians, whom Dionysius Petavius, ^(b) Ptolomaeus and Hypparchus [Page 29] following, accounted their beginning of their day from Sun-rise.

§. 10. But the Custom of Calculating the From Mid­night. days from Mid-night, is chiefly ascribed to the Ausonians, the most Antient Inhabitants of Ita­ly, with whom it is very well known the Ro­mans did agree for many years; and probably this may be the reason of its Institution, be­cause that from that time wherein the Sun hath travers'd the lower part of the Meridian, it will then begin to rise again; so that there might be a sort of Harmony betwixt the be­ginning of the year and day, for of this Ovid thus speaks.

Principium capiunt Phoebus & annus idem.

Plutarch brings other Reasons besides this in his Problems, which may be seen in Varro, and from him in ^(c) Aulus Gellius.

§. 11. And the Ʋmbrians (a People well known From No [...] ­ [...]ide. in Italy) near the Appennine Mountains and the Adriatick Sea, whom the Greeks supposed only to have surviv'd the General Inundation; whence their Name [...], or showery (as Pliny ^(d) and Solinus ^(e) would have their Original) u­sually accounted their Day from Noon; with whom the Hetruscians the Borderers on the aforesaid Appennine Mountains, do agree. And because the Meridian is a fixed immovable Circle (and easie for Observations) the Mathe­maticians have followed this Custom two se­veral Ways; some beginning their Days slower by 12 Hours, and others sooner by the said time, than the Civil; of the former sort were Tycho Braye and his Followers; of the latter, Alphonsus and his Disciples.

§. 12. But many Authors of good Account How by the Aegyptians. disagree concerning the Aegyptians. Alexander ab Alexandro ^(f) says, that the Aegyptians and Athenians began their Day at Sun-set, which lasted to the same time next Day. O­thers there are, who have given out that the Aegyptians together with the Chaldaeans began their Day from Noon- [...]de, whom Christmannus upon Alfraganus follows. Pliny ^(g) says that the Aegyptians computed their Civil Day from Midnight to Midnight. Nor are there wanting Arguments that will prove them to have be­gun their Day from Noon; which way Ptolemy fre­quently follows: But Salmasius, considering those Difficulties, makes use of this unheard of Solution: For he supposeth ^(h) the Aegyptians not to have had Ʋnequal Years, but Equal; and yet the Year consisted of 365 Days and a Quarter; which fourth Part or six Hours he sup­poses to be added every Year; whence it hapned, that if the first Year began at Midnight, the next began six Hours later, or in the Morning, the third at Mid-day, and the fourth at Sun-set: So that the first Day of every Year had not a certain, but fourfold Beginning in respect of the Hour. But since this Opinion seems contrary to all o­ther Authors, it is not to be relied on: And we shall still retain the same Opinion, that the Aegyptians, at least some of 'em, began their vulgar Year at Sun-rise.

§. 13. The Gauis and ancient Germans seem How by the Ancient Gauls and Germans. but little to differ from the Jewish Custom about this matter, since these People observe the Moon in their Affairs, which Tacitus takes notice of, when writing of the Germans: They assemble (says he) on certain Days, either upon a [Page 31] New or Full Moon, unless any thing accidental or unexpected falls out. And it is probable that those Days began from Sun-setting, according to the Custom of other People which observed the Moon's Motion; as Tacitus farther con­firms; For transacting Business, they believe this Juncture of Time the most auspicious: Neither, do they reckon by Days as we do, but by Nights; and they so order and appoint things, as if the Night seem'd to usher in the Day. And Caesar writes almost the same thing of the Gauls. This Custom the English observe to this Day, which our Sennight, derived from Seven Night, and Fortnight from Fourteen Nights, doth con­firm. But in Bohemia and Borders of Poland the ancient German Custom is observed, where the Day is from Sun-set to the same time next Day; so that the Clock at Sun-set may be heard 24 times.

§. 14. The Jewish and Political European Time may be reduced to the Mathematick, How to re­duce the Jewish and Civil Day to the Mathe­matical. beginning at Noon, if you substract from the Jewish 18 Hours, (for so many Hours the Jewish Computation anticipates the Mathemati­cal, both in their Ecclesiastical and Civil Af­fairs;) a whole Day being added, if without it no Substraction can be made, the Remainder will shew the time sought. But if our Political Time, beginning from Midnight, was to be compared with the Mathematical, there will be no need of Reduction, if in the Afternoon: But if in the Morning, add 12 to the given Hour, and substract 1 from the Number of Days, the Sum or Difference is the Mathemati­cal time sought.

CHAP. V. Of Months.

• 1. A Month is that part of Time wherein we usually divide a Year into 12, and sometimes into 13 Parts.
• 2. Months are either Astronomical or Civil.
• 3. Astronomical are those that depend on the motion of the Stars.
• 4. And because we generally have respect to the Luminaries in ordering of 'em, some we call Lunar and others Solar.
• 5. A Lunar Month is that Space of time which is spent in the Revolution of the Moon through its proper Orb; or from a Synod to a Synod; and from the Appearance of the Moon after one Synod, to its Appearance again after an­other.
• 6. Hence Nature seems to produce a threefold Lu­nar Month, that is, a Synodical, Periodical and Month of Illumination.
• 7. The Lunar Periodical Month is that Space of time in which the Moon by her Motion return­eth to the same Place of the Zodiack whence she departed.
• 8. The Synodical is that Space of time from one Conjunction of the Luminaries till the next Conjunction following.
• 9. The Month of Illumination is that Space of time intercepted betwixt the first Day, whereon the Moon is seen after her Conjunction with the Sun, and the last Day of her being visible.
• 10. The Solar Month is that Space of time wherein the Sun runs through one of the twelve [Page 33] Signs of the Zodiack in its proper Motion.
• 11. A Civil Month is a System of Days which different Nations differently observe in their Civil Affairs, as it best pleaseth them.

§. 1. AS to the Etymology of a Month it is The Etymology of the Word. observable that in almost every Lan­guage it is derived from the Moon, as among the Hebrews [...] denoteth as well the Moon as a Month. Among the Greeks [...] signifies the same thing. Cicero derives the Latin Word Men­sis ^(a) from the Courses of the Moon, since they make Spaces which the German Word Monat and our Word Month, both derived from the Moon, do likewise denote.

§. 2. From which it appears that the Hebrews, The Ancient Form of Months. Greeks, Latins, and Germans observed the Course of the Moon: For although Arguments deduced from Etymologies of Words are but of little force; yet they are strengthened if joined with other Proofs, especially if we take notice of the extraordinary Aptness of the Hebrew Language and its Harmonical Com­munion with those others mentioned before: whence Julian in that Hymn dedicated to the King of Kings, says, That all the Months with all other Mortals are numbred from the Moon, save we only and the Aegyptians, who compute our Days of the Year by the Motion of the Sun. Nei­ther was the Lunar Month unknown long since to the Romans, tho' the Apostate excepts them, since that the true time in respect of Parturition; which with them was ten Months, seems to be the same with these: In which Sense these Lines of Ovid are to be under­stood:

§. 3. As to the Mystick Months, consisting of 49 or 7 times 7 Days; although there can be Of Mystick Months. no Nation so barbarous as wholly to lay aside all Analogy with the Motion of the Heavenly Bodies, in appointing their Times; yet the Author of this Mystick Chronology spares not to lay it on the Jews themselves; and though these are foolishly asserted or rather foolishly feigned; yet is this Opinion maintained with great Absurdities: For nothing can be so unreasonable, as that God, who created the Luminaries for set-times, Years and Months, should teach a People peculiar to himself any other thing. Neither is the fore-mentioned Word [...] derived from the Moon, of so late a Date. Beside, who knows not that the Jews in the chief Feast of their Passover observe the Moon, and always celebrate the Feast on the Full Moon, and that on the 15th Day of the first Month. But suppose the Jews had their Mystical Month consisting of 49 Days; yet this Number of Days have no Agreeableness with the Lunar Motion: So that instead of Full Moon, you will have nothing but mere Dark­ness. Nor do the Writers of the Old Testament oppose this Truth, who doubtless were sacred and holy Persons; and these speaking of Sacred and Divine things, have made mention of the 8th and other Months beyond the 7th: So that if only this must be thought a Mystery by rea­son of the Number 7, contrary to the Senti­ments and Opinions of all Men; why did not this Mystery-Expounder likewise surmise the same thing of a Day of 7 Hours, and of Hours of 7 Minutes, and so further on?

§. 4. We here again mention the Periodical Of a Periodi­cal Month. Month, lest due Consideration should be want­ing as to its Use; whence Kepler calleth the Periodical Month the Physicians Critical Month; as to the Quantity of which, it is indeed une­qual, and can be found no otherwise than by Astronomical Calculation, by which it will ap­pear that its mean Motion is performed in 27 Days, 7 Hours, 43 Minutes, 5 Seconds.

§. 5. The difference between a Periodical and The difference of a Periodical and Synodical. a Synodical Month, is, because the first is cal­led Periodical only in respect of the Moon's Orbit, but Synodical in respect of its Con­junction with the other Luminaries. And be­cause the Sun from the time of its Conjunction does not continue in the same Place of the Zodiack, but moves forwards towards the East, it causes, that the Moon finishing its Course does not find the Sun again in the same Point it left him; but is removed almost a whole Sign from its former Place; and that it might overtake the Sun again, it plainly appears that a certain Space of time is requisite, besides the Periodical, to make up the Synodical Month.

§. 6. But as to the true Quantity of the Sy­nodical Of a Synodi­cal Month. Month, we are to gather it from Astrono­mers, who study its Motion; as Chronologers the Time in which the Motion is made; how­ever, since a Synodical Month is apparently un­equal, we shall content our selves with the enumerating from several Authors the mean Motion, as they call it; of which Tycho Brale's we take to be the most Genuine: They are these;

§. 7. The Quantity of a Synodical Month is not the same at all times; for in the Summer Synodical net always the same. Solstice [...] when the Sun seems to move slow­est the Synodic Month appeareth less, being about 29 Days, 6 Hours, and 42 Minutes: But in the Winter, when the Sun's Motion seems faster, the Moon follows the Sun in a slower Space; for which reason the Synodical Month then seems greater, viz. 29 Days 19 Hours, and 37 Minutes, as some Astrologers do observe. So that what has been said in the preceding Section about a Synodical Month, is to be understood as to the mean from which the true differs sometimes 14 Hours; and so is either greater or less.

§. 8. Some Months we have called Pleni and others Cavi; the Pleni are those that consist of Of the Months Pleni and Cavi. 31 Days, the Cavi of 30; and these two in the Lunar Year or Lunae-Solar, are placed alter­nately, by reason of the Dependence of the 12 Hours, which, if omitted in one Month, and doubled in another, make 24: For which reason they can be no longer neg­lected, but are to be compleated by the 30th Day, over and above the 29th.

§. 9. Some by the Month of Illumination Of the Months of Illuminati­on. will have that Space of time which is intercept­ed between the first and last Light of the Moon; which Acceptation of the thing, though it be otherwise well; yet since no such Month was ever used by any sort of People we know of, it is only here mentioned to serve the Curiosity of some.

§. 10. Besides, the Lunar Month of Illumination is The Quantity of the same. not of any certain Quantity, being sometimes seen sooner and sometimes later, as her Latitude is Northward or Southward, her Motion swifter or slower; or in Signs descending or ascending, right or oblique, as Astrologers have observed.

§. 11. The Arabians, Turks, and indeed all that make use of the Epocha of Hegyra, usual­ly Of the Turks and Arabians their Year. reckon their Month from the first Phasis, and observe no more in their Lunar Year, than that one New Moon come before another; and that lest the Mirth of the Calends, which with them were solemn and sacred, because of the Eclipse or Suffering of the Sun, which might then happen, might be turned into Sadness: For which reason the Turks upon their Towers and Turbats always place a Crescent or Half Moon. And this some have asserted about the Ancient Jews; yet is not the Assertion approved of by all Chro­nologers; others supposing that the Jews most commonly made use of a Lunar Calculation, and at the same time to have attended on­ly the Observation of the Phasis, not from thence that they might foretel the New Moon, but that they might sanctifie it, and re­ceive the first Sight of the same, with this Prayer, Be thou a good Omen to us and to all Israel! As also that they might examine the Exactness of their Tables, and from them the Calculation sought for.

§. 12. As for the Britains, they anciently obser­ved The Custom of the Britains. the Phasis of the Moon; but when by reason of the great Winds and Clouds a­rising from the Ocean, the Moon's Phasis could not be discerned, they followed a more certain Guide, the Tydes; according to the Ebbing and Flowing of which they do at this Day make great Account.

§. 13. As to the Solar Month, there is very The Quantity of a Solar Month. great Inequality in it; because the Sun in Cancer seems to us to move slower; for which reason the Month of the Summer Solstice con­tains near 31 Days, 11 Hours and 36 Minutes; but in Capricorn, where the Motion of the Sun appears more swift, Astronomers account the Months of the Winter Solstice only to consist of 29 Days, 8 Hours and 54 Minutes, the mean Quantity therefore of every Solar Month will be 30 Days, 10 Hours and 15 Mi­nutes, that is as long as the Sun is in the Equino­ctial Signs.

§. 14. The Civil or Political Months are Of Civil Months. threefold, either altogether uncertain, having no regard to the Lunar or Solar Motions, as those of the Aegyptians in the Equal Year, of the Romans in the Year of Romulus, &c. or com­ing pretty near to the Solar Astronomical Months as the Julian, or the Lunar Astronomi­cal, as the Jewish, Turkish, and others.

CHAP. VI. Of Years.

• 1. Year is a certain space of time, whose parts are commonly called Months.
• 2. And it is either Astronomical or Civil.
• 3. The Astronomical Year so called, is that whose quantity is so determined by the motion of the Heavenly Bodies, as neither the appendant Hours nor Minutes are omitted therein.
• 4. And because it has peculiar respect to the Luminaries it is twofold, Solar and Lunar.
• 5. The Solar year, is that space of time where­in the Sun by his proper Motion, departing from any one point of the Ecliptick, returns to the same again, and therefore it is either Tropical and Natu­ral, or Sydereal.
• 6. The Tropical or Natural year, is the space of time, in which the Sun departing from one of the Tropical, Equinoctial, or Solstitial points, and running through the whole Ecliptick, returneth to the same point again, and it's Quantity is 365d. 5h. 49′.
• 7. The Solar Sydereal year, is the space of time in which the Sun returns to the same Star from whence he departed, and it's Quantity as Astrono­mers tell us, is 365d. 6h. 9′.
• 8. That we call a Lunar year, (in ordering of which, respect is had to the Lunar Motions) is ei­ther common or embolismal.
• 9. The common Lunar year contains 12 Synodi­cal Lunations, the extent of which is 351d. 8h. 49′.
• 10. The Lunar embolismal year contains 13 Lu­nar Astronomical Months, the Quantity of which is 383d. 27h. 33′. and this year is frequently used in the Lunar or Soli-Lunar Computation.
• [Page 40]11. The Political or Civil years are those whose use is in Civil and Ecclesiastical Affairs, in appointing them as well as may be with respect to the Luminaries, but amongst the several sorts of Civil years, the Julian is the most celebrated, as we shall show in the Sequel of this Discourse.
• 12. And those sorts of years are either equal or mean, or true and unequal.
• 13. The mean or equal are those that always consist of 365d. and 6h. but are not in common use.
• 14. The true Julian years, are either common or Bissextile.
• 15. The common consists of 365 days and 6h. the Bissextile of 366, and such are all the years of Christ when divided by 4 into aliquot parts, according to that Distich.

Tunc bissextus erit, partes per quatuor aequas

Annos partiri cum poteris Domini.

16. But the Bissextile is a day arising from the 4 times 6 hours, which are omitted in the Julian years.

§. 1. THis word Annus or Year in the 3 Ancient The Etymology of the Word Annus. Languages, is derived as it were from a thing that goes round, or a Circle; for so much the Hebrew word [...] does signifie; and for the same reason in the Greek is it called [...], and some will have it the word Annus is derived from the Greek [...] circum, but it is a little ab­surd to derive the Latin from the Greek and they are more in the right, who say that the word did formerly signifie a Circle; however, it is certain that An coupled, did signifie as much as Circum, as in the word ambire, to which the Poet doubtless alludes when he says,

In s [...] su [...] p [...]r [...]stigia volvitur annus.

Or it may be Annus from Anguis a Snake; for that the Egyptians before they had the use of Letters, represented it by a Serpent or Snake biting her Tail, which the Poet very well speaks of.

§. 2. But Astronomical Years do not depend Of Astrono­mical years. wholly on the Luminaries, since by the Stars there could be no denomination of the year, and it is very certain that the Saturnine year is computed to 955 days, 12 hours, or al­most 30 Julian years; and the Astronomers make the Jovian year to have 4331d. or almost 12 Juli­an; the year of Mars 687 days, or almost 2 years, but the years of Venus and Mercury as to their extent, differ not much from the Solar Mo­tion. And the fixed Stars have also their Peri­ods, though they move but very slowly, which is the reason a year of these according to Hip­parchus and Ptolomee is equal to 36000 Julian; to Alphonsus 49000, to Tycho Brahe and Kepler 25806, and to Longo-montanus 26046, as Ricci­olus ^(a) notes these and others opinions, and from him Macrobius observes ^(b) that a year is not only what we commonly call so, but the Stars as well as the Luminaries have their years, that is, a Motion from a certain place of the Hea­vens, to the same again.

§. 3. The Tropical Astronomical year of the Why also cal­led Tropical. Sun is not so termed from the Solstices, as some of the Ancients were of opinion; but ge­nerally from the points of Changings, and the Suns double Motion; for many Authors shew that the Equinoctials, as well as Solstitials are called Tropicks, as Manilius ^(c), and Sextus Empiricus ^(d) in the Edition of Stephanus, do make appear.

§. 4. The Solar Sydereal Year is greater than the Tropical, because the fixed Stars use their Less than a Solar Syde­real. own Motion, and whilst that the Sun performs it's course through the Zodiack, they move 50″ faster towards the East; therefore the Sun wants at least 21′ to be even with them, and by so much is a Sydereal year greater than a Tropi­cal.

§. 5. Some will have it that the Achaians Solar Sydereal years, by whom used made use of this Sydereal Solar Year, which they began with the rise of the Pleiades or 7 Stars, and that the Egyptians nicely observed the ri­sing of the Sun with the Dog-Star, as it appears from their Antient writings; yet it is owing more to fancy than any Astronomical strictness, to have respect to the Sydereal Solar Conjuncti­ons, and that more in such an Age, wherein the slowest Motion of the fixed Stars was not sufficiently known.

§. 6. But the Turks and Arabians make use of the Lunar year some-what adapted to civil use, and the same custom is also observed in Tartary, Si [...]m, Japan, Peru, and other places; and those that attribute this Custom to the Gauls and Germans, seem not mistaken, since Bede, who doubtless was well acquainted with our Ancestor's, their way of Computati­on, is very plain that they made use of the Lu­nar [Page 43] year; these are his words, Cum verò Embo­lismus, hoc est 12. mensium Lunarium annus oc­curreret, superfluim mensem aestati apponebant, ita ut tunc tres menses LIDA vocarentur, & ob id annus ille TRILIDI cognominabatur. Yet the Ancient Names of the German Months oppose this opinion, which as they are marks of the appointed Seasons, so do they supply instances of a Solar year, such are Giuli, &c. but some may say that these are later Names, and our Ancestors only had 'em from the Romans.

§. 7. The Lunar Year has this inconvenience, The Inconve­niences of the Lunar year. that the same Months in several Lunar years, have not the same Season, the occasion of which is, that the Lunar year being less than the So­lar by almost 11 days, in three years time eve­ry Month will have the Season of that which went before it, and so further in succession of time, viz. in 16 years those Months which were in Summer, will be Winter, and vice versâ, a thing the Turks who use this sort of years, are very sensible of.

§. 8. However the Jews who follow the How the Jews appoint their Months, Years. Moons Motion in their Accounts, by intercala­ting an entire Month, retain still the same Sea­sons every Month, and as often as there is the difference of 30 days between the Common Lu­nar, and the Solar Year, they substitute an Em­bolismal Month called the Veadar, and hence it is that they have Lunar Months in the same Sea­son; and their year may not improperly be cal­led Lunae-Solar.

§. 9. But Kepler says that the Jews after their Of their Ca­lendar after their Depar­ture out of Egypt. departure out of Egypt, used only the Solar year so that, thereby he would make the Lunar Solar Calendar but of late date. His Description of it is in the following words, Patriarchas quidem aio, &c. The Patriarchs, says he, made use of the Egyptian year of 365 days, divided into 12 [Page 44] Months, 11 of which contained 30, and the 12th 35 days. But whereas the beginning of the Egyptian year went through all the Seasons of the year at their departure out of Egypt, it hapned in Autumn, whereas it should have hap­ned in the Spring; for which reason Moses com­manded the Month of first Fruits to be made the first Month, by which the Egyptian mov­able year became fixed. But admit this to be true, it does not thence follow, that a Lunar was Esta­blished according to the Egyptian way; I know some Objections, but shall not take upon me the place of an Adversary. However this I confess, the Jewish year until the Graecian Monarchy, to have been Solar, not Lunar; and so he goes on further, page 91. with whom Ly­dial agrees in this opinion (Viz. That the Jew­ish year always began about the N. Moon, and that all the other Months save the last, did consist of 30 days. Now this is not worth contending for, for though it may well be supposed that the Jews after their Departure out of Egypt, did not leave their Ancient Solar Form of the years; for according to Josephus, none of their Ancient rites as to their year were innovated; yet however we cannot be perswaded but that their Ecclesi­astical year from their departure out of Egypt to the time of the Macedonians, were purely Solar, without the least Regard to the Lunar Motion, since we find frequent mention made of it in the Holy Scriptures.

§. 10. As to Mystical Years, since they are on­ly Of the Julian year. the Off-spring of one Man's Brain, and ne­ver yet used by any sort of People, what we have said of Months, may indifferently be ap­plyed to the years which are merely fictitious, and grounded neither on Holy or Prophane Writings, nor Revelation which the Author Hainlinus mostly seems vainly to value himself upon.

§. 11. But Chronologers use the form of the Of the Julian year. Julian year, as a constant and acurate rule of their times, whence it happens that they do not only refer to the Julian Calendar, those things which came to pass after it's first Institution, but by way of prolepsis, make use of the same from the beginning of the World, nay, before the beginning it self; and that for 3 Reasons. 1st. Because this sort of year is universally known, and as equally fitted to the Egyptian, and Nabonassarean as other years. 2ly. That af­ter the Nabonassarean, it is the most plain and easie of any. 3dly. Because the same Months in this year, have the same changes of the Seasons fixed, which and other like Reasons induced that famous Mathematician, Kepler, to lay aside the Gregorian, and make use of the Julian in his Tables of Heavenly Bodies; nay, and Petavius, tho' very much addicted to the Gregorian Stile, cannot but give the Julian this Character, viz, the Julian year (says he) when fitted to use, is the most agreeable to the Nature of things, since that comes as near as can be to the course of the Sun, and is no less fit to Register the times, for which reason it is made use of in the Chronicles and Annals of most Writers, and that not only in recording of things since its Institution, but before nay from the beginning of the World it self. Where­fore for example sake when they would assign the Eclipses of the Sun or Moon, or the Wars of Cities and Kingdoms, and their famous Actions in their years and seasons, they always make use of the Julian Years and Months, as if they were then used by them, which by Anticipation and a sort of fiction they institute, by which ours will more easily agree with them, being fitted to the common times. Nor will the Reader be tired in observing the different sorts of years. For Petavius saith that it is the most exact Account of time, and easiest [Page 46] to be made use of, and which beyond all others is most fitted to common use, and cometh nearer to the Revolution of the Sun, than any other sort of year whatever; and these and many other Rea­sons there are, why the Julian year should in general be explain'd, being likewise the Recep­tacle of all other Epocha's.

§. 12. The Ancients did not add at the end Of the Bissex­tile. of the year that whole day arising from the 4 times 6 hours, but to February, reckoning the 6 of the Calends of March twice over, yet still accounting those two Days for one, in which sense Celsus ^(c) takes it. For (says he) it matters not whether it be on the former or the latter days, since that those are but accounted one, which Mar­cellinus notes, was always thought by the Ro­mans unfortunate.

§. 13. Since a Julian year is taken to be 365 The difference between a So­lar Tropical and a Julian year. days 6 hours, and the Solar Tropical mean years, according to Longo-montanus, to be 365d. 5b. 48′. 55″. it thence appears, that the diffe­rence of quantity between them following the said Longomontanus's Hypothesis, is but 11′. 5″. which Chronologers usually call the Civil Equino­ctial Procession; and that because in so much time the places of the Equinox do vary in the Julian year, by which means in the space almost of 130 years, the Equinoctial and Solstitial points seem to go backward a whole day.

§. 14. As to the space of time of the great Of the great Canicular year. Canicular year, which is called the Stoick or Cy­nick period, Censorinus gives us this account of it (f): The Moon (says he) belongs not to the Egyptian year, which we call Canicular; because it begins the first day of the Month they call the Thoth, when the Dog-Star arises. For their Civil (d) De Die Nat. c. 18. [Page 47] year has only 365 days, without any intercala­tory day; therefore the space of 4 years with them, is almost a day less than the Natural 4 years, by which it happens that in the year 1461. it revolves to the same place. This year is by some called Heliacal, as belonging to the Moon, and by others [...].

§. 15. As the Heathens were destitute of the Of Plato's great year. light of Scripture, and consequently of the Origi­nal of the World, so they err strangely about its end. The great year of Plato was a very notable fiction. The Stoicks as well as the Plato­nicks, thought that the World must have natu­rally an end, when all the Stars were again re­volved to the same point; but what Period of years this Revolution may require, is not as yet known, even Kepler himself despairs of the Possibility of this invention, when he asserts that the Motion of the Stars are incommensurable with themselves.

§. 16. Lastly, as to Aristotle's Greatest year, some Of Aristotle's greatest year. confound it with Plato's great year, from which notwithstanding it differs, which Censorinus fur­ther thus speaks of: There is (says he) another year, that Aristotle calls the greatest, rather than the great, which the Spheres of the Planets con­stitute when they come together, to the same pla­ces where they were before; the Winter of which made the Worlds Deluge, and its Summer will make the last Conflagration, &c. but Mar­silius makes mention of another real year, in which the Soul of Man finishes its Circuit of Transmigration, which time they say is per­form'd in 12000 years, to 3 of which years, the great year of the World is equal, consisting of 36000 years, wherein the Anima Mundi per­forms its Course; but Peter of Aliacus the Car­dinal, does otherwise determine the Quantity of the great year; for says he, as from the be­ginning [Page 48] of Aries to the end of Virgo, is equal to the half of that space, which is from the be­ginning of Libra, to the end of Pisces; so ought there to be from the Birth of Christ, to the end of the World, as much time as was from Adam, or the Creation of the World, to the coming of our Saviour; this space was 5260 years, there­fore according to him from the beginning of the World to the end will be 10400, all the Stars finishing their Courses, &c.

CHAP. VII. Of the Epacts.

• 1. Ʋnder the Name of Epacts, we usually un­derstand the Difference between a Lunar and Julian year.
• 2. The Epacts are either Civil or Astrono­mical.
• 3. The Civil Epacts are days intercepted between the common Julian year of 365 days, and the Lu­nar (taken at large) of 354 days, hence the An­nual Epacts consist of 11 days, except in every 19 year in which there are 12.
• 4. The Astronomical Epacts may be termed those Days, Hours and Minutes, which are intercepted between the common Lunar year, and the mean or equal Julian year, which are 10d. 12h. 11′. 22″. 16‴.

§. 1. THe word Epact is derived from the Greek The Etymology of the Epacts. [...], which besides other things, signi­fies to intercalate: In which sense Plutarch in Numa uses it; and in the Egyptian Nabonassare­an [Page 49] Computation, the 5 days besides 12 Months, consisting of 30 days to compleat the year, are termed the [...] or added days, and therefore because the Epacts are days that are to be added to the Lunar year, this Denomi­nation is no ways absurd.

§. 2. The reason of the Epacts, is the diffe­rence The reason of the Epacts. of the quantity between the Lunar and Julian year; for the common is not Equal, but less than the Julian, but both are made use of in the Ecclesiastical Account; some Authors be­thought themselves of reducing the one to the other, which they effected by appointing the Epacts.

§. 3. A difference indeed was ever between The time when first known. the Lunar and Julian year; but because Sosy­genes the Author of the Julian Calendar, in that form of a year he proposed to Caesar, little regarded the Moons Motion; it is probable that the use of the Epacts was anciently unknown, and came in use with the Cycle of the Moon, in the time of Dionysius: therefore since the first year of the Dioclesian aera, had the first Cycle of the Moon, and no such cause could be taken from the motion of the Moon, it may be supposed that the order of the Lunar Cycle, and conse­quently of the Epacts, may be deduced from the Dioclesian aera; and after that to be taken, or rather the invention of Meto, Calippus and Hipparchus, being lost and obliterated, to have been used amongst the Christians.

§. 4. There are some other Writers, who by How some Writers re­ceive the same. the Epacts understand the difference between the Lunar and Solar Tropical year, and others between the true Julian common, and the mean Lunar year, in which sense Joannes Baptista Ricciolus, ^(a) takes them. In the Rodolphin Tables [Page 50] Epacts are calculated to be 10d. 15h. 11′. 21″. 49‴. 33''''. in the Prutanick 10d. 15h. 11′. 21″. 52″. 24''''. but according to Nicholas Mulerius in the Frisick Ptolomaick Table, that time is supposed to be the Epacts, which is computed backward from the beginning of the year, to the next preceeding new Moon, which agrees to what before we have laid down.

§. 5. The greatest number of the common Number of the Epacts. Epacts is 30, for as often as the number of the Epacts exceedeth this, so often is the whole Em­bolismal Month consisting of 30 days, always to be added to the Lunar year, so that it may be equal to the Solar or Julian year. And the 30 days of the Embolismaean Month, absorbs this Addition, that in the Computation of Epacts they are not accounted for, as the Authors of this way have perswaded themselves and o­thers. The Table of Epacts in this our Age, is as follows.

§. 6. The Epacts as the Cycle of the Moon, resolve The Revel [...]i­on [...]f the Epacts. into themselves again in 19 years, which being elaps'd, the Ancients were of opinion the Cycle of the Epacts were exactly performed, for which reason at the Numbers of this 19 years Cycle, they were wont to fix the Epacts of [Page 51] the Moon, as in the following Table; the mean­ing of which is thus. The Product of the Cha­racter of the Cycle, and 11 being divided by 30 the 3 s. being taken away, the remainder is the Product of the Moons Cycle.

§. 7. Since that an Account of the days in Of the Hours, &c. that re­main besides the Epacts. the common year cannot easily be had, there­fore parts of days belonging to the Lunar and Julian years, although they are really unequal, yet in common use may be made equal one with another till that in the last year of the Lunar Cycle, they may be by the Lunae Saltus laid aside.

§. 8. Chronologers make frequent mention of Of the mean­ing of the leap of the Moon. this Saltus Lunae or the Moon-leap, in treating of the Epacts; this happens in the last year of every Cycle, by reason that in the space of 19 years, the Excess of the Julian year above the Lu­nar is at large computed at 209 days, which being divided by 30, it gives 6 Embolismal Months; and 29 days will remain, which when the Cy­cle is resolved into it self, 30 days are taken in stead of 29, or a 7th Embolismal Month, whence it follows in stead of 11. in the Epacts we must use 12 in the 19th year; wherefore when the Epact of the last year exceeds one day by a Meto­nymia, they call it the Moon-leap, or Lunae Saltus.

§. 9. The Quantity of Astronomick Epacts may The Quantity of Astronomic Epacts. be thus known. The mean Julian Year being 365 Days, 6 Hours, and the Lunar, according to Tycho Brahe's Hypothesis, 254 Days, 8 Hours, 48 Minutes 37″ 44‴. So that the difference will be 10 Days, 21 Hours, 11 Minutes, 22″, 16‴, which difference ought every Year to be subtracted from the Julian Year, that the mean New Moons and Full Moons may return to the same Julian Day again.

§. 10. The reason of the Saltus Lunae, and the Reason of the Saltus Lunae. Use of the Number 12, instead of 11 in the Epacts in the last Year of the Cycle of the Moon, is because the true Difference between 19 Lunar, and 19 Julian mean Years is 206 Days, 18 Hours, and almost 36 Minutes: So that if for every Year 11 Epacts were only used, there would happen 209 in 19 Years; and then the New Moons would change the Epacts 2 Days and more: Therefore to pre­vent this, an Embolismal or 30 Days Interca­lation, which Astronomers define to be 29 Days, 12 Hours, 44 Minutes, 3″, 8‴, 39'''', is always made use of, and so the Quantity of every Embolismal Month exceeds the Astrono­mical 11 Hours, 15 Minutes, and 57 Seconds; which multiplied by 7, is equal to 3 Days, 6 Hours, 5 Minutes, 39 Seconds; and these being aded to the Difference between the 19 Julian and Lunar Years before determined, the same will make 210 Days, 1 Hour and almost 28 Minutes. Now, that the Epacts might attain to this Sum, 12 is assumed to the 19th Year: By which the Number of the Epacts is equal to 210 Days; and the difference is only one Hour and a few Mi­nutes.

§. 11. Yet although the Cyclic Defect Of the Cyclic Defe [...]t. of 1 Hour and a few Minutes may seem [Page 53] but small, for which reason the Ancients took no further Notice of them; yet in the space of near 312 Years they make an entire Day, whereby the New Moons get before the E­pacts: Therefore in this our Age it is necessa­ry aforesaid Epacts be augmented by 3, and they will serve us: Or if the Product of the Character of the Cycle of the Moon, and 11 be divided by 30 the Remainder (be­sides the Quotient) will express the Number of the Epacts, as is shewed in the Table hereafter.

§. 12. The Use of Epacts is to shew in their The Ʋse of the Epacts. Places, the Moon's Age, and chiefly the Full Moon before Easter, which is the Use the first Authors of the Epacts intended them for.

§. 13. The difference of the Epacts of the The difference of Epacts of the Old and N. Calendars. Ancient Calendars from the New is as much as the Sum of Days taken away; whence Unites being subtracted from the Epacts of the old Ca­lendar we have the Epacts of the New One.

§. 14. And if March, or the Month that goes be­fore How to know the Age of the Moon. March be named, the Sum of the Epacts or Days of the Month are said to shew the Age of the Moon; but if that intended follow March, the Number of the Month from March may be added, and the 3 Min. as often as can be, left out; by which means the Age of the Moon every Month may be every Day known.

§. 15. If we would find in the old Calendar How to find Easter. the 14th Moon or Easter from the Epacts, then the Sum of the Epacts being less than 26, must be subtracted from 47; if greater, or equal to 26, they must be subtracted from 46; the Re­mainder will shew the Day reckoned from the Calends of March, on which Easter ought to be assigned in the old Calendar.

§. 16. The Epacts by shewing plainly the Age Why the E­pact's are cal­led the Golden Number. of the Moon, have obtained the Name of the Golden Number; but yet the Wariest Chronolo­gers are often mistaken; who laying aside the more tedious way, make use of this short way, which shews the Errors both of the Julian and Gregorian Stile.

CHAP. VIII. Of a Lustrum, Saeculum, or Aevum.

• 1. A Lustrum is a certain Space of time anciently appointed for Civil Ʋse; and tho' formerly it was reckoned to consist of 5 Years, yet Chronologers do now repute it only as Four.
• 2. An Aevum is sometimes taken for the Age of a Man, sometime it denotes Infinite Dura­tion.
• 3. A Saeculum is the Space of One Hundred Years.

LƲstrum (which signifies a purging by Sacri­fice) is derived à Luendo, from paying or The Lustrum and its Ʋse among the Ancients. expiating: For in times past when the Sacrifi­ces were performed; the Tributes were paid both by Capitation of the Men, till the time of Constantine the Great (as is now done amongst the Turks) and also according to the Custom of Taxing Acres of Land and other Goods. The Ancients also, as Festus remarks, were wont to lett out their ^(a) Farms for the Space of a Lustrum.

§. 2. The ^(b) Ancients unanimously assert, that Twas the Du­ty of the Cen­sors to purifie (lustrate) the People. Lustration amongst the Romans was the Duty of the Censors. These Leased out the Publick Revenues, took care of the High-ways and publick Buildings, examined the Riches of every City, and inspected their Manners.

§. 3. Servius Tullius Son-in-law of Tarquini­us The fi [...]st Au­thor of this Lu [...]ration was Servius Tuliius. Priscus, introduced this Custom: For of him ^(c) Livy thus writes; He instituted the Valuation of every Man's Estate; whence Taxes were laid not by Capitation of Men, as formerly; but ac­cording to their Estate. In another Place ^(d) he ascribes to him the Solum in the Language of the Et [...]ci signifies wh [...]le. Suovetaurilia or Solitauri­lia (an Immolation of a whole Bull, a Ram and a Boar): The Taxation of the Estate being made (says Li [...]ius) which he hastened by fear of the Law being made against those that avoided it; as also by Threatenings of Death and Imprison­ment, all the Roman Horse and Foot appeared in Centuries in the Field of Mars; where, after Exercise, he (Iustravit) purify'd the whole Army by the forementioned Sacrifice, whence this Action was called the Lustrum, being perfect at the finish­ing of the Taxation.

§. 4. This Case is controverted amongst the The Return of the Lustrum amongst the Romans was every 5 Years. Antiquaries: ^(c) Some will have it that the Lu­strum amongst the Latines answers to the Olym­piads amongst the Greeks, viz. a Space consisting of 5 Years from Lustrum to Lustrum inclusive; yet so as that every fourth Year being finish'd, reckoning the Lustrum one; on the beginning of the 5th a new Lustrum was performed; and on the 9th another, and so on: But ^(f) others [Page 56] of better Authority will have but one Lustrum in five Years, reckoning the Lustrum the last of the five. Claudian is very particular in this matter:

But perhaps this difference amongst Authors a­rises from the Change of the Lustrum: For according to Livy, when Aemilius was Dicta­tor, it was changed from 5 Years to one and a half. However, among all Chronologers at this time a Lustrum is reputed constantly for the space of four Years, which was the first Opinion.

§. 5. The Lustrum of Julian and Narbonas­sar There are two sorts of Lu­strum, the N [...]bonassare­an and the Julian. differ but one Day; the former consists of 3 common Years and one Bissextile, which makes 1461 Days; the other is made up of 4 com­mon Years, or 1460 Days.

§. 6. The Aevum of the Ancients in its proper Aevum its Signification. and received Signification pass'd for the Age of one Man; and in this Sense 'tis used by the Nurse in Seneca's Tragedies, dissuading Hippolytus from a solitary Life:

§. 7. Philosophers use the Word Aevum to Other Signifi­cations of it amongst [...]ther Writers. signifie Duration, or that which has a Begin­ning but no End; whence the Duration of finite Minds is commonly expressed by this Word. But Censorinus ^(g) makes no distinction betwixt Aevum and Eternity: Aevum, says he, is tempus unum, &c. is one and the greatest Time, immense without End, which always was, and ever shall be after the same manner; nor is any one concerned in it more than another: And afterwards, That which has no End cannot be compared with Mea­sure: Wherefore I shall not endeavour to measure out an Aevum by any Number of Years, or Ages, or lastly, by any Model of finite Time.

§. 8. Censorinus ^(h) reports, that Men had not Seculum, its Signification. agreed in his time about the Quantity of a Saeculum. He distinguishes it into Secula Natu­ralia and Secula Civilia. The Natural he de­fines to be the longest Space of a Man's Life, which being variable and unequal, he first com­ments upon the manner of the Etrusci: The Ritual Books of the Etrusci (says he) seem to teach us these Naturalia Secula, viz. They exa­mined when any Town or City was founded, who at that time were born; from thence beginning their Secula Naturalia; the last of which dying, the Seculum expired: Again, of all that were lately born and alive at that time, he that lived the longest determined the second Seculum Naturale, &c. The Seculum Civile is the Space ⁽ⁱ⁾ of a hundred Years.

§. 9. Censorinus relates this pleasant Comment out W [...]y a Secu­lum or the Age of Man is [...]mmoni [...] reputed to be of 100 Years. of Varro and Discorides, that at Alexandria, where they were used to preserve their Dead, they took notice of those that died in their ful [Page 58] Strength, and observed the Increase and De­crease of their Bodies, viz. in the first Year they encreased 2 Drams, the second 4, and so on till 50 Years; and after the 50th Year they decrea­sed again, each Year two Drams; till at the End of an hundred Years they returned to the same Weight.

CHAP. IX. Of the Epocha, Aera, Cycle and Period.

• 1. The Epochae and Aerae are solemn remarkable Times, from which Men begin to reckon.
• 2. The Cycle and Periods are such Spaces of time as revolve into themselves again.

§. 1. AMong the Greeks [...] signifies inhi­bere, The Deriva­tion of the Word Epo­cha. insistere, to fix, or limit a certain Point of time from whence all Men may reckon.

^(a) Some will have it come from a vicious Of the Word Aera. Punctation A. ER. A. i. e. ANNƲSERAT AƲGƲSTI; But it being anciently written ERA with a single E, this Etymology may be rejected. ^(b) Others write it Heram, ab Hero, as first fixed from some great Man or Monarch. ^(c) Others will have Aeram, ab Aere, from the Tribute-Money wherewith Caesar Au­gustus taxed all the World, and stamp'd the World upon it, that in its Circulation it might carry a Symbol of Universal Subjection to the Roman Empire. Of the Antiquity of this Word [Page 59] we have no tolerable Satisfaction but that it Antiquity of the Word Aera. anciently was writ ^(d) ERA.

There ought to be Characters ready at hand Of the Care of a Chronologer in fixing and explaining an Epocha. whereby an Epocha may be established; else all Care will be fruitless: For since Epocha's, as Scaliger says, are only Notations and Titles of Time: They ought to have proper and distinct Characters.

§. 3. It comes from the Greek Word [...], Cycle, its de­rivation and Multiplicity Circulus, a Cycle: or that which revolves it self again. Thus there are Horary, Diurnal, Lunar, Solar, Secular Cycles, &c. as hereafter.

§. 4. We almost understand the same by a A Period is different from a Cycle, Epocha or Era. Period as by a Cycle, only here; a Period once ended, never begins again; tho' a Cycle conti­nually begins again after its Revolution. When Cycle, Aera or Epocha is lost and never revived, the Determination is a Period: Therefore it differs from an Epocha and Era in this; 'tis Terminus ad quem: they, Termini à quo.

CHAP. I. Of Chronological Characters in general.

• 1. Chronological Characters are the Principles from which we shew.
• 2. These Characters are either Astronomical or not Astronomical.
• 3. Astronomical Characters are those which are taken from the Stars measuring time by their Motion, and are made use of to decide Chro­nological Controversies, such are chiefly the Aequinoxes, the Solstices, the New Moons, the Lunar Phases, the Eclipses of the Sun and Moon, the Conjunction of the Planets, either with the fixed Stars, or betwixt themselves; and others of the like Na­ture.
• 4. Those Characters which are not Astronomica [...], are such as owe their Original either to the Will of God or Man, and determine ei­ther Days or Years. Of which we shall speak in order hereafter.

§. 1. THAT Chronology does not want its Whether there are any, and what sort of Principles in Chronology. certain Principles is evident, if we con­sider those Characters, which in part we have named; and which hereafter we shall explain: Nor is the Suffrages of Witnesses in this Affair inconsiderable: For well, as St. ^(a) Augustine said, I am equally certain of the Building of Rome and Constantinople. For what if I have seen Rome with my Eyes, I know nothing of it but what I believed from other Witnesses. Therefore Chronology in this part is like other Sciences, in which the Conclusion is not believed except it be firmly proved or demonstrated. But if from Authority only without any Character or other necessary Connection of Years, a Series of time shall be laid down how the whole be­gins to be but Opinion, and has nothing in it to uphold a firm Perswasion. But Chronologi­cal Principles differ from Physical ones in this; the former relate to Knowing, the latter to Being.

§. 2. When we argue from one Science to A Chronolo­ger proving his Conclusions from Astrono­mical Princi­ples does not amiss. another, where the Objects are different in toto genere; this is a Fault: but whereas Chro­nology is subalternate and dependant upon A­stronomy; and has its Object contain'd under the Object of Astronomy, 'tis no Error, any more than for an Architect to use Geometry, or a Musician Arithmetick.

§. 3. Astronomical Characters are not made Astronomical Characters cannot be con­veniently used in Chronology to consider why Acting is but only that it is. use of in Chronology as Conclusions, but as first Principles; then there is no need of demonstrating them: Wherefore we think they act preposterously who gives in their Chronological Writings whole Theo­ries, and those of the Sun, Moon and fixed [Page 62] Stars, which Petavius ^(c) has also done in a very prolix Work: whereas the Knowledge of Astronomy is supposed or taken for granted by a Chronologer.

§. 3. It may sometimes happen the Aequinoxes Not only the▪ mean timex the Aequinoes, Solstices, and Coniun­ctions of the Luminarier, but also the true, is neces­sary to be known by a Chronologer. Solstices, also the mean New and Full Moons may fall upon another Day, as the true may; but whereas to find. out the true Places of the Lumi­naries require a more prolix Calculation, let the Chronologer consult the Astronomer: But whereas such Alteration seldom happens, he may, being not perfect in Astronomy, be con­tent with the Knowledge of the mean Motions.

§. 4. The Conjunction of the Planets, their Other Astro­nomical Cha­racters besides what are laid down, may be assigned. mutual Aspect, their Ingress into other Points of the Zodiack, besides the Cardinal ones, with other Characters yet less frequent, may be made use of in Chronological Concerns.

CHAP. II. Of the Hebdomatic or Weekly Character.

• 1. The Weekly Character is that whereby we distin­guish one Day of the Week from another.
• 2. The Week is a System of 7 Days continually re­curring; and to this end divin [...]ly ordained, That the Memory of the six Days Creation might be preserved, that the seventh might be k [...]pt holy, and that Man and Beast might rest.
• [Page 63]3. One Denomination of the Days of the Week: is vulgar, owing its Original to Gentilism, Another Chronological, repeating the Order of the Days in the Week.
• 4. In common Ʋse the Days of the Week are denominated from the Planets in this Order: The first from the Sun, the second from the Moon, the third from Mars, &c.
• 5. The Chronological Denomination of the Days of the Week is disposed in Order; as, the first Day is called Feria prima, the second, Feria secunda, &c.

§. 1. AT the Creation, the 7th Day was The Observa­tion of the 7th Day or the Hebdomatic Character was in use from the Creation of the World. sanctified; and from hence Men, to whom that Law was given, ought to continue it so, since that Sanction was made only ^(a) be­cause of Man; but upon the 7th Day of the Creation this Sanction was made; from thence there is derived the REmarkableness of this Character, add to this the Mention of the Sabbath in Scripture as a noted thing, even before the ^(b) Law was made; which without doubt, the Author of the Epistle to the (d) Heb. refers, asserting that eternal Rest which God had prepar'd for his Children; not on­ly by the Possession of the Holy Land, but also by that Sabbath which was prefigured from the Original of the World: Some also will refer to this that Passage of ^(d) Noah; who in the time of the Flood sent not out the Birds till after the 7th Day to try whether the Waters were abated; which Argument suffici­ently restrains and fixes the Sanction upon the 7th Day, as a positive and moral Duty upon Men, notwithstanding the Objections of (c) Chap. 6. 3. [Page 64] ^(e) some against it, who would have the Sab­bath take its Original from the raining of Man­na in the Wilderness.

§. 2. All Chronologers who admit the An­tiquity The Order of the (Feri [...]) or Days in the Week, has been preserv'd al­ways incor­rupt till our times. of the Hebdomatic Cycle, always look upon the Order of the Days of the Week to have been the same; so that to deny it, would be to call in doubt one of the first Principles in Chronology.

§. 3. ^(f) Some will have it, that the Roman Why all the Days in the Week are now called Feriae. Church, whom all Chronologers follow, called every Day in the Week Feria; Feria 1 ma, Feria 2 da, &c. because the old Ecclesiastical Year began from the Pasca, and the Pasca was called Annus novus, as now in the Church of Antioch; and for the same reason in that of Constantinople, [...]; but all the Days of the Pascal Week were called feriati, as St. Jerom [...] and other Ancients witness: And hence it obtain'd for the Days of the other Weeks to be called Feriae, in imitation of that. Some say, we follow the Custom of the Jews in this Reckoning; of which hereafter: But Tostatus, and after him, Corn [...]à Lapide, that the Church by the Institution of Pope Sylvester, called all the Days of the Week Feriae; First, because every Day in the Week ought to be a Holy-day to a Christian: Secondly, That so far as related to Ecclesiastic Offices; and the Ministers of the Church, those Days are really Feri [...] or Festa, Holidays; and every thing is to be rested from but Divine Worship.

§. 4. We cannot seek for the Derivation of this Word Sabbath among the Greeks, as Plu­tarch has done from [...], a Name of Revel­lers; nor among the Aegyptians à Sabbo, a Word [Page 65] signifying a Disease in the Groin; but 'tis de­rived from the Hebrew Word [...] which signifies Rest, as referred to the Institution of God, when after six Days Creation he rested upon the 7th. ^(g) Cornelius Tacitus being ignorant of this Jewish Custom, has invented several Fables about the Original of the Word; which may be perused by any one that thinks it worth his Pains.

§. 5. In times past they did not only call the 7th Day of the Week the Sabbath; but from What it is we ought to un­derstand a­bout the use and significa­tion [...]f the Word Sab­bath this very Day all the Days of the Week re­ceived their Denominations; as, our Sunday they called the one or first ^(h) Day after the Sabbath, our Monday the second Day after the Sabbath, Tuesday the third, and so on: that by the Word Sabbath they sometimes meant the whole Week, is evident from that Passage of the proud Pharisee ⁽ⁱ⁾ [...], I fast twice in the Week. On the contrary, for the Word Week the Ancients wou'd some­times use the Term Sabbath, as in this Passage; ^(k) [...] signifies no more than to keep the Sabbath.

§. 6. Amongst divers Opinions about it, that of What we are to understand of the Sabba­tum [...]. Scaliger seems to be most reasonable, and has been approved of by B. Schmidius, Langius, and others, viz. [...], Hebraicè [...] the first Sabbath after the second of the Days of unlea­vened Bread: Upon which there was Oblation of Fruits, and from whence seven Weeks ^(l) were reckoned till Pentecost: and therefore the Sabbaths betwixt the Pasca and Pentecost were thus named:

§. 7. After many other Fabulists, Menasseh Ben Of the Sabba­tic River which the Jews were w [...]nt to al­ledge in Testi­mony [...]f the Sabbath, which was sanctified by God. Israel ^(m) writes, that the Sabbatic River is a Testimony of the Sabbath sanctified by God, where­of mention is made in the Babylonian and the Jewish Talmud: Rabat, Jalcut, and Josephus also an Historiographer of great Authority, makes mention of it as running through Phoenicia in Assyria; which after six Days of its own Accord stops its rapid Course, and afterwards runs after the same manner; and therefore it received the Name of the Sabbatic River, from its Rest on the seventh Day. Others ⁽ⁿ⁾ will have it, that this River is Gozen, over which the ten Tribes pass'd, and at the Coming of the Messiah they shall be freed from their Captivity; and according to the Ancient Wisemen ^(o) Isaiah speaks of the People beyond this River, which is commonly called Flumen Lapidum. But these are child­ish Fables of the Jews: For the above-men­tioned Josephus says, This River runs very swift on the Sabbath Day. These are Rivers that run only out of the Brains of the Rab­bi's, which are near a-kin to the Poets.

§. 8. ^(p) Not only among the Gentiles ac­customed What we ought to judge of the Numb. 7, which de­termines the Cycle of the Feriae. to Superstition, was the Number 7 had in great repute, but also amongst the Chri­stians many wonderful things are spoken of the mysterious Character 7. Nor has Augu­stine ^(q) escaped the Prejudice, who makes 7 of 3 and 4 a very perfect Number. The firstof these (viz. 3.) says he, is wholly odd, and denotes Ex­cellency; the other is perfectly equal, and denotes the Mother of Justice, Equability and a sacred A­greement in things. This Number 7 is also assum'd into the most sacred Mysteries, is concerned in the Formation of Corporeal Things, and appears a Symbol of Perfection. Others, as Philo, Robertus Pontanus, &c. reckon up those things wherein the Number 7 is concerned; as almost all Sacrifices were offered by sevens, as 7 Bul­locks, 7 Rams, which always was observed by that mercenary ^(r) Prophet Balaam. Nor do we want Examples of it among the Gentiles, as in that Passage of the Poet;

And those who reckon up the Mysteries of the Number 7, tell us, that the chief Feasts of the Jews were reckoned to 7 Months of the Year, and continued 7 Days, in the Pasca they the unleavened Bread 7 days and then they reckoned 7 Weeks to the Pentecost; many joyful Days were celebrated in the 7th Month. Wisdom built her House upon 7 Pillars: In the Lamp of the Sanctuary there were 7 Candles: St. John in the Revelations saw 7 Golden Candlesticks; and in Zachary a Stone had 7 Eyes: In the New Testa­ment [Page 68] there were 7 Deacons chosen; and through the whole Apocalypse of St. John the different State of the Church is described by the Number 7: Christ commands him to write to the 7 Churches of Asia, and their 7 Angels: The mystical Book was sealed with 7 Seals: 7 Angels with 7 Trumpets and 7 Vials represented the State of the Church in the last Days. They yet add to these in Na­tural things, that there are 7 Planets, 7 fixed Stars called the Pleiades, the 7 Hyades; and both the Bears are figured with 7 Stars. There are 7 habitable Climates in the Earth: The Structure of the Humane Body is 7 Feet: And innumerable other things are wont to be alledged by ^(ſ) those who seek Mysteries in the Number 7.

§. 9. In Section the 3d and 4th of this Chap­ter The naming of Days in Weeks is not the same now among the Jews and Christians as it was at first. we have given an Account of the Denomi­nation of the Days in the Week among the Jews; and in §. 3d. Ch. 2d. of the account­ing by Feriae, among the Romans and Eastern Christians: But now we all use the Names of the Planets in the Days of the Week.

§. 10. The Order of the Planets, if you The reason why the same order of the Planets in naming the Days of the Week was not observed a­mong the An­cients. consider their Spheres or Orbs, is express'd by this memorable Versicle:

Post SIMSƲM sequitur, ultima LƲNA subest.

But there's nothing attended to less than this in the Names of the Days of the Week. Dio ^(t) Cassius gives us the reason and Original of this, which, he that pleases may read at length, and understand upon what Grounds they [Page 69] first fixed the Musick of the 7 Spheres, and how they would have the Days of the Week concerned in it. The Custom of the Egypti­ans in these musical Proportions (tho' known every where) was formerly unknown to the Ancient Greeks; therefore each had their distinct Way.

§. 10. In ancient times the 7th Day of the Of thrse Days of the Week which among divers People have been kept holy. Week was kept holy; which Custom owing its Original to the Divine Institution, the Jews at this time observe; but the Christians have receded from it, distinguishing themselves in this matter from the Jews, consecrating the first Day of the Week to Divine Worship; And Examples of this Worship seem to be fetch'd even from the time of the ^(u) Apo­stles. Certainly, except Christians could al­ledge Apostolick Tradition, they would scarce with so much Religion and Constancy have observed the first Feria or Sunday: That Melito a Cotemporary of Justin would have wrote a whole Book upon that Matter; that whole Companies of the Faithful would have incurr'd the Su [...]picion of the Idolatrous Worship on Sun­day; that they would even with their Blood ^(w) testifie their Sanction of that Day: For the Martyrs being asked, ^(x) Hast thou kept the Lord's-day? answered, I am a Christian and can­not pass it by. The Africans in Guinea observe Wednesday, which they call Dio Fetissos, and ab­stain from their accustomed Labours on that Day. The Turks every Year observe Friday, either from the Command of Mahomet, or from an ancient idolatrous Custom brought from the Indians to the Arabians; on which those Worship their chief Deity, called [Page 70] Venerem CHOBAR, of which Worship Jerome takes notice in the Life of Hilarius, in these Words; He came to Elusa, says he, by chance on that Day, where the Anniversary had occasioned a Concourse of the People of the Town in the Temple of Venus: For they worship her before Lucifer; to whose Worship the whole Nation of Saracens is devoted.

§. 11. A Common Year, for Example, being The Reason why all Julian Years begin not on the same Day. ended, which begins upon one Day, the second Year begins not upon the same, but the next Day after: And if that should happen to be a Bissextile, the second Year would have begun on the third Day after; the reason of which from the Quantity of our Year is evident: For the Common Year having 365 Days in it, or 52 Weeks and one Day over, and the Bissextile 2 Days over and above the 52 Weeks, divide either 365 or 366 by 7, (the Days in one Week: so that if the Year begins on a Monday, the last Day in the Year will be on a Monday, and then the first Day of the next Year must be Tuesday.

§. 12. Whoever will give himself the Trou­ble What 'tis we understand by Roman Nundinae. of inspecting fully into this matter, may peruse ^(y) Macrob. which in short is this; That upon the 8th Day, (not the 7th) they met in the Fields to sacrifice for the Dead, and con­sult the Country-Affairs, and promulgate Laws that were establish'd; and afterwards upon the ninth Day they consulted about Trade and City-Affairs; and these Concourses of People were called Nundinae: Some say they were instituted by Romulus: Others by Servius Tullius.

§. 13. Among other Praises of Constantine the Of the time the Roman Nundinae were abroga­ted, and the Feriae primae substituted in their room. Great, this is not the least: That on the Lord's Days or Sundays, he commanded the Gentile Legions to pray: For thus ^(z) Eusebius; When he had taught all his Soldiers to sanctifie this Day of Salvation, which we call the Day of Light or Sunday, he gave leisure to those, who by Divine Instinct, believed that they should freely frequent the Church of God, and pray unto him without Molestation: And others, who had not yet been sensible of the Divine Doctrine, he commanded by another Law, That on Sundays they should go out into the Fields of the Suburbs, and there use all together the same Form of Pray­er upon a Signal given.

CHAP. III. Of the lesser Sacred Annual Character or the Sabbatic Cycle.

1. The Sabbatic Cycle is a System of 7 Lunae-solar Years continually recurring, instituted by God for this reason, That the Earth and Men might have their Vicissitudes.

§. 1. THE Sabbatic Years are of Divine In­stitution, as may be seen at large Lev. 25. 2. where the Earth and the Vines were to be plough'd and gathered for 6 Years, and the 7th Year to rest and not be cultivated. See also Exod. 23. 11. The beginning of the Sab­batic Cycle was the 7th inclusive from the [Page 72] time, when the Division of the Land (into which the Israelites were then about to en­ter) was to be made by ^(a) Lot. If this be observed, all the Sabbatic Years will doubtless be rightly fixed, and no Errors about it can happen; if not, we have no certain Character can be assigned us to proceed upon.

§. 2. Calvisius, ^(b) when other Authors disa­gree Of those Years that are cer­tainly Sabba­tic. among themselves, has fixt these. The 15th Year of the Reign of Hezekiah ^(c) King of Juda, was Sabbatic: The Year in which Antiochus Eupater ^(d) besieged Jerusalem, was Sabbatic: The Year in which Simon Maccabae­us was slain by ^(e) Ptolemy was Sabbatic: The Year of the Captivity of Jerusalem by Herod ^(f) was Sabbatic: The Year before the De­struction of Jerusalem ^(g) by Titus Vespasian, was Sabbatic: The Year of Christ, 1189 was ^(h) Sabbatic: The Year of Christ 1602 was ⁽ⁱ⁾ Sabbatic. Besides these of Calvisius, others might doubtless be fixt.

§. 3. There are ^(k) some who tell us, that the Their Opinion must be false w [...] assert that by the Divine Command the Sabbatic Cy­cle was in use among the Jews before the distr [...]b [...]ti­on of t [...]eir Land by Lot. first Sabbatic Year of the Law was that in which the Israelites being brought by Moses to the Borders of Jewry and Land of Canaan, a little after the Death of Moses began to enter and possess it under their Captain Joshua: So that they will have this Cycle to begin 7 before what is assigned by Scaliger, Calvisius, and be­fore these Eusebius. But this agrees not with the Divine Precept: For the Jews at that time did not enter into the Land of Canaan; For altho' the Tribes of Rei [...]ben, Gad, and ½ of Menas­ses received the Kingdom of Sihon and Bashan [Page 73] from Moses; yet it was not to these only, but the whole People that the Divine Command was given: Nor was the Land on this side Jordan properly called ^(l) Canaan: Nor did the Tribes inhabit it to whom it was assigned: For these ought, with the rest of the ^(m) Tribes, to pass over Jordan, from whence, after many Years they ⁽ⁿ⁾ returned again. Add to these things, That Moses in Deuteronomy, which Book he proposed to the People only one ^(o) Month, before his Death speaks of the Land of Pro­mise, not as yet possest, but to be possest. Deut. 6. 10. But when the Lord thy God shall bring thee into the Land, &c. Therefore it can't be said Israel was entred into the Promised Land, to wit, Canaan, before the Death of Moses.

§. 4. Although by what precedes, it is cer­tain Whether we are to think that the Sab­batic Cycle was analo­gous to the Hebdomadic, and conse­quently whe­ther it can be of the same use in deter­mining the first Year of the World. that the Historical Beginning of the Sabba­tic Cycle is to be derived from the Distribution of the Land by Lot, yet we shall not reject their Opinion, who think that God in ordaining this Cycle had respect to the Sabbath of Days; and that therefore the first Day of the World was also the first in the Sabbatic Year; as the first Day of Creation was the first in the Heb­domadic Cycle. For this Opinion seems not improbable, when the Reason of this Cycle was not less universal than that of the Diurnal Hebdomadic Cycle. Therefore the Opinion of Rob. Pontanus Cáledonius a Britain, does not displease us, when he asserts as much, saying, ^(p) That the Reason of this sacred Observation preceeding by sevens, has its Foundation in the Law of Nature, as the Example of God himself, [Page 74] which precedes all Laws, from whence we may fairly gather, that this Reason of reckoning by Sabbaths has respect to the Original of the Word, and by a continual Series to be deduced from the first Sabbath: That as God himself rested from the Work of Creation on the 7th Day, so those Years of Rest, (Sabbaths and Jubile's) came from the same exemplary Principle.

§. 5. Some of the Jewish ^(q) Rabbi's seem to The Sabbatic Cycle is a Cha­racter of cer­tain and indu­bitable credit in respect of Time. derogate from the Certainty of this Character when they tell us, The Israelites had reckoned 17 Jubile's from the time they went into the Land of Canaan, till the time they went out of it again. And the Year in which they went out, when the first Temple was destroyed, was at the end of a seventh Year, and the 36th of a Jubile. For the first Tem­ple stood 410 Years; and after it was destroyed, this Computation was also lost and abolished; from thence the Land lay desart 70 Years, and the 2 d Tem­ple was built, which stood 420 Years: And in the 7th, after it was rebuilt, Esdras returned and re­stored this Aera the 2 d time: And from that Year they began to reckon another Aera, and made the 3 d Year of the 2 d Temple Sabbatic: And they reckoned 7 Sabbatisms, and consecrated the 50th Year, altho' it was not Jubile, yet they reckoned under the 2 d Tem­ple, so as that they did consecrate Sabbatisms. Dionysius Petavius also follows Maimonides, and is also of this Opinion ^(r). But as the Igno­rance of the Jews in Chronological Affairs is very notorious, so there's nothing at all in this Discourse of Maimonides which would shake our Opinion, that is not apparently false; and argues the Author much mistaken about the Computa­tion of Esdras, at the end of 70 Years Restau­ration. For Calvisius most truly ^(ſ) says, For [Page 75] who could suspect that the Jews in a Babylonian Captivity of 70 Years, could forget their Sab­batic Years, and afterwards institute others, which should not be the same in order as those before the Captivity? why should not the Jews as well have forgot their Sabbath Day, and afterwards also institute another? But this is impossible; for God, the Preserver of his own Institutions and Creatures would not have suf­fered such Set-times to have been disturbed from the Creation of the World: So that the true Sabbatic Years were not changed, but truly restored after the Babylonish Captivity: For the Jews in that Captivity had Fields, ^(t) planted Vineyards, mow'd and gather'd Grapes: So that they were busied in those very things as were most proper to put 'em in mind of their Sabbatic Years. Nor did their Exile endure beyond the Memory of any that were then alive. At this Day, where-ever they are dispersed, they truly know and reckon up their Sabbatic Years. How then could these forget them, who had ce­lebrated the Sabbatic Years in Judea, and were returned back again into Judea to celebrate them after their Captivity? But admitting they had forgot 'em, yet after their Return they would have learn'd 'em again of the Samaritans, who celebrated the Sabbatic Years with the Jews before the Captivity, and had constantly retain'd 'em all that time; for they were near Neighbours; the distance betwixt Jerusalem and Samaria being not above 6 German Miles; and the Nation of the Jews was very superstiti­ous and tenacious of their Ceremonies, as is well known. 'Tis therefore a vain thing for any one to suspect a Change in the Sabbatic Years.

§. 6. A certain Author ^(u) does not only con­jecture, Whether the Sabbatic and Jubilean Tears never had, nor could have any o­ther Form than such a mystical one wherein 343 Days are rec­koned for a Tear. but promises a Demonstration of the Affirmative; but we deny both, and our Rea­sons are, 1. Because from the Author's own Confession, neither the Scripture, nor any other, ancienter Book makes mention of such a mystic Year. 2. Because the six Years of Agricul­ture have without doubt sometimes coincided with the Solar Year: For otherwise the times of Sowing and Harvest would have been un­certain. 3. Because the ^(w) Scripture attributes to the Jubilean and Sabbatic Years a fixt Be­ginning and State. Thou shalt reckon (says God) seven Weeks of Years, &c. Then thou shalt cause the Trumpet to sound every where on the 7th Month, on the 10th day of the same Month, the Day of Expiations, ye shall cause the Trumpet to be sounded throughout the whole Land. From which Words Interpreters have hitherto inferr'd, that the Jews ought to begin the Jubilean Years from the same 10th day of the Month Tisri; whereas 'tis immediately added, That ye may sanctifie the 50th Year. And although the Au­thor of Mystical Computation (of whom we shall speak in the next Section) hath sought a Solution in the Ambiguity of the Word [...] as a Proclamation, or a Command of the Solem­nity of the Jubilean Year; indeed it was join­ed to a certain Day of the Civil Calendar, whereas the Jubilean Year, without any Rela­tion to this Command, took its Original else­where. . . . . How ill it becomes a Learned Man to trifle in a serious Affair: For who knows not that a better Account may be given of the Beginning, than of the Proclamation of the Jubilean Years? who is ignorant of [Page 77] the Emphasis of the Word [...]? Or who shall perswade himself that a Year should be sanctifi­ed amongst the Jews some Months before it be­gan? Maimonides speaks much juster ^(x) on this Subject. From the beginning of the Year, to the Day of Expiations, the Servants were neither dismiss'd, nor did they serve their Masters, nor were the Fields restored. What then? They did eat, drink, and were merry; and every one put a Crown upon his Head: But as soon as the Day of Expia­tions was come, the Senators of the Sanhedrin sounded Trumpets, and sent away their Servants free; Fields were then also restored. 4. From that mystic Form which is against the Laws of Syde­real Years, it would follow, that it might be possible that the Product of one should main­tain the Jews for three Years together (against Lev. 25. 21. & sequ. For although mention is there made of three Years; yet by no means were they compleat and separately reckoned, as is evident from the Place just mentioned: On the contrary, 'tis evident that this Hypo­thesis brings in a new Method destitute of all Probability. For if (for Example) the Begin­ning of the Sabbatic Year should fall upon the Vernal Month Nisan; which would sometimes happen, the Jews could not gather the Fruits, because of the Religion of the Year; and consequently on the preceding Year they would hardly have given themselves the trouble of Sowing; but neither was it lawful to sow about Tisri the Autumnal Month of the same Year: Therefore they could not mow about Nisan the Year following. It was therefore necessary for 'em to wait till they could have the Harvest of the 3d Year.—

§. 7. The Absurdity of that Opinion is The Mystic Sabbatic Cycle hence evident: For admitting it, the Sabbatic Years would undoubtedly be wholly deprived of their best Character when amongst the Sab­batic Years, from the faithful Tradition of Hi­storians, the intercepted time divisible into ali­quot Parts should not always be 2401 Days, or the Quantity of a mystic Sabbatic Cycle.

§. 8. The Author of ^(y) the mystic Chrono­logy The manner how the Au­thor of mystic Chronology would prove his Opinion about the Sab­batic and Ju­bilean Years. premises some Hypotheses, which, he says are founded in Scripture, and which are grant­ed by all that allow of the Old Testament, whether Christians, Jews, or Turks.

• 1. That God made the World in six Days.
• 2. That on the 7th he rested from the Work of the Creation.
• 3. That any 7th from this, and consequently all the Multiples of 7 following one another in Arithmetic Progression (as 7. 14. 21. 28, &c.) were made Sabbaths or destin'd for Rest, in Memory of the preceding six Days Creation, and resting on the 7th.
• 4. Therefore if from any Sabbath we go backwards by the spaces of 7 Days, or the In­terval of a Week, we shall at last come to that Day of Divine Rest.
• 5. And this is an inseparable Property, re­sulting from the Institution it self, and the Divine Fact, viz. That it should be a Multiple of the Time, and calls back into our Memory, and points at the Divine Rest, and the very indi­vidual Day thereof.
• 6. That God instituted a Sabbatic Year as w [...]ll as a 7th Day, in memory of his Rest, in which he also would have the same ^(z) Arith­metic Progression.
• [Page 79]7. That in the Sabbatic Years he would have observed and commanded the Observation not only of an ^(a) Arithmetic Progression, but also a Geometric one, viz. the Square of the Sabbatic Year, or 7 7▪49 Years he instituted for the Jubile.
• 8. The Sabbatic Year ought to be neither greater nor less than the time of Labour and (a) Fruits or Culture of the Earth which in this Year God would have omitted.
• 9. That time must be greater than 49, and less than 366 Days.
• 10. That there is no Number betwixt 49 and 366, by which we can return back again to the Root 7, unless 343, viz. the Cube of 7.

From these Hypotheses he says, follows this Apogogic Syllogism. Every memorial time of Divine Rest taken from the 7th Day of Crea­tion, ought to be multiple of the Num­ber 7, and by a given Regression, viz. both A­rithmetic and Geometric in a given Proportion, viz. Septuple, to point out the first of the Divine Rest, or the Individual 7th of the Crea­tion:

But the Mosaic, Sabbatic and Jubilean Years are a memorial time of Divine Rest begun on the 7th Day of the Creation:

Ergo, &c.

And hence further he adds an Epistomonic Syllogism, as he calls it. Whatever Years ought to be multiple of the 7th Day of Crea­tion, and shew the same by a regression as well Arithmetic as Geometric, must consist of some Number betwixt 49 and 366; between which 'tis impossible they should be either more or less than 343:

But the Sabbatic and Jubilean Years ought to be multiple of the 7th Day of Creation, and shew it by a Progression as well Arithmetic as Geometric; and to consist of a Number betwixt 49 and 366: Therefore 'tis impossible that the Sabbatic and Jubilean Years should have either more or fewer Days than 343. 10. 10, &c.

This is the Basis of this mystic Computation; but which is built upon the Sand: For first of all our Mysteriographer puts us in mind of a strange Agreement betwixt Christians, Jews and Turks, in their admitting of the Old Testament. But how great soever the Agreement of the two former be, that of the Turks is a Dream of the Author. Indeed we know the ^(b) Turks value the Law of Moses, believe that Christ is the Son of Mary, the Spirit of God, his Word and his Apo­stle, but only in such a sense as Mahomet has left them. The Turks tell us of many things depraved in the old, many things omitted, and many added: Nor do they acknowledge the History of the Creation or the first Week from the Mosaic Writings, as the Christians and Jews do; but are wont to report many Fables of them, which that Impostor invented; as when God made Adam, the Throne of God, Paradise, &c. he held in his Hand a Pen [...]00 Miles long, and 80 broad. Besides, the Turks keep not the 7th but the 6th Day of the Week holy, con­trary to Moses. So little occasion has our Au­thor from the Agreement of the Turks for the Foundation of any of their Hypotheses; nor according to the sense of his 5th Hypothesis will meet with great Agreement betwixt the Christi­ans and Jews. The Times of our Saviour's Nativity, his Circumcision, of the Eremetic [Page 81] Fast, &c. are Memorials of those things which hapned long since; though no one ever yet of any mystic Multiples. Further, the 6th, 8th, and 9th Hypotheses are no where extant in the Old Testament; nor are they received by any Christians, if you except our ^(c) Author and his Disciples; nor are they granted by the Jews (not to mention the Turks.) God had no respect to the first Sabbath in constituting this System of Years; that from the 7th Day of the Creation the Quantity of the Year should be deduced by an Arithmetic and Geometric Progression; there are no Footsteps of it in that place our Author has cited in Leviticus. But the rest are evident. So very false do we find our Author's Philoso­phy, when we consider the ^(d) Amplitude of of the Divine Promises. In short, the Author of this mystic Computation has acted ignorant­ly, when he makes one of his Limits a System of 366 Days, when the Jews knew nothing of it, their Annus Communis being 354 Days, their Annus Embolimaeus 384, and the Mean 367. Having shewed the Falsity of these Hypo­theses, we easiy see what Answer ought to be given to the Discoverer of such Paralogisms, in which there is not the least Probability.

§. 8. Although the Divine Wisdom is inscru­table, Of the chief Reasons why the Sabbatic Cycle was in­stituted. yet we ought not to reject their pious O­pinions, who observe these as Reasons of such a Divine Institution. ^(f) 1. God. 2. the Earth. 3. the Poor. 4. Strangers. 5. Brutes. 6. Servants. 7. Debtors. 8. all the Israelit [...]s promiscuously.

§. 9. 'Tis the allowed Opinion of ^(e) Alphons. In the 7th Year the First-Fruits were consecrated to God, and the Ty [...]hes to the Priests. Abulensis Episcopus, That the Oblation of First-Fruits did not cease; because though the Fruits [Page 82] were not gathered in for the use of their Ma­sters as being common for any one, yet the Right of their Fields did belong to them, or the Privilege, or Excellency, as some say, before all others. So that it's probable they might gather the First-Fruits, and offer some part to the Priests. But as to the Tenths, the Priests had nothing to complain of, if in that Year wherein the Fruits were not gathered (that they might be preserved for their Masters Use) they did not receive the Tenths. 1. Because in that Year wherein God did bestow as much as was necessary, for three Years, the Tenths of the Priests were multiplied. 2. Because it was free for them in common with poor Persons and Strangers, to enjoy the Benefit of such gather­ing, provided they laid 'em not up in Barns or Granaries.

§. 9. So long as the Jews lived in obedience to Of the Streights that every [...] year reduced the Jews to. the Law, they wanted not abundance of En­crease: but when they began to rebel and grow stubborn, they sufficiently experienc'd what things God had forbidden the Transgressors of his Laws. For when their Conquerors impos'd Tributes upon them they could not discharge 'em on the 7th Year. Josephus often mentions this Calamity, and his Relation about Alexander the Macedonian, sufficiently proves it: For when at Jerusalem he had learnt, that a Graecian should have the Government of the Persians, glad of the Prophecy, as to be fulfilled in him, he bid the Jews ask some great thing of him; to whom they answered, he could give nothing greater than a Relaxation of the Tributes for the 7th Year; and that was their ^(g) Request.

CHAP. IV. Of the greater sacred Annual Character, or the Jubilean Cycle.

1. The Jubilean Cycle is a System of 7 Sabbatic Cycles, or 49 Lunae-Solar Years continually re­curring; and for this end divinely instituted, that in the Judaic Republic, the Wealth of a jew should not oppress the rest; but that the Good of the Tribes should always be immovable; as also that the Years of Servitude might cease.

§. 1. THE Word Jubile is not à Jubilo, as those Why this Cycle and first of all its last year should be cal­led a Jubile. little read in Hebrew suppose; nor from the rustic Inclamation of the Greeks, [...]; but either from [...] which Word signifies a Ram, because this Solennity was promulgated with a (h) Ram's Horn; or else from [...] which Root signifies a bringing back; and that, as Serarius notes upon Joshua, with a certain sin­gular Emphasis of Joy and Mirth.

§. 1. ^(b) Torniellus supposes it probable that Whether we have yet any Footsteps of the Observati­on of the Ju­bl [...]ean Year. the Jews never observed any Jubilean Year be­fore the Babylonian Captivity. But we dare not assert so much; whereas not only in the time of Joshua, but the pious Kings, as David, Joshaphat, and others, its very probable they would have some respect to the Reason of such a Divine Institution. In the 2d Kings ^(c) the Jubilean Year seems to be described, when K. Joram graciously gave the Shunamitish Woman (a) Josh 6. 5. [Page 84] those Privileges that were proper to a Jubilean Year; and yet the Circumstances of History seem to render this Opinion suspected: For Joram lived about the Year 3053, and in 3061 was killed by Jehu, in which 8 Years no Jubi­le could happen. Perhaps that in Ezech. 29. 17, more probably refers to a Jubile, where he makes mention of a 27th Year: For I cannot see how that can relate to any other Epccha at this time known; Of which more here­after.

§. 3. Whereas 'tis very certain we have not The Jubilean Cycle consisted of 49 Years so many Jubilean as Sabbatic Years: And therefore from the latter we can scarce judge of the Jubilean Cycle. From hence it happens that Chronologers so little agree about the Quantity of this Cycle, but dispute with the greatest Heats of these Darknesses of the ancient Laws. Of the five Opinions about this matter, the first is, That the Jubilean Cycle consisted of 50 ^(d) Years; the second is that of the famous William Langius, who ^(e) contends that the Jubilean Year depended upon the Sabbatic ones yet so, that after the Expiration of [...]7 annual Sabbatic Years the same was one with the 50th: so that the Jubilean Year was always the first in the Annual 7: The third is the O­pinion of our Mystic Chronologer, who makes the Jubilean Cycle to be of 45 Julian Years and 271 Days over: The fourth Opinion is theirs ^(f), who assert the Jubilean Year was the same with 7 times the 7th Year, or 7 times the Sabbatic Year, and so the Jubilean Cycle pre­cisely made 49 Years: The fifth Opinion is on­ly [Page 85] proposed as probable by the same Cloppen­burgius ^(g); where he supposes impossible for the Jews to mix their Computation, and reckon both by 49 and 50 Years, which he supposes very easie for 'em to do, the great Period of Jubilean Years being admitted, which is made by multiplying 49 into 50, whose Product makes that Period 2450. We assent to their O­pinion who assert the Jubilean Cycle to consist of 49 Lunae-Solar Years: For besides that; the Sabbatic Year had many Privileges in com­mon with the Jubilean Year, which is inferr'd from the Biblic Style, the Consent of the Jews, and Rabbi Adda's Calendar, it would follow also that if the Jubilean Year was different from the Sabbatic; the Earth would rest for two whole Years and the Jews must sustain them­selves with the Produce of one Year for four Years together, which seems wholly repugnant to the Sense of the Divine Command: Nor does it hinder that the same Jubilean Year in the Mosaic Text is sometimes called the Quinqua­gesimus, whereas that is not to be otherwise un­derstood than as Pindar called the Olympiad, [...], and as we are wont to call the 7th Day the 8th. Of those Cha­racters which the Popes In­stituted for their Jubilean Years.

§. 4. The Roman Pontiffs, after the manner of Apes, have endeavoured to imitate the In­stitution of God in their Jubilean Institutions; but divers of 'em after different manners. The first Author of a Jubilean Year was Boniface the 8th, whose Encomium Platina ^(h) gives: He ordained that every 100 Years the Treasury of Indulgences should be open'd; but the Publication of a peculiar Bull which is ⁽ⁱ⁾ ex­tant, and which instituted the 1300th Year to [Page 86] be Jubilean. But Clemens the sixth, (this pre­carious Institution of Boniface, since the Age of Man not extending to 100 Years, might see no Jubile) made every 50th Year Jubilean; to which end he gave notice in the Year 1345 that the following 1350 should be a Jubile. This Bull is extant in the Book last cited in the Chapter of Ʋnigenitus, in that Year, as Petrar­cha witnesses, there was such a Concourse of People at Rome, that it was no wonder if from such a defiled Air a most grievous Plague arose, which so exhausted all Italy, that there were scarce Ten Thousand left alive. But Ʋrban the sixth corrected this Institution, transferring the Jubile from the 50th Year to the 33d; and he appointed that the Year 1390 should be Jubile: And afterwards be continued every 33 Years; whereof he saw not the first, but died in 1389: yet Boniface the ninth celebrated the Jubile which was forbidden by Ʋrban the sixth; yet so as that in the Year 1400 he again forbad the Jubile; as ^(k) Onuphrius witnesses. Lastly, when the Romans perceived that these Jubi­lean Concourses were advantageous to them, Paul the second reduced the time of the Ju­bile to 25 Years, the Sanction whereof his Successor Sextus the fourth confirmed by a peculiar Bull in the Year 1473, which is extant in the same Book c. Quemadmodum. And by that it was ordained, that in the Year 1475 the Jubile was celebrated, and every 25th Year following. But of these Annual Jubilean So­lennities, and their Privileges (which are In­dulgences) and of which you may read more largely in their Bulls above-cited, this is not the least Solennity, viz. At that time the Pope [Page 87] opens (as they call it) a golden Gate, to which an infinite Concourse of Men approach for ob­taining the Remission of their Sins; then he strikes the Gate with a little golden Mallet, which afterwards, as a Token of Honour, he gives to somebody; then the Workmen break the Gate with Bars, and the People who force in, scramble for the Ruins of it among the Dirt▪ and under the Feet of one another.

CHAP. V. Of the Solar Cycle.

1. The Solar Cycle is a certain System of Time, consisting of 28 Years, or 7 Julian Lustra's, which being elapsed, the same Order of Bissextiles or Dominical Leters, return again, according to the old Method.

§. 1. THE Solar Cycle is call'd a Period of 28 The Reason why the Solar Cycle is called a Period of 28 Years. Years; not because it shews the Moti­on of the Sun, but because by its help we know the Dominical Letter or the Character of Sunday; and hence it appears, that this Appel­lation is Metonymical, not proper; altho' the Cycle, if it be wholly considered, does retain the Characters of each of the 28 Years, and the Denomination of the whole from the Number of the Cycle sought. Why the An­cients made the Period of Biss [...]xtiles▪ [...] Dominical Letters to consist of 28 Years.

§. 2. The Reason is, because neither sooner nor later than after 28 Years, all the Varieties return again which arise from the Changes of the Dominical Letter and Bissextile: For if in the Nabonassarean Year there had been no Bis­sextile (l) Vide Polyd. Virg. de invent. rerum, c. 8. [Page 88] the Cycle of 7 Years would have suf­ficed, because when on the same Day that a common Year ended, upon which it began, the following year would also begin on the following Day, &c. But the Bissextile Year renders this Affair more difficult: So that a Cycle of 7 Years will not be sufficient, because the last Day in the Year is not the same on which it be­gan, but the following: so that in the space of 7 Years all the Variety cannot recurr as before, but there must be the Number of Years for a Bissextile, viz. 4. and the Number of Days in a Week, viz. 7. that are concerned, which mul­tiplied, make 47 = 28 the Solar Cycle. Vide Monach. Method. cap. 3.

§. 3. The time of this Institution is not cer­tain. Of the time of the Institu­tion of this Cy [...]le. ^(a) Scaliger deduces it from the Year of Christ 328, when the Nicene Council was dis­solved. From which Dionysius ^(b) Petavius blames Scaliger, as his way is; saying, Scaliger only guesses it, and derives a false Opinion of it, in thinking that the Nicene Council con­tinued till that time. In like manner ^(c) Lan­gius thinks the Solar Cycle was owing to the fourth Year after the Nicene Council, but with no greater Certainty than Scaliger had proposed his Opinion before him. We cannot from any ancient Books find any Cer­tainty about it.

§. 4. It shews the initial Day of every Of the Ʋse of the Solar Cy­cle. Year in the Julian Account, and conse­quently it directs us to the Weekly Cha­racters of the other Days, the Dominical Let­ter, and the Quantity of the Year.

§. 5. This varies according to the diversity Of the Dispo­sition of the Domi [...]c [...]l L [...]tt [...]s [...]nd the [...]tial in the Solar Cycle. of the Julian and Gregorian Calendar. For the Julian the following Table will serve for ever.

But in respect of the Gregorian Calendar, the last Table fails; and for the present Age that which follows will serve.

§. 6. There are not now eight Letters as Of the Order how the Cha­racteristic Let­ters of the Days in the Week are pla­ced. were in the old Julian Calendar, but only 7; and they are placed in a retrograde Order, as is evident from the preceding Tables: Whence also Beda exprest the Order of the Dominical Letters in this Versicle:

Grandia, Frendet Equus, Dum Cernit Belli­ger Arma.

§. 7. If we consider the Constitution of the Of what would be desi­rable in the ancient dispo­sition of the Solar Cycle. Civil Year, th [...] Cycle is convenient enough; but it answers less accurately to the Reason of the Solar Year; because it supposes that every Year is 365 Days and 6 Hours; whereas there are 11 Minutes wanting of that time.

CHAP. VI. Of the Lunar Cycle.

1. The Lunar Cycle or Golden Number, consisting of 19 Lunae-Solar Years, whereof 12 are of 30 Days, 7 of 28 Days to the Month, as a System of Julian Solar Years; which being elapsed, the mean New Moons are supposed to return up­on the same Days.

§. 1. BEcause the Greeks were taught by their Ora­cles, Of the Num­ber of Years. that are re­quired for the Sun and Moon to coin­cide again. that their accustomed Sacrifices were to be offered [...], which they interpreted of the Years of the Sun, of their Days and Months, which they referr'd to the Moon; and were always sollicitous, how by certain Peri­ods and disagreeing Motions of the Luminaries they might reduce these to a Third something in which they might agree; Hence in the anci­ent times they are said to have used a Biennium, intercalating every other Year: But Fault was found with this, and 'twas succeeded by a Quadrennium; upon whose Returns the Olym­pic Games were celebrated. After this came the Octennium, of which mention is made in rehearsing the times of ^(a) Cadmus. [...], &c. But Cadmus sewed Mars every Year for those whom he slew: But that Year was then the space of 8 Years. ^(b) Hyppolitus, Cleostratus, Tenedus, [Page 92] Harpalus, and others of the Ancients seem to have interpolated this Period of Years. Next come the Duodennium, which seems to have been observed by the Learned only, and may be gather'd from Censorinus c. 18. The next was the Dodecaeteris, consisting of 12 Years. To this Chaldaic Year there is a Name, which those that deal in Nativities accommodate not to the Course of the Sun or Moon, but other Obser­vations: Because then, say they, Tempests, the good Success of Fruits, Barrenness, and Diseases hapned. But amongst all the Cycles of the Ancients, there's none more famous than [...] of Meto the Athenian, which is used to be called The great Year of Meto, although it's uncertain whether Meto was the first Author of this Cycle; tho' Livius seems to attri­bute this Invention to Numa Pompilius, and Geminus to Euctemonus and Philippus. This is certain, that this Cycle consisting of 19 Years comprehends 6946 Days, or 19 Solar Years, and almost so many Lunar years, in which they inter­polated 7 times in this Order, according to Diony­sius Petavius, 3, 6, 8, 11, 14, 17, 19. But in the Course of this time Meto, or whoever was the Author of this Cycle, thought that 235 Luna­tions would be exactly compleated, a hundred and ten New, and a hundred and twenty five Full Moons, making nineteen Solar Years; afterwards Calippus attempted to correct this Period by conjoining four Metonic Cycles, and giving to them 22759 Days, taking away one Day in the space of 76 Years. And yet Calippus found many other Censors and Cor­rectors, as Democritus, Hipparchus, Ptolemy, and others: All which did not wholly re­ject, but only interpolated the Metonic Cycle.

§. 2. All this was done at first that the Pasca Why not only Greek Inso­dels, but also Christians at the beginning of the N. Te­stament were so sollicitons of the Harmeny of the Lunae-So­lar Motions. might be rightly observed, and that in one Night the Sacrifice of Prayer might every where be offered for the Resurrection of the Lord; for 'tis certain in rightly celebrating the Pasca, they had respect in the force of the Divine Institution, both to the Reason of the Sun and Moon, though they a little mi­stook themselves; because they thought the Julian Year and Solar Tropic did agree well to­gether.

§. 3. In ancient times the Asiatic Christians Of the chief Disagreement of the Anci­ents in the Command of the Pascal Solennity, and for what rea­son the Lunar Cycle was ob­served. did continually celebrate the Pasca upon the 14th Moon, or in the Full Moon, viz. at the same time with the Jews; and these alledged John the Evangelist, from whom they received this Custom. But the Eastern Christians never celebrated the Solennity of the Pasca, except upon the Lord's Day; nay, when they seemed to have this Solennity in common with the Jews, and they alledged for themselves the Cu­stom of St. Peter. The Montanists, receded from both, neglecting the Lunar Course; but looking only to the Solar, appointing the 9th Calendar of April to be the Vernal Aequinox, and the Pasca to be observed upon the 14th from this Day. Among the French Martinus Dumiensis and Beda relate that the Pasca was anciently observed the 25th of March, the Cu­stom of whom, when Cirvelius would again introduce, he was for that stigmatized for his Rashness by Mariana.

§. 4. And they kept not the Solennities of their Fasti as indifferent things; but against the Rule Of the great Esteem that Christians ad f [...]r these Con­troversi [...]s. of St. Paul, they condemned one another for neglecting the Punctilio's of time. Now Pius the first, and after him Eleutherius were taken up with this Affair; but above all the rest, Victor acted most violently, sending the Thun­der [Page 94] of his Anathema against the Greeks; but was successless, as many others of the Popes were. The venerable Session at Nicea at last by degrees asswaged his exasperated Disposition, as afterwards this Custom of the Western Christians obtained, according to Eusebius, Theo­doret, &c.

§. 5. ^(c) Anatolius upon Eusebius mentions, Of the time in which the Ʋse of the Lunar Cycle was known to Christians. that first of all in the time of the Nicene Council the Use of this Cycle had been known: and this appears from an Epistle of St. Ambrose, 'Tis not a mean part of Wisdom to define the Day of the pascal Solemn Assembly; both Di­vine Scripture instructs in it, and the Tradition of our Ancestors, who assembling at the Nicene Synod, amongst other things relating to Faith, did collect as well true as admirable Decrees; for in that memorable Assembly, several Persons skilful in Calculation, being gathered together, did as it were constitute a Circle of 19 Years, as an Example for following Generations. This Circle they called Enneadecaeterida. Let us fol­low that Example; not that we ought to doubt with any vain Opinion concerning so great an As­sembly; but true Reason being found in it, let the Affections of all so concur, that upon the same Night our Sacrifice may be offer'd for the Resur­rection of our Lord.

§. 6. Altho' we say that we have those things Whether the Christians received the Lunar Cycle from the Jews. which the Christians first invented from the Latter Jews, yet from the Scope which the first Authors of the Cycle intended, it seems appa­rent that they examined the secret Writings of the Jews, lest they should celebrate at the same time the Feast of the Pasca with Unbelievers: For suppose the ancient Lunar Cycle together with the Pascal Times were different from the [Page 95] Cycle of the Jews, certainly Christians, could not know by the Use of the same Cycle at what time the Jews would celebrate the Pasca, nor how they ought to refrain from the sacred Things of their Adversaries ^(d): Isaacus Argyrus con­firms my Opinion in this, that before the Pasca of the Christians the Judaic one was placed; which in the Holy, and first Oecumenic Synod, the Holy Fathers so constituted, that it might be observed in what Day of the Week the Pasca of the Jews fell, that on the following Lord's Day the Christians might perform theirs.

§. 7. Tho' the first Authors of the Lunar Cycle thought that 19 Lunae-Solar Years were equal to Whether or no the first Au­thors of the Lunar Cycle thought that 19 Luna-So­lar Tears, or 235 Lunati­ons were e­qual to 19 e­qual Jul. Years The manner how the An­cients us'd the Lunar Cycle, noting down Pascal Li­mits from its Numbers. 19 Julian Years, yet 'tis not so, if we regard Mathematical Rigour; for they will fall betwixt both: For 19 Julian Years make 6939 D. 18 H. but 19 Lunar Solar Years contain only 6939 D. 16 H. 32′, 20″, whose difference is 1 H. 27′, 40″, yearly. And so much do 19 mean New and Full Moons, lose every 19 Years which in about 1257 Years make four Days almost.

§. 8. To find the just time of the Pasca. the ancient Christians, as was now said, used the Lunar Cycle; and that the Use hereof may more largely appear, we shall lay down the whole Lunar Cycle, with the Pascal times, in which the utmost Limits are the 23d of March, (for upon this D [...] the Author of the Vernal Equinox would have it fall, which the Full Moon Pascal ought always to precede very nearly; and April the 19th; whence Chri­stians would never celebrate their Pasca be­fore the 22d of March, or after the 25th of April. To which the ancient Verses of those Computers have Relation.

Extremum Pasca monstrat tua passio Marce, [Page 96] Item,

But in the Gregorian Year the Pascal Limits are found by the Lunar Cycle till the Year 1700 from the following Table:

§. 9. Some think that for its Worth and The Reason why the Cha­racter of the Lunar Cycle was in times past called [...]he Golden Num­ber. great Use that it might be compared with Gold, and from this Comparison take its Name; whereas it was a Rule for the Ancients in calculating the Full and New Moons, [Page 97] upon which account ^(e) Petavius says, Beginning at any Year. For Example, from that which gives a New Moon on the 23 d of Jan. Feb. 21st, March 23 d, &c. Ʋpon those Days he wrote the Fi­gure 1 in the Margin of the Calendar, on the 2 d Year they considered and found the New Moons got forward about 11 Days, viz. on Feb. 10. and March the 12th, &c. and against those Days they placed in their Calendar the Figure 2. So on the 3 d, 4th and following Years upon those Days, that the New Moon fell every Month they placed the Figures 3, 4, &c. against them in the Calendar. And at last having past over 19 Years, they renewed the same Figures again. These were the Figures or Numbers in the Ca­lendar which were called the Golden Number. Others relate that the Alexandrians in times past sent this Cycle to the Romans in a Silver Table, writ with Golden Figures, and thence they took their Name.

CHAP. VII. Of the Cycle of Indiction.

1. The Cycle of Indiction is a System of 15 Julian Years perpetually recurring, that the times of certain Pensions might be made known to the Roman Subjects.

§. 1. SOme of the Graecians will have Indictio quasi in Actio; and Cedrenus is ad­mired What we ought to un­derstand by t [...]e Name In­diction. for following this Opinion. Onuphrius will have Indictio to come ab Indice Crucis, seen [Page 98] by Constantine when he fought against Maxen­tius: But these are frivolous Conjectures. In­dictio rather comes ab indicere, and was particu­larly used at first to denominate a certain Species of Pensions. ^(a) Ascanius reckons up three kinds of Pensions or rather Pensitations, well known to the ancient Romans. First, the Canon to which Imposts, Tributes, &c. were referr'd. Secondly, the Oblation, at this time called the Aids: And Thirdly, the Indiction, which the Ancients called Collecting. Cicero also calls it collected. The Greeks call this Cycle [...]. Dio calls it [...]. In the same Sense that the Olympias is called [...]. Also [...], &c. which last Words are used by the Wri­ters of the Antiochian History. By the ^(b) Latines Distributiones and Fusiones were commonly used instead of Indictiones.

§. 2. There are many Opinions in this mat­ter. The chief are these: ^(c) First, Dionysius Of the Origi­nal and An­tiquity of these Indictions. Petavius brings a great many Opinions about the time; but thinks them all Conjectures. ^(d) Joseph Scaliger thinks this kind of Pension of long standing; and that anciently 'twas the same with the Lustrum of 5 Years; whence we find this Inscription on Moneys [...]. B. and [...]. T. viz. [...], &c. There are ^(e) others which deduce these Indictions from the Antiochian Aera, which was about 48 years before Christ; from whence they also deduce the Julian, Adrian, Antonian, Constantinian, Valentinian, &c. Indictions. ^(f) Others will [Page 99] have the Aera of Indictions begin with the 2d of Augustus. Others again ^(g) will have the Indictions begin at that time when Augustus overcame Antoninus at the Promontory of E­pirus near Nicopolis; which hapned about 31 years before Christ. Sixthly, the famous ^(h) Langius proposes a Conjecture to be examined by the Learned, whether or no this Cycle be­longs not to the Emperour Adrian, from the Annotation of a certain anonymous Author in the first year of the 224th Olympiad. Adrian coming to Rome, remitted those things which were done to the publick Treasury of the Emperour and Roman People, constituting a time of 16 years, from whence, and to which it should become due. He whom this Learned Writer calls Anonymus, is the same with Dio. Cassius, who has almost the very same Words in the History of Adri­an; as also in the History of Marcus Antoninus. Seventhly, There are those ⁽ⁱ⁾ who settle these Indictions in the Year of Christ 313. because in that Year Constantine overcame Maxentius; and suppose that this Tyrant was cast off the Milv [...]an Bridge and drowned. The Eighth and last Opinion is the Vulgar; that the Cal­culation of Indictions began on the 24th of September in the Year of Christ 312, which must certainly be true, from the Words of ^(k) Eusebius. [...]. This Baronius, and his Epitomizer Spondanus, ob­ject against Sc [...]liger. ^(l) Calvisius ad­mits of no other Original of Indictions than this. Also Petavius, because he would not contend against either Opinion, says, The vul­gar Indictions were deduced from the year [Page 100] of Christ 312. The same is also held by ^(m) Albericus Gentilis. We also are of the same Judgment; yet, First, we distinguish betwixt the Lustra and Indictions, which Scaliger con­founds. Secondly, bewtixt the common Indicti­ons, and those which kept their stated Intervals, and the Uncommon, which were instituted ac­cording to the Will of the Emperor and the Exigence of the Republick, as other Pensions were. Thirdly, betwixt the Indictions them­selves and the Cycle of Indictions; or betwixt the Political and Chronological Use of Indicti­ons. For it is certain, that the Indictions which are referr'd to the ancient and more modern Times can be deduced only from the Year of Christ 312, except any one had rather under­stand by a Year the remote Interval of [...]. Fourthly, we again note that the first Year of Indictions may be joined to the Year of Christ 313. if we have refe­rence to the last 9 Months, the greater part of that Cyclic Year: for the first year of Indictions began Sept. 24, or the 8th of the Calends of O­ctober, Anno Christi 312; whence it is evident that the rest of the indictionary Months may very commodiously be referred to the Year 313.

§. 3. So (m) dreams a certain Person, when in Whether the Custom of rec­koning the times was [...]st thought on by the Christians to re [...]oncile the Eva [...]elists with pr [...]fane H [...]st [...]rians. his new, true and exact Chronology, falsely so called, he delivers a great many Falsities about the Original of Indictions; which it would be too troublesome to relate and confute. Those that please may consult the Author.

§. 4. Historians labour under great Incertainties in naming the Cause of this Institution. Her­wart's Opinion is rejected: Scaliger's agrees not W [...]y [...] Cycle of Indiction was 1st [...]sti­tuted (n) Joannes Georgius Herev. d [...] Hohen [...]. [Page 101] well with himself, where ^(o) he labours in one place for the Antiquity of the Antiochian Indicti­ons; and elsewhere that they were deduced from the Quinquennales and Vicennales of Constantine; but if the Elapsed from 15 years to 20 was cal­led an Indiction, consequently all the rest of the [...] may be so called: which Opinion about Constantine is as different from the Principles of Historians. So it is well con­futed by D. ^(p) Behmius, and rejected even by Scaliger's own Followers. Nor was Cardinal Baronius more happy in opining; for he sup­posed that the Cycle of Constantine ceased, espe­cially as to its Use, among the Roman Soldiers: In the year of Christ 312, when by the Institu­tion thereof it came to pass, that having served 15 years, might have his Dismission, and go free where-ever he pleased without any Capitation: Or if he would tarry, he should then have grea­ter Advantages; whereas formerly they were to serve 16 years; which Opinion of Baronius, as it seems improbable, so it is opposed by ^(q) Petavius. Our Opinion is, that this Cycle was at that time known, when Constantine the Em­peror had need of Money to pay off his Soldi­ers, and renew the War against Licinius; but this Aera of Indictions was made more solemn; because the same seemed to the Christians to be an Epocha of their restored Liberty after the Conquest of Maxentius.

§. 5. There are commonly reckoned up three How many Indictions were there, or are there [...]w in use. sorts of Indictions, whereof the first was called the Caesarean; because the Caesars had respect to it in paying Persons, and signing the Instruments of Causes. This Indiction fell upon the 8th of the Calends of October, or on the 26th Day of [Page 102] September; For after Harvest was over, the time of Autumn was thought most proper for paying Tributes. The second was called Con­stantinopolitanean, in which they signed (as they do at this Day) the more Oriental Calendars, as appears from the Briefs of the Hieremian Patri­arch, and of the Turco-Graecian Crucius. This be­gins upon the Calends of September; whence some think that its Use began when the Graecians at the Solemnity of the New Year chose the Autumn of the first Month thereof. Ambrosius understands one of these Indictions, when he thus writes to the Bishops of Aemilia; This is the first Month according to coming out of Aegypt, and the First according to the Law, and the Eighth according to our Custom: For the Indiction begins on the Month of September. The third is called Pontifical, or the Roman, which begins upon the Calends of January, and continually follows the 2 former, within 4 Months almost. To these may be added the Antiochian, which ^(r) Scaliger by the Authority of Causa­bon, and the Patriarch Ignatius, certainly de­termines Of the reason why the Ro­man E [...]pe­rors wou [...]d have this Cycle of Indictions known i [...] the Common People. to the Month of May.

§. 6. We are commonly wont to preserve those things which appear useful to us. In like manner the Caesars, when at the stated times of Indictions, their Treasuries were encreased, ordained that the Character of Indiction should be noted in the publick Instruments. Thus we read what the Emperor Justinian commanded in the 47th Novelia: Whence we oblige those who mini­ster in Affairs; or where-ever any Acts are per­formed, and the Notaries who write their Instru­ments in any Form in this great City, and in all other Nations whom God has subjected to us, that they thus begin: In the third Year of the Empire [Page 103] of the most Sacred Emperor Augustus, &c. and afterwards to name those Consuls which are in that Year; and in the third place, the Indiction, the Month and the Day: So the Time shall be pre­served in all Affairs: And these things are to be fixt in Writings for the Memory of the Empire, the Order of the Consulate, and other Observations What it was that the Sub­jects of the Ro­man People were to pay 'em at the Expira­tion of this Quindecennial Time. that may be interposed.

§. 7. And 'twas not for the sake of Remissions but of collecting Subsidies, that those Indicti­ons were chiefly constituted; but what, and in what Order the Subjects of the Roman People were to bring, the Ancients have not remarked. Elegius Noviomensius Episcopus, who flourish'd about the middle of the 7th Age in the 2d ^(ſ) Hom. speaks of divers Tributes (as the Moderns after him) according to divers Lustrums in which the Cycle of Indictions was finished. In the first Lustrum there was a Tribute of Gold colle­cted: In the second, one of Silver; and in the third, one of Brass: And the Annotator upon the 47th Novella delivers the manner very diffe­rent. Anciently, (says he) the Romans in eve­ry 15 Years, received a Tribute from the whole World. In the first 5 Years, Iron to make Armour for the Roman Soldiers. In the 2 d Silver, out of which the Soldiers were to be paid their Wa­ges. In the 3 d Gold which was laid up in the Treasury for the Roman Republick. But since, the Writers of the following Age make mention of this Matter in so different a manner, that we can hardly believe this Tradition.

CHAP. VIII. Of the Character of the Roman CONSƲLATE.

1. The Roman Consulate is a Character wherein two Roman Consuls were named; whence we come to the Knowledge of anything done in that time.

§. 1. THE Reason of the Roman Consulate being mentioned among the Chara­cters of Times, is because both Latin and Greek Writers by nam [...]ng two Consuls were wont to Of the reason why we men­ti [...]n the Ro­man Consulate among the Char [...]cters [...]f the Times. fix the times of things done; and that by a most ancient Custom, which Lucan intimates while he calls these Years Consular Years: And amongst the Latins, Pacatus in a Panegyric delivered to Theodorus Emperor of Rome, speaks remark­ably; A certain Captain is promoted to perform the Discipline of Sieges; a Prefect is preferr'd to look after a Province; a Consul is created to give a Name to the Year, &c.

§. 2. After the Ravishment of Lucretia by Of the time in which the Of­f [...]e, Dignity and Character of a Consul [...] in use [...] the Romans. the Son of Tarquinius Superbus, the Romans ha­ving abolished the Regal Dignity, created Con­suls to govern the Empire, rather to consult with, than to domineer over their Liberty, or one King two Consuls were created; that if one should prove bad, the other having equal Power might restrain him: And 'twas the Pleasure of the People that they should not enjoy the Em­pire above one Year, lest a Continuation of their Power should render them insolent; but they were always civil, knowing that after one Year they should be deprived of all again ^(a).

§. 3. Lipsius ^(b) disputes about this, and those What it is we ought to un­derstand by the Name and Office of Con­suls. who derive their Name from the End or De­sign of it; which was to consult and provide for the Citizens. ^(c) Others derive their Name from their Office, which is to consult; that is, ask the Senate. Others interpret 'em à judicando, which, in the sense of Quin­tilian ^(d) is the same thing as consulendo; from whence this Proverb, boni consulas, i. e. judices. But the Judgment of Lipsius about this Diversi­ty is, that the first Etymology is more popular, the third more subtle, the middle more true; because 'twas the Business of a Consul to in­terrogate and refer to the Senate; as Livius ^(e) hath written; 'twas his part to enquire into their Judgment. Cicero ^(f) also says, Let there be two in the Regal Empire, and let 'em be called Praetors, Judges, Consuls, à Praeeundo, Judicando, Consulendo: Let 'em have the chief Power of the Militia: Let 'em obey no one: Let the Safety of the People be their Supreme Law, &c.

§. 4. As to the time of the Year the Consuls Of the time of the year in which the Roman Consuls under­took the Consu­late. began, we find great Variation according to the Diversity of Times, which does not a little disturb Universal History; we shall al­ledge some from Dionysius Halicarnassaeus and Livius. First of all therefore, who is he that cannot gather from the Character of the ^(g) Regi­fugium held on the 6th of the Calends of March, that the Election of Consuls fell upon February? For the Consuls followed the Kings, as is the Com­mon Opinion: The Successors of the first Con­suls began their Consulate on the Ides of March, on the Ides of May, on the 3d of the Ides, Sextil. on the Ides of Sextil. on the Ides of December, on [Page 106] the Calends Sextil. on the Calends of September, &c. as is evident from the two Writers above­mentioned. At length the Custom obtained, that the Calends of January were destined for the Consulate, lest the Years of the Curulean Magistrates, especially the Consuls, should differ from the Civil or Common Years; at which time we dare not say, that the Heads of the Roman Republick undertook the Affair. 'Tis the O­pinion of Justus Lipsius, that from the Year 598, the ^(h) Calends of January were sacred for the Change of the Consuls: Nor in the Times of ⁽ⁱ⁾ Ovid was it different, as appears from these Verses:

And in ^(k) another Place,

In like manner also Lucan;

§. 5. The Consulate ordinarily continued a Of the time that the Con­suls remained in their Office. Year; though some think 'twas more than the Common Year; and although the Roman People conferred upon Africanus a continual Consulate; yet some Examples break not a General Rule: For the Consulate, (as say [Page 107] ^(l) Seneca) was an Annual Honour; or as ^(m) Tertullian has it, the fleeting Joy of one Year.

§. 6. There were ordinarily two Consuls, ex­traordinarily Of the number of Consuls that yearly praesided over the Ro­man People. sometimes more, one of the two dying, or being removed at the Pleasure of the Caesars: For thus Julius Obsequens speaks of those that were removed; 'Tis evident that no one that had taken away the Office of his Colleague lived a Year. And ⁽ⁿ⁾ Lampridius, speaking of those that were unduly elected, says, For then 1st there were 25 Consuls chosen for one Year, all the Provinces were sold, &c. And of Extraordinary Consuls Seneca thus writes; He made me a Consul, but not an ordinary one, &c. Also Suetonius ^(o) in six Consulates he had but one that was Ordinary. And Suetonius seems to refer to this in his Observati­ons of the Emp. Augustus, he also required that so often as a Consulate was given to him, he should have two Colleagues: And adds, Yet all crying out against him, he could not obtain that the Majesty should be lessened; because he bore that Honour not himself alone, but in Conjunction with the other.

§. 7. Those that anciently wrote of the Ro­man Of the Certain­ty that may be attained from the Series of Consuls, and the Signature of the Times. Affairs, were wont to note diligently that there were two Consuls, which acted for the space of four Years, as is evident from Cus­pini [...]nus's Monument, which four Years they cal­led Chronica Consularia; but we cannot be so happy as to consult these Consularia of the Con­suls, since time has wholly destroyed these anci­ent Writings, or miserably defaced 'em: but 'tis thus that ^(p) some would make good this Defect: And first of all, the Capitoline Marbles disco­vered in the last Age conduce much towards it: For in the Year of Christ 1547, (as Caivi­sius [Page 108] has it, the Capitoline Tables written for­merly out of the Minutes of the Senate by Verrius Flaccus the Grammarian, and publickly set up in the Roman Forum by the Command of the Emperor Augustus; and afterwards being broken in pieces, and dispersed by the Injury of Times, were lost and covered under Ground; by which ancient Guides (found afterwards a­gain) very many Antiquaries have endeavoured to correct the Roman Fasti or Calendars; but no one has been more successful in those Enquiries than Onuphrius, an Acquaintance of the Cardi­nal Alexander Farnesius, to whom these Tables were brought when first found: For he after­wards published at Venice the Roman Calendars and Triumphs, from the time of Romulus, till that of Charles V. in the Year 1557; yet the Alexandrian Chronicle is not to be wholly neg­lected, which carries the Name of the Sicilian Calendars: For this Book having been taken from amongst the most ancient Writings, was first found in Sicily, being part of the ancient Library of Jerone Surita, and sometimes [...]ted by Scaliger and Causabon. This Book Antonius Augustinus (Auditor rotae) first brought with him into Italy: Fr. Sylburgius bought it for six Pieces of Gold, and gave it to Heschelius, who brought it to the Augustine Bibliotheque; from whence it was published by Matth. Raderus.

§. 8. Some suspect that a Lustrum of 4 Pairs That all the Pairs of Con­suls for every year since the first Insti [...]uti­on of the Con­sulate answer­ing to the Mo­numents of Antiquity al­ready cited, do not at this Day appear, nor are now known. and consequently of 4 Years, was observed in the Roman Calendars; for many Years are wont to be reckoned from the Solemnity of the Con­suls; which we have already remark'd, were 2. This Defect, it seems, has given the best Wri­ters much Trouble: For, first of all, there are some who think that either the Names of some Consuls were lost, or that there were Dictators [Page 109] put in the room of Consuls; or that a Quadren­nium (or Space of Four Years) was mana­ged without Consuls; which Opinion, not to mention other Difficulties, seems to labour un­der this, viz. That it does not sufficient­ly appear in what place the new Pairs of Consuls were inserted. Also the Govern­ment of Dictators was half-yearly, nor de­creed but by the Consuls: There are some in the second place that guess, the Order of Consuls had respect to the Years of the City. I always suspected, and I think not without Grounds (says Onuphrius) that four Years were inserted in the Calendars, either of Dictators without Consuls, or without either Dictators or Consuls; because Livius, who wrote the History of those Times; found no such thing in the Annals whence he made his History. Therefore I sometimes thought that they fixed the Building of Rome with C. Fabi­us Pictor in the 29th of the Olympiads, That the Order of Consuls might an­swer to the Years of the City. But it seems not safe to contradict the unanimous Con­sent of the best Writers. Thirdly and Last­ly, There are some who seem, not without Grounds, to suspect that from the very cor­rupt Disposition of the Romulian and Pompilian Year; and because the Consuls at that time did enter upon their Office. There­fore these Doubts have arisen.

§. 9. And as 'twas said before that there were What 'tis we ought to think of their Opini­on, who are yet perswaded that there were five Pair of Consuls in the Consular Ca­lendar. four Pair of Consuls, so we have ^(q) some that will have the same Calendars to abound with Five Pair of Consuls: But since, what this Author has advanced, as any one may read him if they think it worth the while, is repugnant to Universal Histo­ry; and if his Hypothesis were admitted, it would rather disturb Chronology, than bring any Light unto it: Besides, the same Authorities he makes use of to advance his Hypothesis, he rejects them in other Places: Therefore we also shall reject all that he has said upon this Matter.

§. 10. The Consuls were mark'd in the Of the time that the Dig­nity of a Con­sulate was in use amongst the Romans. Calendars till the Year of Christ 541; but after Julius Caesar, as he himself speaks, Rome had only the Shadow of a Common-wealth, and only the Names of Consuls were retained: For then indeed,

Omnia Caesar erat.

For what betwixt the Affection of Popula­rity, and (mostly) by the Counsel of their Authority, the Caesars drew the Consulate to themselves, sometimes using Force in it. For so Suetonius remarks of his Augustus in these Words; In the twentieth Year of his Age he invaded the Consulate, moving his Legions after an hostile manner towards the City; and hav­ing sent an Embassy to treat for him in the Name of the Army; whilst the Senate delay­ed, Cornelius Centurio the Chief of the Em­bassy throwing open his Cloak, shewed him the [Page 111] Head of his Sword, and was not afraid to speak in the Court, If you will not do it, this shall do it. At length, on the 15th Year of Justinian, in which only Basilius was Consul, this Order of Consuls was wholly extinguish'd; and after this Year, for 25 of the following Years they wrote thus: After the 1st, 2 d, 3 d, &c. Years of the Consulate of Basilius. Thus the Character of the Consuls fell, and the Times in the Roman Affairs were noted with the Years of the Em­perors, and a little after with the Years of Christ.

§. 11. Custom at last obtained, that upon the The Reason why Justinian the Emperor to [...]k away the Dignity of the Consulate from the Senate. 1st Day of the Consulate, the new Consuls were used to excessive Expences; Cesar, therefore as appears from the 105th Novella, endeavoured to restrain them by a certain Law, in which he not only forbid that they should throw Gold about, but in general▪ that they should not do any thing so immense and irregular: But when the Consuls again ambitiously violated these Limits, the Em­peror prescribed, so that upon this Account they often ruined their Families, and reduced them to extream Necessity the Consular Dig­nity was taken away from the Senate: after that the Name of the Consuls, which had al­most continued 1000 Years, was extirpated, and the Republick of Rome began to fail, as Justi­nian speaks in the Novella above cited.

CHAP. I. Of the Period of Calippus. DEFINITIONS.

• 1. The Calippic Period is a System of 76 years as well Lunar as Solar; which being elapsed, the Reckoning of the Solar and Lunar Motion recurrs, as at first, the Ancients thought that when this Period was finished, the Con­junctions of the Sun and Moon hapned again upon the same Day of the Solar as they were observed to have done before.
• 2. This Sum of Years arises by the Multipli­cation of 19 (the Metonic Cycle) into 4.
• 3. This Calippic Period comprehends 58 Common Years, and 28 intercalatory Ones, 940 Lunati­ons, and 27759 Days.

§. 1. THE Greeks being advised by their Of the Reason and Occasion of the Calippic Period, or a System of so great a time. Oracle that they ought to sacrifice as well by Lunae-Solar Times, as by Days, Months and Years, after various man­ners [Page 113] of Cycles, as that of 2, 4, 8, 12, Years space; in which they committed great Mistakes, the Moon, (as we have it in Aristophanes) com­plaining out of the Clouds that the Athenians had no consideration to the Lunar Motions: At length Meto thought of the 19 years Cycle, and published the same at Athens in the 86th year of the 4th Olympiad; so that the Metonic Cycle was in the 1st year of the 87th Olympiad, or the 4282d. of the Julian Period. Of him Diod. Sic. thus writes, That when Bosphorus K. of the Spar­tans was dead, and Seleucus, who reigned only four years, succeeded him, there was one Meto, Brother of Pausanias at Athens, famous for Astronomy; who on the 13th day of Scirrophorion (an At­tic Month) published his Enneadecaterides; for in so many years the Stars return to the same Places, and as it were, finish a great Year: Therefore this Year is by some called Meto's Year; for that Man seems to have followed the Truth in this Prediction and Description: For the Stars have their Motions and Significations answera­ble to this Description: So that very many of the Greeks who follow this Account, even to this time seem not to have erred. But since the Ob­servations of succeeding Times have sufficient­ly shewed us that this Metonic Cycle does not exactly answer to the Lunae-Solar Motions. Calippus endeavoured to reform it by a new Period, subtracting one Day from every 4 Cycles.

§. 2. Calippus Cyzicenus of Mysia, as he is cal­led That Calip­pus Cyzice­nus was the Author of this new Peri­od. by the Ancients, not Cygicenus, as 'tis read in Josephus Blancanus's Chronology of fa­mous Mathematicians. Yet though this Pe­riod had its Name from Calippus, yet 'tis without doubt, but Timcchares, Aristellus, Pole­marchus, who all flourished about that time, consulted the Author of this System; and whereas we read that he came with Polemarchus to [Page 114] Aristotle at Athens upon Account of some O­pinions of Eudoxus, Aristotle in his 62d Me­taph. Text. 47. makes mention of this Ca­lippus.

§. 3. The Period of Calippus began in the Of the time when Calip­pus his Period began. Summer of that Year that Alexander the Great conquered Darius in a difficult Battle at Arbela, which was in the 3d Year of the 112th Olym­piad, or in the Year of the Julian Period 4384. which is manifest from ^(a) Ptolemy, who brings 4 Observations from Timochares at certain years of the first Calippic Period.

§. 4. 'Twas said above that Calippus interca­lated Of the Order of Intercala­tory Years to be observed in the Calippic Period. 18 times in the space of 76 Years; but upon what Account, and in what time he has inserted those Months, would seem difficult, if Geminus had not noted that Calippus in his new Period had changed nothing in the computing of Intercalation in the Metonic Cycle: From whose Testimony we gather that Calippus in­tercalated so often as Meto's Cycle required: But we have above shew'd that Meto's Interca­latory Years were 3. 6. 8. 11. 14. 17. 19. Moreover, the first Year of the Calippic Period was the 8th in the Metonic Cycle, which we gather from the space of 102 Years, betwixt the Beginning of Meto's Cycle (in the Year of the Julian Period 4282) and the Calippic Period (in the Year of the Julian Period 4384:) There­fore it seems probable to us that the intercala­tory Years of the Calippic Period were these following: 1. 4. 7. 10. 12. 15. 18. 20. 23. 26. 29. 31. 34. 37. 39. 42. 45. 48. 50. 53. 56. 58. 61. 64. 67. 69. 72. 75.

Seventy six Solar Tropic Years, allowing That the [...] Period [...]. 365 D. 5 H. 48″, 40″, to a Year, make 27758 D. 9 H. 57″, 40″; but the Days in 940 Lu­nations [Page 115] are 27758 D. 18 H. 7′, 0″, supposing the Quantity of one Lunation to be 29 D. 12 H. 44′, 3″, the Sum of 27759 Days are attributed to one Cycle, which agrees with neither of the other, being less than one by almost 10 Hours, and less than another by above 18 H. But that the Examination of the Cycles and Lunae-Solar Periods may be liable to less Difficulties, we have thought fit to construct the following Tables, whose Use is very great and obvious.

[Page 118]

CHAP. II. Of the Period of Hipparchus.

• 1. Hipparchus 's Period is a System of 304 years Lunar and Solar, which being elapsed, the Ancients thought the Reckoning by the Lunar Motion would exactly coincide again with the Solar ones.
• 2. This Period comprehends 3760 Months, and 111035 Days.
• 3. The Sum of these Days arises from the Multiplication of the Calippic Period, viz. 27759 into 4, subtracting Ʋnity from the Pro­duct.

§. 1. THIS is the Author that corrected the Of the Au­thor of this Cycle. Computation of Calippus, and thought of a new one: His Name was Hipparchus of Nicaea in Bithynia, (according to Strabo) or the Island of Rhodes (according to Ptolemy;) and he made such Proficiency in Astronomy, that ^(a) Pliny says of him, Nunquam satis landatus. But whether this was the same with another fa­mous Astronomer, who was called Abrahis or Abrachis, according as Lucas Gauricus and Jose­phus Blancanus thought, you may read Clavius's ^(b) Disputations,

§. 2. The Age of this Astronomer is suffici­ently Of the time that Hippar­chus lived and published his Period. fixed from his own Observations; for he takes notice of a Vernal Aequinox in the 3d Year of the 150th Olympiad, that it hap­ned [Page 120] upon the 30th of Messori, which is Octo­ber the 3d. of the Jul. Period 4552; and on the following Years he gives us other Obser­vations; whereof Ptolemy mentions 8; and the difference betwixt the first and the last, is 3 [...] Years: Therefore he flourished in the time of the third Punic War; and he gave him­self up to this Study from the Year 4552, to the Year 4586, according to the Julian Ac­count; in which time 'tis indisputable but he must have fixed his Period.

§. 3. He found that the Period of Calippus Of the Reason why Hippar­chus corrected the Calippic Period. was assumed too great by near a Quarter of an Hour; so that 4 Periods being elapsed, the Moon would come to the old Place again in the Solar Calendar, if one Day were subtracted; which he accordingly did. Of this Affair Longomontanus ^(c) thus writes: Meto in 304, which hapned nearly betwixt him and Hippar­chus, had committed an Error of 5 Days, in his Cycle then, because he look'd upon the Solar Year to be almost 365¼ Days; because he found the Conjunction of the Sun and Moon not so pre­cise as it should be, which Calippus thought of, whilst examining an Eclipse of the Moon 6 years before the Death of Alexander the Great; So that he corrected Meto, subtracting one Day in every 4 Cycles; from whence he made his own Period of 76 Years: But whereas Calippus himself had usurped, that the Solar Year consisted of 365¼ Days; and also in the Course of the Moon it lost something. Therefore Hipparchus in like manner corrected Calippus, taking from him in 4 Periods or the space of 304 Years, one whole Day, and consequently 5 from Meto in that time. But this Error of one Day committed by Calippus, Hipparchus rejected for a whole Solar Year, [Page 121] subtracting only so much after 304 years and one Day altogether in 304 years. Hence it comes to pass that the Measure of the Tropick Year 365¼ Days is lessened by Hipparchus by the 300th part of one Day; that is, 4′. 48″: So that time should, according to him, be thought but 365 D. 5 H. 55′. 12″.

§. 4. For if according to the Rule of the pre­ceding That Hippar­chus did not follow in his Period what he thought of in his mind. Tables, you examine this Period, 304 Solar Tropical Years make 111033 D. 15 H. 50′. 40″. But 3760 Lunations make 111035 D. 0H. 37′. 24″. So that there remains an evi­dent Disparity, and the Error is owing to this, that the Quantity of the Solar Year was as­sumed greater than the constant Account of the Solar Motions require.

§. 5. The Gregorian Hypothesis is this, that That the Au­thors of the Gregorian Calendar have not rightly corrected the Fault of Hip­parchus▪ Pe­riod. the Sun and Moon are not together in the same Place of 304 years as Hipparchus had taught, but after 312; which Cycle of Years the Gre­gorian Correctors have substituted instead of that of Hipparchus, hereby acting absurd­ly two ways: First, the Authors of this Cyclic Method have taken away from this Lunar Cy­cle worse than any before them and without any reason have deduced their Reckoning ra­ther from Cycles than Computation: 2dly, nor have they rightly observed the Laws of the Celestial Motions; for which way soever you cal­culate, you shall never make 312 Solar Years, and 312 Lunar Years, that they should exactly coincide with a constant perpetual Revolu­tion.

§. 6. Those who undertake to correct the How the Er­rors of the Ancients have been corrected by Lunae-Solar Calculations. Lunae-Solar Cycles and other Periods of the same nature, seem to me not very unlike those who take up Water in a Sieve; for both of 'em lose their Labour: We cannot successfully find the Lunae-Solar Morions except by Tables [Page 122] built upon Celestial Observations, whereby we fully know the Times of the Aequinoxes, the Varieties of the Lunar Phases, coming this way only to the Archives of the Stars; when those that have declined this way, and endeavouring to substitute another Period in the room of that of Hipparchus, could never have another Re­compence, but Errors for their Errors: So that the Pope himself was once amazed when he saw the Jews, the Slayers of Christ, his Colleagues in the Paschal. So that Christophorus Clavius was compelled to write, to the Eternal Infamy of the reformed and ancient Periods: Demonstran­dum erit Maestlino in Kal. Greg. alios errores prae­ter quatuor reperi. Oh the Folly of the Age! Pray, how many Full Moons, Paschals (for 'twas for their sakes that so much Pains were taken, partly in mending, partly in constituting a-new the Periods of the Ancients) could those little Parasites, while they were nourished 10 Years at Rome by Gregory, be able to compute with a little diligence for the Tables of Celestial Mo­tions, without the use of fallacious Cycles and Periods! So that they were able to avoid many Errors, of which Clement VIII. wrote foolishly enough, when he said, vitari non potuerint. In short, there is no Cycle, no Period, however ingeniously contrived, which we can pronounce sufficient to reconcile the Motions of the Sun and Moon by an accurate, useful and perpetual Agreement.

CHAP. III. Of the Victorian Period.

• 1. The Victorian Period is a System of 532 Lu­nae-Solar and Julian Years, which being elap­sed, the Characters of the Moon fall again upon the same Day and Feria, and revolve in the same Order, according to the Opinion of the Ancients.
• 2. 'Tis otherwise the great Paschal Cycle; because the Christians first used it to find the true time of the Pascha's.
• 3. But the Sum of these Years arises from the Multiplication of 29 into 28, the Numbers of the Lunar and Solar Cycle.

§. 1. THO' there were many Victorius's by Name, as Victorius Pictaviensis, who Of the Au­thor of this Period. suffered Martyrdom under Dioclesian, and ano­ther about the Year of Christ 324, who in a Roman Synod met in Trajan's Baths, was con­demned because he presumed to argue about the Paschal Cycles received into the Church: But the Learned agree, that one Victorius different from the former, and by Nation, and Aquitane, was the Author of the Cycle of 532 Years. Theo­philus and C. Cyrillus computed the times of the Pascha's for only 95 Years: For Dionysius Exi­guus remarks upon both, and wrote thus to Pe­tronius the Bishop: That Pope Theophilus dedica­ting a Course of 100 Years to Prince Theodosius the Elder, and S. Cyrillus composing a Cycle of Times for 95 Years, both kept in all things this Tradition of the holy Council, to observe the 14 [Page 124] Paschal Moons. When therefore Hilary I. Arch­deacon, after Pontifex R. had observed that those Particulars were found out, and that the Table of Theophilus Alexandrinus was almost at an End, he commanded Victorius, who at that time was lookt upon as the best Com­putator of the Age, to assist the Church in this Necessity; who for this substituted the Period I have described, that the same being elapsed, the Feriae and Conjunctions might return and happen again upon the same Day.

§. 2. 'Twas before Hilarius received the Pon­tificate Of the time of publishing this Period. that Victorius had his Command about this Cycle, which is gathered from an Epistle of Hilarius to Victorius; which, it's said, is now extant in the Sirmondian Codex, which has this Inscription: Dilectissimo, &c. To the most beloved, honourable and holy Brother Victorius, Hilarius, Bishop and Arch-deacon of the City of Rome, &c. But till some Years were clapsed, and Hilarius made Pope, this Cycle was not published; as appears from the Prologue writ­ten to the same Pope: Domino, &c. To Hila­rius the truly Holy Lord and Pope, venerable in Christ, Bishop of the City of Rome, Victorius, &c. Marianus Scotus speaks the clearest of this Matter, who upon the Year 463, writes the following Words: Victorius upon the Command of P. Hilary wrote the Paschal Cycle of 532 Years.

§. 3. And Victorius fixed his Period, not from the Of the time that victo­rius fixed his Period. time he first discovered it, but from the Passion of Christ, which he makes to be in the Year of the Consulate of Ruffus and Rebellius, which Character seems to agree with the 29th Year of the common Aera.

§. 4. Yet the Annals of the Ancients witness, How victo­rius's Period was accepted. that Victor, a Bishop of Capua, wrote against the Faults of the Victorian Cycle; and Beda [Page 125] seems to take his part against Victorius. But how Victorius was mistaken, is not so evident to us, since we find no Copy at this Day of his Cy­de; for that Fragment which Petavius ^(a) cites, he himself thinks spurious. But this is certain, that Dionysius Exiguus upon the Oc­casion of Victorius's Period found out a more accurate and newer Paschal Cycle, viz. of 525 Years: Who desires to see more of these, may consult ^(b) Authors.

CHAP. IV. Of the Constantinopolitan Period.

• 1. The Constantinopolitan Period is a System of 7980 Julian Years, whereof the first has the Solar Cycle of 28 Years, the 2 d the Lunar of 19 Years, the 3 d the Indiction of 15 Years.
• 2. This Sum arises from the continual Multipli­cation of the Number of Years in the Solar Cycle, Lunar Cycle and Indiction.
• 3. The Greeks do not reckon the same Cycles as the Romans do.
• 4. The first Solar Cycle of the Greeks is the 18th of the Latines, and the 1st of the Latines is the 12th of the Greeks.
• 5. The 1st Lunar Cycle of the Greeks is the 4th of the Latines, and the 1st of the Latines is the 17th of the Greeks.
• 6. But for the most part, they reckon the Cycle of the Indictions as the Romans do: For what Number the Greeks give to the Cycle of In­dictions [Page 126] from the Calends of September, the same the Romans give from the Calends of January.

§. 1. ALtho' we dare not assert with Josephus ^(a) Scaliger that the Constantinopolitan Of the Origi­nal of the common Grae­cian Aera, and in what sense the Greeks un­derstood it. Computation was a Period merely artificial, which the Ʋnlearned that followed, fetched from the Creation of the World with the same Ʋnskil­fulness as the Jews do their Reckoning; Yet the Number of the Greek Version of the 70 Inter­preters do very nearly agree with this Aera: Nor hath it been denied by ^(b) Petavius, that this was the Reason of preferring the Con­veniency of certain Cycles, chiefly that of the Moon and Indictions, to others, which were to be interpolated by the Greeks, and that e­specially which we now use; which Cycles that they might commodiously agree, the Greeks studied to follow Panodorus Monachus, or some other Author; by a Subtraction or an Addition of a few Years to that old and well-known Sum: So that nothing hin­ders why we should less call that Com­putation a Period which the Greeks call by the Name of an Epocha or Aera (the Com­modity and Disposition of the Cycles in the Computation being considered) for by that Name (viz. Period) we take notice that not only Sca­liger, but also Langins and others used to call that Computation, tho' 'twas afterwards oppo­sed by Petavius.

§. 2. The Use of this Epocha is very great, Of the Ʋse of the Constan­tinopolitan E [...]ocha or P [...]i [...]d. when at Constantinopolis and Alexandria they make both use of it for noting their Kalendars; [Page 127] whence the same Aera is called by both their Names. ^(c) Leo Allatius doubts not to call it the Calculation of the whole Eastern Church, which is almost every where solemn, and which all make use of not only for the direction of the times, and showing the solemn Days of their Calendars, but in their Trades and familiar Conversations.

§. 3. The Graecian Year was two-fold, first Civil, which they began with the Indiction Of the Begin­ning of the Graecian Years. from September; 2d, the Ecclesiastic, which they began from the Cycle of the Sun and Moon from April. Hence the Computations of these years divided by the Cycle of the Sun and Moon, are to be lessened by Unity in the former Months, which, as Petavius notes, Scaliger had not considered.

§. 4. The 1st year of Christ in relation to this Period may be shewn from many Examples of Of the first Year of Christ in relation to this Period, and how o­ther Years of Christ are to be connected with the Years of this Aera. Authors which used the Constantinopolitan Aera: As for Example, by Isaac Argyrus, it is gathered that the first Year of the vulgar Aera began on the 4th Month of the Year 5509; whence it's evi­dent that betwixt the beginning of this Epocha, and that of the vulgar Aera, there were 5508 Years and 4 Months, which, if added to the Year of the Christian Aera, it shews the time according to the Greek Account; or if subtracted from the time of the Constantinopolitans, it shews the time answering to our vulgar Com­putation: so that there is no use of those large Tables invented by Leo ^(d) Allatius.

§. 5. And from the Sum of the Years and How the Graecian Years [...] Julian. Months reckoned according to the Greeks, subtract 795 Years, 4 Months, and the Remainder is the Time answering in the Julian Ac­count; or if you add to the Julian Years and [Page 128] Months the 795 Years 4 Months, you have All the Greek Writers did not make use of this Com­putation. the Graetian Year.

§. 6. Although at this Day many of the Greeks make use of this Aera; yet there are others especially amongst the ancient Writers, that use another Epocha different from this; whence Jacobus ^(e) Capellus reckons upon divers Aera's which are distinctly made use of by the Greek Writers. The first is, if you look back to the Creation of the World, according to the Reckon­ing of the Latines, the Constantinopolitan Reckon­ing just now explained, will be found false: The 2d is the Graec. Aera, us'd by the Aethiopians, which begins the 9th Year from the Alexandrian or Constantinopolitan Aera upon the 9th Indiction, and the 26th Julian Solar Cycle, and commen­ces upon the Autumn: The third also is a Grae­cian Aera frequently used by Cedrenus. He de­duces it from the 16th year of the Alexandrian Epo­cha, the 8th of the Aethiopian, and from the first Indiction: The fourth is that which Maxi­mus Monachus usurps, and is deduced from the 17th Year current of the common Graecian Ae­ra; for betwixt the Epocha of the World's Cre­ation, and the Year of Christ, Miximus rec­kons 5492 Years. Petavius reckons up the Varieties of the Greek Computations after ano­ther manner, who in respect to Dionysius's Christian Aera, admits only two Aera's of the Greeks, whereof the first makes the Nati­vity of Christ upon the 5493d Year of his Aera; the other upon the Year H [...]w the Greek and Latin Cycles may be com­pared. 5509; about which ^(f) Petavius may be consulted.

§. 7. The Latin and Greek Cycles may be compared by Help of the following Table, which shews the Lunar and Solar Cycles of [Page 129] both: For we have already shewn how the Latin Cycle of Indictions agrees with the Graecian Cycles; to which we may add that the Graecian Cycles answer to the Latin Cycles till March or April: If therefore the Character of the following Months in relation to the Solar Cycle of the Latins, answering to the reckoning of the Greeks be sought, the Ta­bular Numbers in the Column Graec. ought to be encreased by Unity. Indeed I am not ignorant that Isaac Monachus wrote that the Year, in respect of the Solar Cycle, began from October; but in respect of the Lunar Cycle, from the Calends of Janu­ry; but if we consider the usual Greek Com­putations, that Method we have now prescri­bed, will be more natural.

CHAP. V. Of the Julian Period.

• 1. The Julian Period is a System of 7980 Years, whose first Year had 1 for the Character of the Solar Cycle; also of the Lunar Cycle, and also of the Indiction, all reckoned according to the manner of the Latines, from Noon upon the Calends of January.
• 2. This Period arises from the continual Mul­tiplication of 28, 19, and 15, the Cycles of the Sun, Moon and Indiction.
• 3. In respect of its Ʋse, this Period contains in it the Reason of all other Epocha's; so that we are chiefly to reduce all other Aera's to it.

§. 1. THIS Period was not called the Julian, because it was invented by Julius Of the reason why this is called the Ju­lian Period. Caesar, since 'twas not received till the Year 4669; but because this System consists of Ju­lian Years.

§. 2. This Epocha is not Historical but Ar­tificial, Of its Au­thor. since 'twas invented only for the Use of true Epocha's: For Scaliger considering that the Calculation was very intricate, since, if we consider the Years of the Creation, the year of Christ, or any other Epocha whatever, ano­ther Person could not understand what Year this or that Writer meant; therefore to remove such Doubts about reckoning upon the times, he thought of this Period; and when he saw that there was no other Epocha, whose Beginning was incontestable among Chronologers, he fixed this: For he continually multiplied the [Page 132] three Cycles of the Sun, Moon, and Indi­ction together, and the Product resulting he called the Julian Period. By this means, a­voiding those Inconveniencies, which were wont to arise from the different Computation of Years; but no one can doubt, who has conside­red the 2 Periods, viz. the Constantinopolitan and the Julian; but that the former was the occasion of the latter. For they agree in Quantity and in Principles; since, as Scaliger has taught, both arise from the Multiplication of the Cycles; but they disagree in respect of the Terminus à quo, since the Beginning of the Const. Period is supposed to precede the other Period by 795 years: Nor have the Years of the Julian Period the same Beginning as the Const. have; since we begin those from Noon upon the Calends of January; but these part­ly from the Autumn, partly from the Spring. But what Praise Scaliger has deserved, even from his Enemy, because of the Use of this Julian Period, is evident from the following Words of ^(a) Petavius, where he says, Truly there is scarce any thing in all Scaliger 's Chrono­logical Books which is of any Moment, or may a­void Reprehension, besides his Explication of the Julian Period. And as we have deservedly, con­demn'd the rest, and because of their intolerable Er­rors, and have rejected them from all Ʋse in Hi­story; so we ought much to esteem this Artificial Cycle of Year and its Ʋse. Which is sufficient from an Enemy and constant Adversary.

§. 3. The first Use of the Julian Period Of the most remarkable Ʋses of the Julian Period. is this; that we can explain our Minds to one another: For every Year of this Period has its Cycles; all of which no other Year in the whole Period has. And on the contrary, the [Page 133] Year of the Creation being stated, we may first enquire how many years any Author rec­kons from the Creation to the Year of Christ which Multiplex Inquisition, Experience will teach any one who doubts of it, is troublesome and full of Difficulties, according to the Method of other Periods. The 2d Use is, that the 3 Cycles are found in this Period: The 3d Use is this, that if it can be found how the Chronological Cha­racters can be found, and that the Years of any other Epocha can be connected with the years of the Julian Period, the same Characters also with little Labour may be applied to the years of all other Epocha's, which also is the Cause why we shall explain in certain Sections the In­vention of the Chronological Characters in the Julian Period, and afterwards in particular, the Connexion of Historical Years, with the Julian Period. For whereas in all other Chap­ters we have particularly spoken how those Characters might peculiarly be applied to Ae­ra's: So it shall be sufficient that we have men­tioned how they may be compared together in the Julian Account; so that it only remains, that in the mention of Epocha's we only shew how all the Years reckoned from any Period a­gree with some certain year in the Julian Period.

§. 4. The first Year of Dionysius's Christian Of the Princi­ple that Sca­liger followed in instituting the Years of the Julian Pe­riod. Epocha by the consent of all the Latines, had for its Characters 10, the Solar Cycle: 2. the Lunar, 4. the Roman Indiction; which three Cycles being found in no other year of the whole Julian Period, besides 4714, the first of the Christian Aera: Therefore this Dio­nysian Epocha must rightly agree with that year of the Julian Period, and each with each, as Scaliger noted, and as Petavius truly wrote: The Beginning of the Years of Christ, which [Page 134] Men call, the Christian Aera is as it were the Li­mit and Hinge of Chronology, and the common Term in which the Reasoning of all Chronologers meet, as if they are drawn through many Turn­ings and Windings into the same Computa­tion.

§. 5. Whereas the first year of the Julian Period, reckoning back from the true begin­ning An Enquiry whether the System of the Julian Period is sufficient to assign all the Epocha's of the World of all Chronologers. of the World, is 764; it easily appears, that the disagreeing Opinions for many years may commodiously be referred to the Julian Period: Nor is it found amongst those Wri­ters who reckon from the Hebrew and Latin Codices of Bibles that ascends the assigned Epocha of the Creation, ascends beyond the beginning of the Julian Period: But if we examine the Reasons of profane History, and first of all, of the Aegyptian and other Authors, who follow the Numbers of the 70 Interpre­ters, we cannot deny this Period to be insuf­ficient to reconcile all the Disagreements that happen about the Epocha of all the World's Creation till Abraham, the Computation of the Greeks exceeds that of the Latines by more than a thousand years, as shall be shew'd in its Place; for which reason, be­sides that we now mentioned, we call the Julian Period Postulatitious; by means whereof we can commodiously explain those Opini­ons which differ so much from the Hebrew Truth.

§. 6. Let the given Number of years be The Cycle of the Sun, Moon and Iudiction of any Year in the Julian Period being given to find the Dominical Letter, the 1st F [...]a, and the Quantity of the Year. divided by 28, 19, and by 15; look at the Remainders, not at the Quotients, and we have the Character of the Cycle sought: If nothing remains, 'tis the last of the Cycle sought. Afterwards, the Solar Cycle being known, the Dominical Letter, the first Day of the Year, and the Quantity of the Year, are [Page 135] readily found from the last Table, Page 130: For easier Computation in this Matter, we have added the following Table.

§. 7. Cast away the Thousands and Hun­dreds; How it may be known whether any assign'd Year is Bissex­tile er Com­mon. divide the Remainder by 4: If nothing remains 'tis Bissextile: If 1, 2, or 3 remains, 'tis the common Year, and the 1st, 2d, or 3d after a Bissextile.

§. 8. 'Tis necessary by the Praxis in the preceding Section to find the first Day in the How the Cha­racter belong­ing to any given Day in any given Year of the Julian Period may be sound. given Year, and the Quantity of the given Year, if the Day sought be after February; which being known, diminish the Sum by 1, and add it to the Number of the Days, from the beginning of January inclusive; afterwards divide by 7, and the Remainder shews the Day of the Week. For easier Calculati­on the following Table is subjoined; wherein the Days, for any Number of Months are set down.

§. 9. From the compleat Sum of the Bissex­tile How the Cha­racter of the Feria of any Day in a gi­ven Year may be found without know­ing the Solar Cycle. years of Christ, and of the Days of the current Year, subtract Unity; (and for the New Ka­lendar, besides Unity, the other Days that are to be subtracted) divide the Difference by 7, and the Remainder shews the Feria or Day of the Week sought.

§. 10. Observe the Order of the Dominical How the Do­minical Let­ter, which is otherwise known by the Solar Charac­ter in the years of the Julian Period, may without it be found in the years of Christ. Letters in the subjoined Scheme:

By 7 divide the Sum of 5, and of the elapsed Bissextiles of the Year of Christ (whose Sum is known by dividing the Years of Christ by 4) subtract the Remainder from 8, and you have the Dominical Letter in a Bissextile Year to be reckoned from the 6th of the Calends of March; But in the new Kalendar you first sub­tract [Page 137] the Number of Days that are to be sub­tracted.

§. 11. Divide the Number of Days elapsed The manner how the Let­ter answering to any Day in any Year of the Julian Kalen­dar may be readily found. from the Calends of January, and the Remainder is the Number answering to the Letter sought, putting A for 1, B for 2, &c.

§. 12. The chief Use of this System of Time is, that we cannot only assign the Characters of any given year; but also if the Characters be The Cycle of the Sun, Moon and Roman Indiction be­ing given, the corresponding Year in the Julian Period may be thus found. given, we can find the year answering. To do the last, we shall propose two ways: The first is this; The Number of the years of the Solar Cycle being given, subtract from them those of the Lunar (adding 28, if the Subtraction cannot be made with it), multiply the Diffe­rence by 56: Again, take the Sum of this Pro­duct, and that Number from which the Sub­traction was made, and by 532, the Quantity of the Victorian Period) you have the year of the Victorian Period, the difference betwixt this year, and that of the given Indiction divided by 15, and the Remainder multiplied by 1064; the Sum of the Product of the Victorian year found as above (if not exceeding 7980, the Quantity of the Julian Period) will give the year sought.

§. 13. With the Number of the Solar Cycle Or thus. enter the following Table, and under the Cha­racter ☉ take out the answering Numbers; as also under the Character ☽, take the Num­bers answering to the Lunar Cycle, divide the Aggregate of these by 15, subtracting the Remainder from the Number of the given In­diction, add the Difference to the former Ag­gregate; and against the Sum under the Title Indict. is the Year of the Julian Period fought.

§. 14. Altho' we think that the true Use of Of the Obscu­rity of the Julian Period. this System does abundantly compensate for any Difficulty that can occur, and that nothing could be more proper to remove the intricate Perplexities of Chronologers than an Obser­vance of the clear Disposition and evident Rea­sons of its Characters, yet there is one thing we cannot pass by; that if any Person is not pleased with the Use of this Period, he may more commodiously use the Dionysian Aera of Christ, with the years before it began than any other Epocha whatever: For altho' (a) Peta­vius concludes, Ca [...]ebit; qui hanc Periodum omit­ [...]et, praesenti illius fructus, ut per singulorum tri­ [...]n Cyclorum [...]ulus divisi annorum numeri Cyclos corum proprios exhibeant. But this Diffi­culty may be removed if one will observe that these Numbers 9, 1, 3, are to be added to the year of Christ forwards, and the Sums to be divided by 28, 19, 15. But if the years should happen to be before Christ; then let the Sums be divided by the Numbers 28, 19, 5, and subtract the Remainders from 10, 2, 4, assum­ing Circles as oft as is necessary, we have the Characters answering to the year before Christ's Nativity. For Example; to the year of Christ add 4713; or from the year before Christ subtract 4714, the Sum or Diffe­rence gives the corresponding year in the Juli­an Period.

§. 15. Whereas the Sabbatic and Jubilean years How to find the Character. of the Sabbatic Cycle for the Years of the Julian Period. begin not as the Julian do; (for we reckon these from 120, a-clock on the Kalends of January: But those from the 10th Day of the first Autumnal Month Tisri as above) it further appears that any Sabbatic or Jubilean year is concerned with Petavius Lib. 1. c. 4. [Page 140] two years of the Julian Period, with the first in respect of the 3 Months, the latter in respect of 9. This premised, note that to all the year of the Julian Period, considered in respect of the 9, we are to add 6, and divide the Sum by 7, and the Remainder is either [...]o, and then 't [...]s a Sabbatic year; if any, it is the Cycle of the Sabbatic year belonging to the year gi­ven: But if the same Character be sought in respect of the latter Months of the Julias year, omit the Addition of 6, and let the gi­ven Sum of years be divided by 7, and you have it as before. But the Rule of Scaliger in this ^(c) Affair is this; All the Sevens of the Solar Cycle are the 7th Years of the Week; And therefore what year soever shall happen after the next 7 of the Solar Cycle, that is the first year of the legal Week, &c. is to be understood of the years of the Julian Period, considered not in respect of the former but latter Months.

§. 16. Although in the Opinion of the Mystic Chronologer, the way of finding this Chara­cter The manner of finding the Character of the Jubilean Cycle in the years of the Jubilean Pe­riod. in the Julian Period may seem intricate, since the Quantity of the mystic Jubilean year has nothing common with the Quantity of the Julian; yet we shall not deliver a less easie Method of finding the Character of the Julian Cycle; and 'tis that whereby we found before the Character of the Sabbatic Cycle; Therefore to any years of the Julian Period considered here in respect of the 1st 9 Months nearly, add 20 to the Number of the years of the Julian Period, divide the Sum by 49, and the Remainder is either of which always shews the Jubilean year; or else 1, 2. 3, when it shall determine that year [Page 141] in the Jubilean, which the remaining Number expresses.

§. 17. The Ancients thought the Solstices, &c. The Cardinal Times of the Aequinoxes and Solstices are constantly applied to cer­tain days of the Julian Ka­lendar. fixt; and they relate of Sosygenes, that he thought that neither in his nor succeeding A­ges, the Winter Solstices could happen but upon the Calends of January. Thus also the Fathers in the Nicene Council, that the Vernal Aequinox cou'd not recede from the 20th or 21st of March; but the Event shews that both were deceived: For 'tis now evident that the Winter Solstice, with the other Cardinal Times have fallen otherwise.

§. 18. Although very many after different Of finding the time of the Vernal Ae­quinox. ways, were wont to think of a Method how to find the time of the Aequinoxes and Solstices; yet we doubt not but ours which follows is most compendious, easie, certain, and accommo­dated to Chronological Calculations. The Foundation of it, and first of all of the Ta­ble, by whose Help the Computation is per­formed, is twofold: First, it's evident that Ty­cho Brahe at Ween in the year of Christ 1584, observed the Vernal Aequinox on March the 9th, 21 H. 30 M. Afternoon; and that the same Day of Observation was on a Bissextile, 70 D. from the Calends of January; in like manner in the following year 1585, he observed the Ver­nal Aequinox to happen on the 10th day of March, 3 H. 19 M. and in the year 1586, March 10th, 9 H. 8 M. Secondly, ^(d) Longe­montanus thus determined the Quantity of the Tropic Year: The Quantity of the Tropic Year says he, is now more subtilly, and with greater diligence observed by us than any one before to be 365 D. 5 H. 48 M. 58 Sec. the Anticipation be­ing limited and subtracted from the Mean of the [Page 142] Julian Year 365 D. 6 H. &c. From these Hypo­theses we have constructed the following Table, whose Use is this: At the compleat given Year of the Julian Period in which the time of the Vernal Aequinox is sought; take out the Num­bers of Anticipation, and subtract them from a Radix answering to the current year, the time of the Vernal Aequinox is known, reckon'd from Noon-day at Ween.

§. 19. From the time of the Vernal Aequinox, subtract 89 D. 5 H. 40 Min. the Remainder To find the Solstices. is the time of the Winter Solstice, where you must note that in both the present and follow­ing Ages the Winter Solstice does not fall upon the mentioned, but the preceding year; and therefore that a Subtraction may be made, the [Page 144] Days of the preceding year, or at least, of the last Month, are to be added to the Sum from whence you subtract; but if 93 D. 9 H. 15 M. be added to the time of the same Vernal Aequi­nox, the time of the Summer Solstice is had; to which last Sum let 93 D. 9 H. 15 Min. be again added, and you have the time of the Autumnal Aequinox sought; or if immediately you desire to know the Autumnal Aequinox from the Vernal, add to that 186 D. 18H. 30 M. and you have the time of the Autumnal Aequi­nox, which again the following Aequinox mani­fests by adding to the time of the Autumnal 178 D. 11 H. 19 M. &c.

§. 20. Whereas the Tables which Astrono­mers use, begin either from the Epocha of the To find the Characters of the mean, new and full Moons in the Julian Period. World, or that of Christ; and therefore are not universal: Ours shall be fitted to the years of the Julian Period; whereby we can apply all Chrono­logical Characters to all times. The Use of the Tables constructed for this end, is this; Let there be taken out under the Title Rad. P. Jul. the compleat time proposed, and let the correspon­ding Motions of the Moon's Longitude be added thereto, computing 60 Minutes to a Degree, 30 Degrees to a Sign, and 12 Signs to a Circle or one whole Period. If then the N. Moon of any Month is sought, subtract the above Addition from 12 Signs or 360 Days; but if a F. Moon, then from six Signs, assuming a whole Circle to make the Subtraction possible, if need be; if nothing remains, the Character of the Moon's Conjunction which is sought, falls upon the end of the preceding Month; if any thing remains, and that Remainder be 12 D. 11′ 27″, (in which case one Day's Addition is necessary,) or if greater, enter the 4th Table therewith, which is constructed for Days, and there seek the Re­mainder, which if it answers exactly, 'tis done; [Page 145] if not, take the next less and subtract; with the difference enter the 5th Table of Hours, and if need be, proceed to Minutes and Seconds. The Sum of all which, is the time to be reckoned from 12 a-clock at Ʋranburg, the beginning of the Month Current: If for other Places, the difference of Longitude in time must be added or subtracted. But you are to note, 1st, That if the proposed Month be not January, you must first work for the So­lar Cycle of the given Year, by which you may know whether these Motions being taken out, belong to a Bissextile or common Year. 2dly, The N. Moon of one Month being known, that of the next is also known, by adding 29 D. 12 H. 44 Min. or of the preceding, by subtract­ing so much; Wherefore if you take the time of the N. Moon, and want the time of the fol­lowing F. Moon, add 14 D. 18 H. 22′. to the time of the N. Moon; or if by the given F. Moon you would seek out the N. Moon pre­ceding, subtract the same Sum from the known time of the F. Moon; and from hence the Conjunction of the Luminaries being known for any one Month of the Julian Year, they are easily found for any other; and for this the Table Lib. 3. C. 1. will be useful.

§. 21. For the given time of Conjunction How to distin­guish the E­cliptick Con­junctions from the N [...]n-Eclip­tick in the Juli­an Period. under the Title Radix P. Jul. take out the cor­responding Numbers under Motus Latitudinis Lunae, and let the Numbers thus found be ad­ded together; and let the Signs multiplied by 30 be changed into Degrees and added to the rest if any. Further, note that by frequent Observations Astronomers gather, that the So­lar Eclipses happen, when in the time of the N. Moon the mean Motion of the Moon's Latitude is under 12 D. or above 168 D. and below 192 D. or above 348 D. also the Lunar Eclipses do happen when in the time of the Full Moon the mean Motion of the Moon's Latitude is below 17 D. 30′. or above 162 D. 30′. and below 197 D. 30′. or above 342 D. 30′. And although these Notes in finding out the Lunar Eclipses are sufficiently true, yet the Solar are not so certain: For it may happen, tho' seldom, (for certain Reasons) that an Oc­cultation wholly, or (what's more frequent) in a certain Place only, may be hindered; but of this doubtful Momentous Case let the Astrono­mer be consulted.

§. 22. Since those Parts of the Aequator which are Of the Reduc­tion of time f [...]om o [...]e Me­ridian to an [...] ­t [...]er. above and below the Horizon are the vulgar Measure of time, and that the same Point in the Aequator can't ascend or descend at the same time every where, it follows, that it can't be the same Hour of the Day in all Places at once; but the Sun will arise sooner towards the Eastern Parts, and later towards the Western Parts of the World. For Example; if we would compare the Hour of the Day at Ʋ ­ranburg and Jerusalem together, at which Place the Sun rises first, there will be more Hours reckoned. Now a good Watch shews the Jews to be 2 H. 16′. before the Ʋranburgers, in the difference of Meridian; but besides the Jews [Page 152] began their Days different from the Ʋranburgh­ers, viz. at Sun-set, whereas all Europe else be­gin their Political Day from Midnight, and the Mathematicians from Noon; which last Com­putation being observed here, the Jews are 18H. and 2″. adding 16 Min. or is a whole Day, excepting only 3 H. 14′. for generally in all Places by the Satellites of Jupiter, the dif­ference of Longitude in Degrees and Minutes are known, which are easily converted into Time, by allowing 15 Degrees for an Hour, and so on Proportionably.