СНА Р. II.

Of the Period of Hipparchus.

RULES.

1. Hipparchus's Period is a Syftem of 204 years, both Lunar and Solar, which being elapfed, the Ancients thought the reckoning by the Lenar Morion would coincide again with the Solar Meafures.

2. Thi: Period comprehends 376 Lunar Months, and 111039 Days.

3. The Sum of these Days arifes from the Multiplication of the Calippic Period, into 4, fubftracting Unity from the Product.

§. I.

TH HE Author who corrected the Computation The Author of Calippus, and invented a new Period, was of this CyHipparchus of Nicea in Bithynia, (according to Stra-clc. bo) or of the Ifland of Rhodes (according to Ptolemy.) He made fuch proficiency in Aftronomy, that Pliny lib. 2. c. 26. calls him, Nunquam fatis laudatus. But whether this was the fame with another famous Aftronomer, who was called Abrahis or Abrachis, according as Lucas Ganricus and fofephus Blancanus thought, you may be informed by the Difputations of Clavius,comment. ad Foan. de Sacrobofco Sphæram.

of the time

that Hip

parchus li

S. 2. The Age of this Aftronomer is fufficiently fixed from his own Ŏbfervations; for he takes notice that a Vernal Equinox in the 3d year of the 151ft Olym- ved in, and piad, hapned upon the 30th of Meffori, which is Octo- published ber the 3d, of the Ful. Period 4552, and on the fol- bis Period lowing years he gives us othe Obfervations; whereof Ptolemy mentions 8; the difference betwixt the firft and the laft being 34 years: Therefore he flourished in the time of the third Punic War; and he gave him

felf

parchus

felf up to this Study from the year 4552, to the year 4586, according to the Julian Account; in which time 'tis indifputable but he must have fixed his Period.

S. 3. He found that the Period of Calippus was laid The reafon too great by a quarter of a Day; fo that 4 Pewhy Hip riods being elapfed, the Moon would come to the old place again in the Solar Calendar, if one day were corrected fubftracted; which he accordingly did Of this AfThe Calip pic Period. fair Longomontanus Daxic. Theor. l. 1.c. 2. p. 171. thus writes: Meto in the Space of 304 years, which elapfed betwixt him and Hipparchus, committed an Error of 5 Days in his Cycle, because he look'd upon the Solar year to be 365 Days; and laid the Periodick Conjunction of the Sun and Moon not fo precifely as it should be, which Calippus thought of, whilft examining an Eclipfe of the Moon 6 years before the Death of Alexander the Great, fo that he corrected Meto, fubftracting one Day in every 4 Cycles; from whence he made his own Period of 76 years: But whereas Calippus himself used the Solar year as confifting of 365 Days; and was likewife out in the courfe of the Moon; Therefore Hipparchus in like manner corrected Calippus, taking from him in 4 Periods or the pace of 304 years, one whole Day, and 'con/equently 5 from Meto in that time. But this Error of one Day committed by Calippus was by Hipparchus imputed altogether to the Solar Tears; and thereupon he fubftracted one intire day from the measure of 304 years; Hence it comes to pass that the measure of the Tropick year 365 days is leffened by Hipparchus by the 300th part of one day; that is, 4, 48"; So that according to him, a Solar year is but 365 D. 5 H. 55'. 12′′.

bis end in

Lis Period.

Hippar §. 4. If according to the Rule of the preceding chus did Tables, you examine this Period, 304 Solar Tropical Hot compus years make 1 1033 D. 15 H. 50' 40". But 3760 Lunations make 1035 D. OH. 37. 24". So that there remains an evident Difparity, and Hipparchus's Error is owing to this, that the quantity of the Solar year was affumed greater than the conftant measures of the Solar Motions require.

Calendar

have

rightly cor

S. 5. The Gregorian Hypothefis is this, That the The AuMoon gets before its former ftations by a whole day, thurs of the not in the space of 394 years as Hipparchus taught, Geo ian but in 312 years; which Cycle of years the Gregohet rian Correctors have fubftituted inftead of that of Hipparchus, hereby acting abfurdly two ways: Firit voted the the Authors of this Cyclic Method have taken away faul of from this Lunar Cycle worfe than any before them, Hi parand without any reafon have took their measures rather chus's Pe from Cycles than Computation: 2dly, nor have they riod. rightly obferved the Laws of the Celeftial Motions for which way foever you calculate, you fhail never make 312 Solar years, and 312 Lunar years, exactly coincide with a conftant perpetual Revolution.

How the

Errors of

the Arci

ents have

§. 6. Those who undertake to correct the LuræSolar Cycles and other Periods of the fame Naru e, feem to me not very unlike thofe who take up Water in a Seive; for both of them lofe their Labour: We ben corcannot fuccefsfully find the Lure-Solar Motions ex rected by cept by Tables built upon Celestial Obfervations, Luna Solar whereby we fully know the Times of the Equinoxes aud Calculati the varieties of the Lunar Phafes. This is the only way ons. to reach the Archives of the Stars; which being neglected by the Emendators of Hipparchus's Period, 'twas impoffible they fhould find any other reconpence for their labour, than that of fubftituting Errors in the room of Errors: So that the Pope himfelf was once amazed when he faw the fems, the Slayers of Chrift, his Colleagues in the Pafchal: And Chriftophorus Clavius was compelled to write to the Eternal Infamy of the reformers of the ancient Periods: Demonftrandum erit Mæftlino in Kal, Greg, al os errores prater quatuor reperi. Oh the folly of the Age! Pray, how many Fall Moons, Pafchals (for 'twas for their fakes that fo much pains were taken, partly in mending, partly in conftituting a-new the Periods of the Ancients) might those little Parafites, while they were nourished 10 years at Rome by Gregory, have computed with a little diligence from the Tables of Celestial Motions, without the ufe of fallatious Cycles and Periods! So that they were able to void many Errors, of which Clement VIII. wrote. foolishly, when he faid, vitari non potuerunt. In fhort there is no Cycle, no Period, however ingeniously contriv'd

contrived, which we can pronounce fufficient to reconcile the Motions of the Sun and Moon by an accurate, useful and perpetual Agreement.

CHA P. III.

Of the Victorian Period.

RULES.

1. The Victorian Period is a Syftem of 532 LunaSolar and Julian years, which being elapfed, the Characters of the Moon fall again upon the fame Day and Feria, and revolve in the fame Order, according to the Opinion of the Ancients.

2. 'Tis otherwife called the great Pafchal Cycle; becaufe the Chriftians firft ufed it to find the true time of the Pafcha or Eafter.

3. The Sum of thefe years arifes from the Multiplication of the Numbers of the Lunar and Solar Cycles, viz. 19 by 28.

The Author S. 1.THO' there were many Victorius's by Name, of this Peas Victorius Pictavienfis, who fuffer'd Marriol. tyrdom under Dioclefian, and another about the year of Chrift 324, who in a Roman Synod affembled in Trajans Baths, was condemn'd because he prefumed to cenfure the Pafchal Cycles received into the Church: Yet the Learned agree, that one Victorius different from the former, and by Nation an Aquitane, was the Author of this Cycle of 532 years. Theophilus and C. Cyrillus computed the times of the Pafcha's for only 95 years: as Dionyfius Exiguus remarks upon both, taying, Pope Theophilus wrote a series of a Century of years, which he Dedicated to Prince Thedofius the Elder; and C. Cyrillus compos'd a Cycle of 95 years in both which performances, they had an inviolable regard to the tradition of the holy Council relating to the fourteen Pafchal Moons. When therefore

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