BOOK I

OF THE

Moft Celebrated Periods.

CHAP. I.

Of the Period of Calippus.

RULES.

1. The Calippic Feriod is a System of 76 years as well Lunar as Solar; which being elapsed, the reck oning of the Solar and Lunar Motion recurrs, as the Ancients thought, fo that when this Period was finished the Conjunctions of the Sun and Moon hapned again upon the fame day of the Solar year as they were observed to have done before.

2. This Sum of years arifes by the multiplication of 19 (the Metonic Cycle) into 4.

3.The Calippic Period comprehends 48 common years, and 28 intercalatory ones, 940 Lunations, and 22759 days.

of the res S. 1.THE Greeks being advised by their Oracle that fon and ge they ought to Sacrifice by Luna-Solar Times, cifion of the

Calippic

Period,or syliem of 10

as by days, months and years; after various manners of Cycles, as that of 2, 4, 8, 10, 12 years space; in which they committed great Mistakes, the Moon, great a (as we have it in Ariftophanes) complaining out of spice of

1 2

the time

116 the Clouds that the Athenians had no confideration to the Lunar Motions: At length Mero thought of the 19 years Cycle, and publifhed the fame at Athens in the 4th year of the 86th Olympiad; fo that the first year of the Metonic Cycle was the first year of the 87th Olympiad, or the 4282d. of the Fulian Period, Of him Died. Sic, thus writes, When Spartacus King of Bofphorus dy'd, and Seleucus, who Reigned only four years, fucceeded him, there was one Meto, the Son of Paufanias at Athens, famous for Aftrology who on the 13th day of Scirrophorion (an Attic Month) published his Enneadecaterides; for in so many years the Stars return to the fame Places, and as it were, finifh a great year: Therefore this year is by fome called Meto's year; for that Man feems to have followed the Truth in this Prediction and Defcription: And the Stars have their Motions and Significations answerable to it So that very many of the Greeks who follow his Account, even to this time, feem not to have erred. But fince,the Obfervations of fucceeding Times have fufficiently fhewed us, that this Metonic Cycle does not exactly anfwer to the Lunæ Solar Motions; Calippus endeavoured to reform it by a new Period, fubftracting one day from every 4 Cycles.

pus Cy

zicenus was the

§. 2. Calippus Cyzicenus of Myfia, as he is called ThaiCalip by the Antients, (not Cygicenus,as 'tis read in Jofephus Blancanus's Chronology of famous Mathematicians,) was the Author of this Period; tho' after all, Author of Timochares, Ariftyllus, and Pole marchus, who all flouthis new rifhed about that time, confulted with the Author of Period. this Syftem; as upon another occafion, we read that he came with Polemarchus to Ariftotle at Athens upon the Account of fome Opinions of Eudoxus. Ariftotle in his 627 Metaph. Text. 47. makes mention of this Calippus.

Period be.

§. 3. The Period of Calippus began in the Summer The time of that year in which Alexander the Great conquer'd when Ca Darius in a difficult Battle at Arbela, which was in Tipous's the ad year of the 112th Olympiad, or the 4384th of the Julian Period, which is manifeft from Ptolemy 1.7. Almag. cap. 3. Where he refers four of Timocheres's Obfervations to certain years of the firk Calippick Period.

1710

S.4. 'Twas

ferved in

pic Period.

117: S. 4. 'Twas faid above that Cal ppus intercalated 28 The Order times in the space of 76 years; but upon what Account of Interca and in what time he inferted thofe Months, would latory years feem difficult, if Gem nus had not noted that Calip- to be obpus in his new Perio! computed his intercalations af the Calipter the Meronic Cycle: From whofe Teftimony we gather that Calippus intercalated as often as Meto's Cycle requir'd: But we have above fhew'd that Meto's Intercalatory years were 3, 6, 8, 11, 14, 17, 19. Moreover, the first year of the Calipp ck 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 Fulian Period 4282) and of the Calippic Period (in the year of the Fulian Period 4384) Therefore it feems probable to us that the intercalatory years of the Calippick 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.

3. 5. Seventy fix Solar Tropic years, allowing 365 The CalipD. 5 H. 48, 55", to a year, make 27758 D. 9H.57 pic Period 40"; but the days in 940 Lunations are 27758 D. 18 does not ex H. 7', o", fuppofing the quantity of one Lunation toly few be 29 D. 12 H. 44, 3. Now the Sum of 27759 the Agree Days attributed to one Cycle, agrees with neither of ment of the thefe Computations, which is clear evidence of the Luna Solar defect of the Calippick Period. But that the exami Motions. nation of the Cycles and Lunæ Solar Periods may be liable to lefs difficulties, we have thought fit to form the following Tables whofe ufe is very great and obvious.