the different facts which history can furnifh, and by examining the form of the principal cycle which the Egyptians ufed, known by the name of the canicular cycle, we may determine the precife date of the inftitution of the year of 365 days.

In the description which Diodorus makes of the tomb of Ofymandes, King of great Thebes, he speaks of a circle of gold whofe circumference was 365 cubits, and one cubit in breadth. Each of the 365 cubits anfwered, fays he, to a day of the year: they had marked there for each day, the rifing and setting of the stars, with the prognoftic of the times, conformable to the ideas of the Egyptian astrologers. Ofymandes is called Ifmandes by Strabo, who adds, that the prince called Ifmandes by the Egyptians, was the fame as the Memnon who is fo often spoke of by the hiftorians of antiquity, as fovereign of Ethiopia. It is very probable, that Ofymandes, a very warlike prince, had conquered that kingdom *; an event, which may have thrown the ancients into an error. Whatever it be, we find this Memnon in fome lifts of the kings of Egypt'. And we know moreover, that he was extremely revered under that name among the Egyptians. His reign falls about the time of the war of Troy. We may prove this as well from the authority of Homer, of Hefiod, of Pindar, and of Virgil, as by the teftimony of the most ancient monuments, fuch as the coffer of Cypfelides, the throne of the Amyclean Apollo, the ftatues of Lycias, the pictures of Polygnotus, &c. 8. Thus we have been before affured, that,

© L. 1. p. 59. This circle was taken away by Cambyfes, when he made the conqueft of Egypt. Diod. ibid.

d L. 17. p. 1167.

e See Diod. 1. 1. p. 57.

* Ancient infcriptions, of which Tacitus speaks, atteft, that Rhampfes, King of Thebes, had conquered Ethiopia. Annal. I. 2. c. 63.

I should think, that this prince might well be the Ofymandes of Diodorus. We know how much the Greek and Latin hiftorians have disfigured the names of the Egyptians.

f Syncell. p. 72. & 151.

Odyff. 1. 4. v. 188. 1. 11. v. 52t.; Hefiod. Theogon. v. 984.; Pind. Olymp. 2. V. 148.; Pyth. 6. v. 30.; Virgil. Æneid. 1. 1. v. 489.; Pauf. 1. 5. c. 19, & 22, l. 10. c. 31. 1. 3. c. 3.

1.1.3

at

at the time of the war of Troy, the folar year of the Egyptians was of 365 days, and by confequence that the reign of Afeth must have preceded that epoch. But the examen of the cycle that the Egyptians called the caniculary cycle, will furnish us with a much more precife date.

The ancients fpeak very often of the great year of the Egyptians nominated by fome authors the year of God. Cenforinus and many other writers inform us, that this year of God, which fome authors alfo call the heliac year, commenced every 1461 years. It was nothing elfe but a canicular cycle*. We fee very plainly, that they only spoke of the duration of this cycle in the number of 1461 years, fo ill applied by Tacitus for the duration of the life of Phoenix, by Dio to the Roman calendar, and by Firmicus to the general revolution of the planets.

This being granted, we find from the year 1322 before Chrift to the year 139 of the Christian æra, a canicular cycle well attested by the authorities and by the calculations of a number of authors. There is not then any thing farther to be done at present, but to fee if the establishment of the year of 365 days agrees with the commencement of the cycle. For it is evident, that in the times which the Egyptians give for the first time of 365 days for their year, Thoth was canicular, and one of the characters of that first year ought to have commenced with the rifing of the canicular. This is a fact of which we may acquire fufficient proofs, by collecting what is faid by the ancients of the manner in which the Egyptians regulated their years by the rifing of the

The firft month of the Egyptian year was called Thoth. When the heliac rifing of the canicule fell on the first day of the month, they said that Thoth was canicular, and they comprehended under the name of canicular cycle, the time which elapfed from one canicular Thoth to the fucceeding one. That interval was neceffarily 146 Julian years. For the Egyptian year of 365 days being too short by about fix hours, the rifing of the canicule would anticipate a day every four years, and running retrograde all the days of thofe years one after another during four times 365 years, or 1460 years. Thus it was only after 1461 Egyptian years, equivalent to 1460 Julian years, that the heliac rifing of the canicule would return to the first day of the month Thoth, and would commence a new canicular cycle.

Dog

Dog-ftar*. I think then we may fix the inftitution of the year of 365 days to the year 1322 before Chrift +.

The manner in which the Egyptians placed their five intercalary days, was very different from that which we fol low at prefent. They had not diftributed those days in the courfe of a year. Thus, inftead of having as we have equal and unequal months, theirs were all of 30 days each. At the end of the twelve months they placed their five intercalary days following each other, between the laft month of the finishing year and the beginning of the following ‡.

I

By means of this correction, the Egyptians approached very near the exact determination of the folar year. They had found it very near to a quarter of a day. Their aftro ́nomers at last came even to discover that the year precisely of 365 days was too fhort by fome hours of the folar natu ral year. But I doubt if they had attained to this point of precifion in the ages we are now running over.

We only go step by step in the difcovery of truth. The Egyptians began by perceiving the difproportion there was -between the folar year and the lunar year, which had originally ferved them for a rule, as well as all the firft people. They at firft determined this excefs to fix days. Having af terwards found out that this number was not fufficient, they then added five days to their year. But it was not for fome time after the epoch of which we are speaking in this fecond part, that they came to know precisely how much the duration of the folar year exceeded that of the lunar. Their

These people had a particular attention to the rifing of the canicule, whofe appearance announced the overflowing of the Nile; an attention which was one of the principal causes of the progress which they made in aftro nomy.

† I refer for the proof of all that I have just advanced about the epoch of the inftitution of the year of 365 days in Egypt, to the hiftory of the Egyptian calendar, given by M. de la Nauze, in les memoires de l' academie des infcriptions, 1. 14. M. p. 334.

The Mexicans use them in the fame manner; they place their five interçalary days at the end of the year. During thefe five days, which they think have been expressly left out by the ancestors, as void and without being reckoned, they abandon themselves totally to idleness, and only think of lofing, in the most agreeable way poffible, these days which they look upon as fuperfluous. Hilt. de la conquête du Mexique, 1.3. c. 17. p. 554.

obfervations,

obfervations, for the ages we now speak of, had not acquired fufficient juftness to give the exact measure of the annual revolution of the fun from west to east. The Egyptian aftronomers had not then discovered that that ftar takes up more than fix hours befides the 365 days, to return to the fame point of the heavens from whence it went. This fact, is not difficult to prove. It fuffices to recall what I have faid above of the circle of gold placed over the tomb of Ofymandes. That circle, as we have feen, was divided into 365 cubits, each of which answered to a day of the year. Yet the natural year including about the fourth of a day more, it follows, that a circle thus divided into 365 equal parts could not give an exact calendar. For there is no point mentioned where they could have the part reserved for the fourth part of a day, which the true year requires befides the 365 days. Moreover, we do not fee that this fort of calendar was accompanied with any rules which could correct the defect. It is for this reafon, I think, the Egyptians had not difcovered the true duration of the folar year till ages pofterior to those which at prefent engage us,

I

ARTICLE III.

of geometry, mechanics, and geography.

Shall not enlarge much about the progrefs of the Egyptians in the other parts of the mathematics of which I have to speak. I have fhewn in the preceding books, that furveying must have been known very anciently among thofe people. The tributes which Sefoftris imposed upon all the lands of his kingdom, and the manner in which he ordered they fhould be gathered, must have contributed to the advancement of geometry in Egypt. The taxes were proportioned to the quantity of land each inhabitant poffeffed. They had even regard to the diminutions and to the

It is alfo the fentiment of Marfham. See p. 237. i Part 1. book 3. chap. 2. art. 3.

VOL. II.

Kk

alterations

alterations which the Nile might cause each year to the lands over which it extended *. Such an establishment muft, without contradiction, perfect the first practices of geometry, and by a neceffary confequence occafion new discoveries. Moreover, we cannot determine to what degree that science had then been carried in Egypt.

:

Of all the parts of mathematics, mechanics is that which the Egyptians appear to have known beft in the times we are about; indeed there does not remain to us any precife teftimony about the discoveries of these people in mechanics hiftory does not furnish us in that refpect with any lights. But as it is certain that the Egyptians had cultivated geometry in the first times, and that it is by the application of the theories of that fcience to the different queftions which concern motion and the equilibrium, in which consist mechanics properly fo called; there is great room to prefume that these people corrected readily their firft practices, and rectified and fubjected them to fome fixed and conftant methods. It would be difficult enough in reality to conceive, that without any other guide but a blind practice, and destitute of principles, the Egyptians could have elevated on their bafis fuch maffes as the obelisks 1.

ratus

It may be asked, what machines the Egyptians used for fuch works? Were they like ours? Laftly, did they execute thefe grand enterprises with lefs apparel than the celebrated Fontana ufed when he fet up again the fame obelisks by the order of Sixtus V.? That is what we know not how to decide. We only fee that the Egyptians took very extraordinary precautions and measures, to execute fuch like undertakings.

Geography alfo received great increase amongst the Egyptians in the ages which we are now employed about. The

* See Herod. 1. 2. n. 109.

1 See fupra, book 2. chap. 3. p. 132.

Yet we must fay that Zabaglia, who had lately drawn from the earth an obelifk, was abfolutely ignorant of mathematics, and only worked from genius and practice. See Trev. Mai, 1751. p. 1202.; Acad. des infcript. t. 23. mem.

P. 370.

m See fupra, book 2. chap. 3. p. 132.