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Dog-star *. I think then we may fix the institution of the year of 365 days to the year 1322 before Christ t.

The manner in which the Egyptians placed their five in. tercalary days, was very different from that which we follow at present. They had not distributed those days in the course of a year. Thus, instead of having as we have equal and unequal months, theirs were all of 30 days each. At the end of the iwelve months they placed their five intercalary days following each other, between the last month of the finishing year and the beginning of the following 1.

By means of this correction, the Egyptians approached very near the exact determination of the solar year. They had found it very near to a quarter of a day. Their astronomers at lait came even to discover that the year precisely of 365 days was too short by some hours of the folar natural year. But I doubt if they had attained to this point of precision in the ages we are now running over.

We only go step by step in the discovery of truth. The Egyptians began by perceiving the disproportion there was between the solar year and the lunar year, which had originally ferved them for a rule, as well as all the first people. They at first determined this excess to fix days. Having afterwards found out that this number 'was not sufficient, they then added five days to their year. But it was not for some time after the epoch of which we are speaking in this second part, that they came to know precisely how much the dura. tion of the solar year exceeded that of the lunar. Their

These people had a particular attention to the rising of the canicule, whose 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.

t 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 history of the Egyptian calendar, given by M. de la Nauze, in les memoires de l' academic des inscriptions, 1. 14. M. p. 334.

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

observations,

observations, for the ages we now speak of, had not acquired sufficient justness to give the exact measure of the annual revolution of the sun from west to east. The Egyptian astronoiners had not then discovered that that star takes up more than fix hours besides the 365 days, to return to the same point of the heavens from whence it went. This fact. is not difficult to prove. It suffices to recall what I have faid above of the circle of gold placed over the tomb of Osymandes. That circle, as we have seen, 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 besides the 365 days. Moreover, we do not see that this fort of calendar was accompanied with any rules which could correct the defect. It is for this reason, I think, the Egyptians had not discovered the true duration of the solar year ull ages posterior to those which at present engage usb,

ARTICLE III,

of geometry, mechanics, and geography,

I

Shall not enlarge much about the progress of the Egyp

tians in the other parts of the mathematics of which I have to speak. I have shewn in the preceding books, that furveying must have been known very anciently among those people i. The tribuies which Sesostris imposed upon all the lands of his kingdom, and the manner in which lie ordered they should be gathered, must have contributed to the advancement of geoinetry in Egypt. The taxes were proportioned to the quantity of land each inhabitant polfelled. They had even regard to the diminutions and to the

} It is also the sentiment of Marmam. See p. 237,
i Part 1. book 3. chap. 2. art. 3.
Vol. II.

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alterations which the Nile might cause each year to the lands over which it extended . Such an establishment must, without contradiction, perfect the first practices of geometry, and by a necessary consequence occasion 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 best in the times we are about ; indeed there does not remain to us any precise testimony about the discoveries of these people in mechanics : history does not furnish us in that respect with any lights. But as it is certain that the Egyptians had cultivated geometry in the first times, and that it is hy the application of the theories of thật science to the different questions which concern motion and the equilibrium, in which consist me. chanics properly so called; there is great room to presume that these people corrected readily their first practices, and rectified and subjected them to some fixed and constant 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 basis such masses as tlie obelisks!.

It may be asked, what machines the Egyptians used for such works? Were they like ours? Lastly, did they execute these grand enterprises with less apparet than the celebrated Fontana used when he set up again the same obelifks by the order of Sixtus V.? That is what we know not how to decide. We only see that the Egyptians took very extraordinary precautions and measures, to execute fuch like undertakings m;

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

} See Herod. 1. 2. n. 109.
* See supra, book 2. chap. 3. p. 132.

Yet we must say that Zabagliż, who had lately drawn from the earth an obelisk, was absolutely ignorant of mathematics, and only worked from genius and practice. See Trev. Mai, 1751. p. 1232.; Acad. des infcript. t. 23. mein. p. 373. na See fupra, book 2. chap. 3.p. 132.

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vast conquests of Sefoftris contributed greatly to the progress of that science. That monarch applied himself to have a map made of all the countries which he had gone over. He did not content himself with having enriched Egypt with his geographical productions ; he had still a further care to make them disperse copies even into Scythia, from a defire to make his name go into the most distant climatest.

The memory of these maps of Sefoftris was perfectly well preserved in antiquity. In the poem composed by Apollonius Rhodian on the expedition of the Argonauts, Phineas King of Colchis predicted to those heroes the events which thould accompany their return. Aigus, one of the Argonauts, explained that prediction to his companions, told them that the route which they must keep was described on tables, or rather on columns which an Egyptian conqueror had before left in the city of Oea, capital of Colchis. He adds, that the whole extent of the roads, the limits of the earth and the sea were marked on these columns for the use of travellers The scholiast of Apollonius calls the Egyptian monarch Sefonchosis, of whom mention is made in this passage: but he observes that many authors also called him Sefoftris p. We know moreover, that this prince had conquered Colchis, and that he had even lest there a colony 4.

For the rest we ought not to be furprised that geography made so great a progress in Egypt. At all times the learned of that nation had made it a particular study. That science was one of those to which the priests particularly applied themselves r.

I could yet speak more largely about the geographical knowledge of which we find so many proofs in the writings of Moses. I have already spoken of it in the first part of this work. The division of the land of promise begun hy Moses, and finished under Joshua, gives a very perfect te. stimony of the progress which geography had made at that

o Eust. in fine epift. ante Dionys. Perieg.
• L. 4. V. 272. &c. p Ibid. ad verf. 272.
4 Herod. 1. 2. n. 103. & 10.4. r Clem. Alex. strom. 1. 6. p. 757.
Book 3. chap, 2. P. 258.

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time. We cannot help being struck when we read in the Bible the circumstances and the detail of that division. That fact alone will suffice to convince us of the antiquity and af. siduity with which certain people had applied to geograpby. The degree to which we shall see that this science was carried in the time of Homer, will be sufficient to give us a complete proof of it. I shall give an account of it in the third part.

In treating of the article of sciences among the Egyptians, we must not forget one circumstance which does honour to there people. It was among them that we find the example of the most ancient library spoken of in history. Among the number of buildings with which the superb tomb of Ofymandes was accompanied, there was one which con. tained the sacred library. One read above it this inscrip tion, The remedies of the fouil,

CHAP. III.

Of Greece.

Here is scarce any nation which has not pretended to

in the first part of this work, to what degree this pretension might be depended upon. It is certain, that each people has had notions about the first practices which have given birth to arts and sciences. But it is equally true that these first notions were readily perfected in certain countries, while in others the people remained a long time confined to those gross practices which we ought not to honour with the name of sciences; perhaps even these nations would never have at. tained to more elevated theories, if they had not been instructed by colonies which came from countries more en

* Dent. chap. 3. v. 12.; Jos. chap. 13. & chap, 18.

a Diod. 1. 1. p. 58. See what I have said of this monarch, book 3. chap. 2. art. 2. P. 255. 1 Diod. loco cit.

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