ters of the Egyptians, before they knew the use of letters. I fhall propofe the conjectures of one of the moft judicious critics of the prefent age, on this question.

Towards the top of moft part of the obelifks, we discover nine perpendicular lines, with fome horizontal lines placed above them. M. Bianchini imagines that these nine lines are numerical characters. This thought was fuggefted to him by. the refemblance he fancied he remarked between these lines, and the difpofition of those which ferve for arithmetical columns, in that table published by Velfer, and in that which the Chinese afcribe to Lixeus. He was confirmed in this opinion by the testimony of the authors I have now mentioned, and of Hermapion and Ammianus Marcellinus. These were the reafons which made M. Bianchini fuppofe that the Egyptians 'ufed thefe lines to exprefs all kinds of numbers .

From one to nine, fays he, there is no difficulty, but to place a ball or point underneath one of the nine perpendiculars, to reprefent fo many pounds of gold, according to the place of that perpendicular, counting from right to left. Suppofe, for example, that the point was under the fifth line, that expreffed five pounds of gold; if it was under the feventh, it expreffed feven. The numbers above nine might be reprefented by means of the horizontal lines placed above the perpendicular. The horizontal lines probably determined the perpendicular ones to fignify tens, hundreds, thousands, &c. inftead of units, according as the number of thefe tranfverfe lines were one, two, three, &c *.

An

La iftoria univ. p. 106. &c.; Effai fur les hierogl. des Egyptiens, p. 612.

note d.

* M. Bianchini proposes some examples to confirm these conjectures. Let us fuppofe, fays he, that the Egyptians had a mind to represent, that a prince undertook an expedition in the seventh year of his reign. They might draw a bee, (the emblem of a king, according to Ammianus Marcellinus), with wings extended, and make it answer to the seventh perpendicular line. If they were to exprefs that Lybia paid yearly 70 pounds of gold, they had only to draw one tranfverfe line, and put a proper fign above the feventh perpendicular. Then the fign which would have expreffed only 7 units without the tranfverfe line, by means of that line would exprefs 7 times ten. By increating in this manner the number of thefe tranfverfe lines, they might exprefs 7 hundreds, 7 thoufands, &c. To fhew that thefe numbers reprefented fo many pounds of gold or filver, they might place under the numerical ign, the hieroglyphic which reprefented gold or filver. The fame may be faid

of

An arithmetic of this kind, compofed of perpendicular and tranfverfe lines, was the origin of the numerical figures both of the Greeks and Romans. Units in the primitive operations were reprefented by lines drawn perpendicular, like the letter I in our alphabet ". There is reafon to believe, therefore, that the Egyptians used these nine lines, which we find on their obelifks, rather than any other kind of characters, to exprefs numbers, especially as we know that the ancients used only thefe two kinds of figns, perpendicular and transverse lines, in arithmetic *.

The Egyptians were not the only people who found means to preserve the refult of their arithmetical operations, without the knowledge of letters. I have fpoke in the preceding book of the quipos of the Peruvians. This was, as we have heard, a kind of fringe, compofed of threads, or cords of different colours, loaded with a certain number of knots. Thefe quipos, by the combinations of their knots and colours, ferved the Peruvians for books, and for regifters of their fubdivifions, taxes, and, in a word, of all their arithmetical operations *. From the monuments of the Mexicans, which are

of the numbers of foldiers, of presents, &c. as also of years, months, days, when they were recording aftronomical obfervations.

The inspection of the obelisks inclines us to think, that these signs were ranged from top to bottom; from whence it will be natural to conclude, that the hieroglyphic writing of the Egyptians was also disposed in this manner, and formed perpendicular columns. This feems very probable; for the Chinese, the greatest part of the people of India, and several other nations, have ob ferved, and ftill obferve this order in the difpofition of their letters. They do not place their words horizontally, as we do, but beginning at the top, they write to the bottom in a straight line. This may be confidered as a relic of hieroglyphic writing.

Bianchini, loco cit. p. 112.

* This confirms what we faid above, that the origin of cyphers or numerical characters was confounded with that of hieroglyphic writing. To this day the Arabian cyphers are real hieroglyphics, and do not represent words but things. For which reason, though the nations which use them speak different languages, i.e. express themselves in different founds, yet these characters excite the ideas of the fame numbers in the minds of all.

* Hift. des In as, t. 2. p. 53.

It is the fame with the negroes on the coast of Juida. They know nothing of the art of writing, and yet they can calculate the largest fums with great facility, by means of cords and knots, which have their own fignification. Hift. gen. des voyages, t. 4. p. 283, 373. & 394.

ftill remaining, it appears, that hieroglyphics were used by that people, both for letters and numerical characters ».

Finally, I do not imagine that the wifeft and most civilized nations had carried their difcoveries in arithmetic beyond the four operations of addition, multiplication, fubtraction, and divifion, in the ages now under confideration. Men are only induftrious in proportion to their wants. The focieties which were formed in the ages immediately after the confufion of tongues and difperfion of families, did not probably derive all the advantage from the arithmetical fymbols they had invented, they might have done. The calculations they had then occafion to make, could not be very extensive. The four firft rules of arithmetic would be fufficient to answer all their purposes. We may even affirm of these first arithmeti cians, that it was rather the use than the fcience of numbers, that they were acquainted with. The invention of these four rules was a great deal for 700 years. We could mention several fciences, which, every thing confidered, have not made fuch rapid progrefs.

(

WE muft never hope to be able to determine with certainty the precife time when men began to study the course of the ftars. The origin of aftronomy, if by this expreffion we understand the first obfervations which were made on the motions. of the heavenly bodies, is loft in the abyss of antiquity. We fee from the facred books, that, in the very firft ages, men must have had fome method of measuring time. The calculation which Mofes gives us of the length of the firft patriarchs lives, and the manner in which he defcribes the circumftances of the deluge, leave us no room to doubt of this. The memory c

Acofta, hift. nat. des Indes Occident. 1. 6. c. 7.

of

VOL. I.

Ff

thefe

these things was undoubtedly preferved by the pofterity of Shem, otherwife Mofes could not have informed us of the facts I have mentioned.

These remains of aftronomical knowledge, however, which might escape the deluge, could not be of much service to the bulk of the defcendents of Noah. I have already reprefented the effects which the confufion of tongues and difperfion of families produced in the several regions of the earth. If the arts perished in thefe tranfmigrations, we have still greater reason to believe that the sciences would be entirely lost. The deluge seems to have swept away every monument of the arts and sciences from all mankind, except Noah, and a few of his defcendents, who continued in the place where that patriarch had fettled after he left the ark.

Neceffity foon obliged the new inhabitants of the earth to Study the course of the stars. The operations of agriculture are regulated by the observation of the feafons. Navigation depends on the motions and revolutions of the heavenly bodies. Nothing but the divifion of time into years, months, &c. could introduce order into the affairs of civil fociety, and diftinguish the seasons deftined to religious folemnities. Men would foon apply therefore to the ftudy of a fcience of such general utility. Yet as there is no science which depends fo much on the length of time as aftronomy, it must have been very long before it arrived at any great perfection.

The nations who were first fettled under a regular form of government, would make the firft improvements in this fcience. The advantages of a fettled ftate and happy situation, would enable them to make the earliest and the greatest progrefs in this kind of knowledge. In Egypt and feveral parts. of Afia, the air is perfectly pure and ferene almoft through the whole year; this gave their inhabitants a favourable op'portunity of contemplating the heavens, and obferving the various motions of the stars, and of repeating the fame obfervations as often as it was neceffary. If mens talents are unfolded in proportion to the opportunities they have of exercising

* Supra, l. I. p. 3.

a Ibid.; Academie des fciences, t. 8. p. 1. & 2.

? Ibidem.

them