HISTORY OF ARITHMETIC.
As most of the sciences were cultivated, in some measure, before mankind were fully qualified to trace their progress, or appreciate their value, their early i history is either entirely unknown, or involved in doubts and obscurity, beyond which, no diligence of re search can penetrate. This is particularly the case with arithmetic, so that we find it impossible to deter mine, with any degree of accuracy, at what time it was first introduced, much less to what individual the world was indebted for so useful an invention. Nor will this excite our wonder, if we consider the very abstract nature of numerical computation, and the slow and im perceptible steps by which it must have advanced to the dignity of a science. Doubtless, the first notions of property would suggest the necessity of employing some method for denoting quantity, and the similarity. observable between various objects, would give rise to number ; but arithmetic, probably for many ages, con sisted in a very imperfect kind of numeration. It is only in a more advanced state of society, when the in tercourse of man with man is frequent, and commercial transactions are multiplied and extended, that mankind feel the necessity of simplifying and improving the me thods of calculation. Of what use, indeed, would cal culation be to him who has no treasures to count, no complicated relations of number to consider ? Accord ingly, it has been affirmed, that many American tribes are not only ignorant of the operations of arithmetic, but almost totally unacquainted with the first principles of numeration. " Some of them cannot reckon farther than three, and have no denomination for any number above it. Several can proceed as far as ten, others to twenty : when they would convey an idea of a number beyond these, they point to the hairs of their head, in timating that it is equal to them, or with wonder de clare it to be so great that it cannot be numbered." In short, the state of arithmetic among a people, offers a kind of standard for estimating the degree of their in tellectual improvement. See Robertson's Hist. 4nzer. hook iv. p. 91. Locke's Essay on the ffum. Under. book ii. chap. 16. § 6.
The East, which, by the concurring testimony of his tory, and sacred writ, appears to have been the cradle of the human race, seems likewise to have been the quarter of the globe where the light of science first began to dawn. The Chaldeans, the Egyptians, but particularly the different inhabitants of India, distin guished themselves at a very early period by their knowledge of astronomy. Their acquaintance with se
veral periodical appearances of the heavenlr bodies. some of which embraced many ages, was truly astonish ing, and indicates a very advanced state in the art of computation. Wken Alexander the Great entered Ba bylon, the sages of that city already reckoned 430,000 years from the commencement of their astronomical ob servations. (Elenzens de la Philosophic de Newton, par Voltaire.) This is so enormous a period of time, that it has been regarded, perhaps not without reason, as a monument of the vanity of a conquered people, who flattered themselves that in the pretended antiquity of their history, they discovered a consolation for the loss of national independence. But if this period be com pared with the rate of the annual diminution of the in clination of the ecliptic, it will be found, with surprise, to agree nearly with that state of things, when the eclip tic coincided with the equator ; when the seasons were always the same ; and when the days and nights were every where equal over the face of the earth. Such a period was certainly well adapted for an astronomical Rra ; and the people who employed it, whether they ac quired a knowledge of it by tradition, or calculation, must, previously, have made great progress in nume rical science.
At this remote distance of time, however, it is diffi cult to ascertain, who were the real inventors of arith metic, or even to whom we owe its earliest improve ments; but many circumstances induce its to believe that it is of Indian origin. The acuteness and erudition of modern times have made it abundantly evident, that most of the religious rites and opinions of the Greeks, as well as of the Egyptians, were borrowed from the East ; and they are of too capricious a nature to be viewed as accidental coincidences. At any rate, the manner in which the Egyptians account for the first in troduction of arithmetic, renders it probable that they were not its inventors. That people only assume the merit of having first cultivated it : they deemed the in vention of so sublime an art to be above the reach of human ingenuity, and piously believed that it was re vealed to men by the gods. It was a prevailing opinion among them, as we are informed by Plato, that Thcut or Thoth was the inventor of numbers, and geometry. The Greeks probably borrowed from the Egyptians the idea c ascribing to Mercury, (between whom and Theut there is a manifest resemblance,) the superintendence of commerce and arithmetic.