EUCLID OF ALEXANDRIA. A writer who has given his own name to a science cannot be fairly treated of in any other place than its history. We shall therefore devote tho present article to such an imperfect sketch of the early progress of tho science of geometry as its meagre history, combined with the narrowness of our limits, will allow.
There is a stock history of the rise of geometry, supported by the names of Strabo, Diodorus, and Proclue, namely, that the Egyptians, having their landmarks yearly destroyed by the rise of the Nile, were obliged to invent an art of land-surveying in order to preserve the memory of the bounds of property—out of which art geometry arose. This story, combined with another attributing the science directly to the gods, forms the first light which we have on the subject, and both in one are worthily sung by the poet who figures at the bead of an obsolete English course of mathematics : "To teach weak mortals property to seen, Down came Geometry and form'd a plan." There is no proof whatever that the Egyptians were more of geometers than of astronomers, and the supposition that the rise of the Nile obliged the builders of the Pyramids to make new landmarks once a year, requires at least contemporary evidence to make it history. At the same time, the question of the actual origin of geometry is n very difficult one, and any conclusion can only be of very moderate probability.
Among the Chinese the Jesuit missionaries found very little know ledge of the properties of space: a few rules for mensuration, and the famous property of the right-angled triangle, being all that they could ascertain. Of all the books which Gaubil could find professing to be written before tic. 206, there is only one which contains anything immediately connected with geometry. From this writing (called Tcheou-pey ') it is not very certain whether the Chinese posse sod the property of the right-angled triangle generally, or only one parti cular cue, namely, when the sides are 3,4, and 5; and noosing appears which directly or indirectly resembles demonstration. Tile Hindoos produce a much larger body of knowledge, but of uncertain date. The works of Bmhmegupta and Bhaacara, of the 7th and 12th ceuturica of the Christian era (according to Colebrooke), contain a system of arithmetical mensuration which is certainly older than the compilors mentioned, and in which the property of the right-angled triangle is made to produce a considerable number of results; for instance, the method of finding the area of a triangle of which the three aides are given. By a figure drawn on tho margin of some manuscripts, it
appears that a demouetration of the property in question had been obtained. The circumference of the circle is given as bearing to the diameter the proportion of 3927 to ]250 by the later writer, being exactly that of 3.1416 to 1. Brahmegupta takes the proportion of the square root of 10 to 1, or 316 to 1. The superior correctness of the later writer could not have arisen from tiny intermediate commu uication with Europe, since the truo ratio was not known so near am 3'1416 till after the l2th century; and the Persians (as appears by the work of Mohammcd-ben-Musa) had adopted this ratio from the Ilindoces, before the discovery of an equally exact retie in Europe. We shall enter into more details on this subject in the article Vio ()ANITA, merely observing that though no date eau be fixed to the commenceineut of geometry in India, yet the certainty which we now have that algebra and the decimal arithmetic have come from that quarter, the recorded visits of the earlier Greek philosophers to Ilin dustln (though we allow weight rather to the tendency to suppose that philosophers visited India, than to the strength of the evidence that they actually did so), together with the very striking proofs of originality which abouud in the writings of that country, make 1; essential to consider the claim of the Ilinduoe, or of their predecessors, to the invention of geometry. That is, waiving the question whether they were Hiudeoe who invented decimal arithmetic and algebra, we advance that the people which first taught those brauchos of science is very likely to have been the first which taught geometry ; and again, *mein that we certainly obtained the former two either from or nt least through India, we thiuk it highly probable that the earliest European geometry came either from or through the 8.1`00 country.