GEOMETRY is that branch of mathematics which treats of the properties of extension and figure. The name is de rived from yreolhereice, the science of land measuring.
There is a certain degree of geometrical knowledge, which naturally arises out of the wants of man, in every state of society. It is impossible to build houses and tem ples, or to apportion territory, without employing some of the principles of geometry. Hence we cannot expect to find a period of society, or a country, in which it was alto gether unknown.
Ancient writers have generally supposed that it was first cultivated in Egypt ; and, according to some, it derived its origin from the necessity of determining every year the just share of land that belonged to each proprietor, after the waters of the Nile, which annually overflowed the country, had returned into their ordinary channel. It may however be remarked, that the obliteration of the land marks, by the inundation, is quite a conjecture, and not a very probable one.
Some writers, among whom is Herodotus, fix the origin of geometry at the time when Sesostris intersected Egypt by numerous canals, and divided the country among the in habitants. Sir Isaac Newton has adopeed this opinion in his chronology, and has supposed that this division was made by Thoth, the minister of Sesostris,.who, according to him, was the same as Osiris; and this conjecture is supported by some ancient authorities. Aristotle has how ever attributed the invention to the Egyptian priests, who, living secluded from the world, had leisure for study. Thus, various opinions have been entertained respecting the origin of geometry, but all have agreed in fixing it in Egypt.
The celebrated philosopher, Tholes of Miletus, trans planted the sciences, and particularly mathematics, from Egypt into Greece. He was born about 640 years before Christ, and being unable to gratify his ardent desire for knowledge at home, he travelled into Egypt, at an advan ced period of life, where he conversed with the priests, the only depositories of learning in that country. Diogenes
Laertius relates, that he measured the height of the pyra mids, or rather the obelisks, by means of their shadow ; and Plutarch says, that the king Amasis was astonished at this instance of sagacity in the Greek philosopher; which is a proof that the Egyptians had made but little progress in the science. It is also stated by Proclus, that Tholes employed the principles of geometry to determine the dis tance of vessels remote from the shore. On his return to Greece, his celebrity for learning drew the attention of his countrymen: he soon had disciples, and hence the founda tion of the Ionian school, so called from Ionia, his native country.
There were some slight traces of what may be called natural geometry in Greece, before the time of Tholes: Thus, Euphorbus of Phrygia is said to have discovered some of the properties of a triangle ; the square and the level have been ascribed to Theodorus of Samos ; and the compasses to the nephew of Daedalus. But these can only be considered as a kind of instinctive geometry ; the origin of the true geometry among the Greeks must be fixed to the period of the return of Tholes. It was he that laid the foundation of the science, and inspired his countrymen with a taste for its study ; and various discoveries are attributed to him concerning the circle, and the comparison of trian gles. In particular, he first found that all angles in a semi circle are right angles; a discovery which is said to have excited in his mind that lively emotion, which is perhaps only felt by poets and geometers : he foresaw the import ant consequences to which this proposition led, and he ex pressed his gratitude to the muses by a sacrifice. This, however, is but a small part of what geometry owes him ; and it is much to be regretted that the loss of the ancient history of the science should have left us in uncertainty as to the full extent of the obligation.