GEOMETRY, (from the Greek, yewoel-pca, formed of yea or earth, and iterptm, to measure) the doctrine, or science of extension, or things extended, viz, of lines, surfaces, or solids. Geometry has also been defined in general terms as the science of space.

According to Ilerodotus, Strabo, and Diodorus, the Egyptians were the first inventors of geometry, and it is asserted by these ancient writers, that to the annual inunda tions of the Nile, we are to attribute the first steps in this science. That river, in its overflowings, bearing away all the bounds and landmarks of men's estates, mid covering the whole lace of the country, the people were obliged to distin guish their !ands by the consideration of their figure and quantity ; and thus, by experience and habit, they formed to themselves a method, or art, which was the origin of geometry. A farther contemplation of the draughts of figures of fields thus laid down, and plotted in proportion, might, naturally enough, lead them to the discovery of some of their excellent and wonderful properties ; and as these speculations continually improved, so the art gradually improved also, until it attained the perfection of the present day. J osephus, however, seems to attribute the invention to the llebrews ; and ushers, among the ancients, make _Mercury the inventor.

Front Egypt, geometry passed into Greece, being carried thither, as some say, by Thales, where it was much culti vated and improved by himself, Pythagoras, Anaxagoras of Clazomene, Hippocrates of Chios, and Plato. The latter testified his conviction of the necessity and importance of geometry, in order to the successful study of philosophy, by the following inscription on the door of his academy : `• Let no one ignorant of geometry enter here." Plato, con ceiving that geometry was too mean and restricted an appella tion for this science, substituted for it the more extensive name of mensuration ; and others have denominated it pantometry. Other more general and comprehensive appella tions are perhaps more suitable to its extent, especially in the present advanced state of the science ; and accordingly, some have defined it as the science of inquiri»y, inventing, and demonstrating all the affections of the maynitude. feuefus calls it the knowledge of magnitudes and figures, with their limitations ; as also of their rink's, affections, positions, and motions of every kind. About fifty years after Plato, lived

Euclid, who collected together all those theorems which had been invented by his predecessors in Egypt and Greece, mid digested them into fifteen books, intitled the Elements of Geometry ; and those propositions which were nut satisfac torily proved, he more accurately demonstrated. The next to Euclid, of those ancient writers whose works are. extant, is Apollonius Pergleus, who flourished in the time of Ptolemy Euergetes, about two hundred and thirty years before Christ, and about one hundred years after Euclid. The third ancient geometer, whose writings remain, is Archimedes of Syracuse, who was famous about the same time with Apollonius. We can only mention Eudoxus of Cuidus, Architas of Tarention. Philolaus, Eratosthenes, Arista relms of Samos, Dinostratus, the inventor of the quadratrix, lencelinitis, his brother, and the disciple of Plato, the two A nsteuses, Conon, Nieoteles, Leon, Theudius. llernwtintus, and Nicomedes, the inventor of the conchoid ; besides whom there are many other ancient geometers, to whom this science is indebted.

The Greeks continued their attention to geometry, even after they were subdued by the Romans. Whereas the Romans themselves were so little acquainted with this science, even in the most flourishing time of their republic, that they gave the name of mathematicians, as Taeitus informs us, to those who pursued the chimeras of divination and judicial astrology. Nor were they more disposed toeultivate geometry. as we may reasonably imagine, during the decline, and Wier the fall of the Roman empire. The case was different with the Greeks ; among whom we find many excellent geometers, since the commencement of the Christian era, and after the translation of the Roman empire, Ptolemy lived under Marcus Aurelius ; and we have, extant, the works of Pappas of Alexandria, who lived in the time of Theodosius ; the commentary of Eutocins, the Ascalonite, who lived about the year of Christ 540, on Archimedes' mensuration of a circle; and the commentary on Euclid, by Prochis, who lived under the empire of Anastasins.