GEOMETRY, HISTORY or. The origin or geometry is ascribed by Herodotus to the Egyptians, who, in consequence of the inunda tions of the Nile, which carried away all their landmarks, were under the necessity of distin guishing and laying out their lands by the consideration of their figure and quantity, whence the word in the Greek sig nifies literally land-measuring. The Greeks, who cultivated this science more than any other people, doubtless learned the rudiments from the Egyptians ; for Thales, who travel led into Egypt and acquired a sufficient know ledge of astronomy to calculate, must also have first become acquainted with the princi ples of geometry to assist him in his astro nomical inquiries. Pythagoras, the pupil and friend of Thales, distinguished himself by his discoveries in arithmetic, as well as geometry. He invented the multiplication table, called' after him the Abacus Pythagoricus ; and in geometry he discovered the thirty-second and forty-seventh propositions in the first book of Euclid's Elements. Soon after this flourished Anaximander, Anaximenes, Anaxagoras, Cle ostratus, /Enopides, and Zenodorus, all cele brated geometrician; of whose works nothing, remains except of the last. They were suc ceeded by Hipparchus, who rendered himself celebrated by the quadrature of the lines called after him, as also by his attempt at the qua drature of the cube, which was a matter of great interest the ancient mathemati cian; and is said to have taken its rise in an answer of the oracle at Delphi, which, when consulted on the occasion of some public ca lamity, answered, Double the altar,' which was an exact cube. Notwithstanding the failure of Hipparchus, others renewed the attempt, which, although it proved unsuccess ful as to that particular object, nevertheless is said to have led to the discoveries of other geometrical properties, as the conchoid of Ni comedes the cissoid of Diodes, and the qua dratrix of Dinostratus. This latter geometri cian was the follower and friend of Plato, whose devotion to the science of geometry was such that he caused it to be inscribed over the door of his school, Let no one enter here who is ignorant' of geometry.' To Plato we are indebted for that branch of geometry known by the name of conic sec tions, of which his scholar, Aristeus, is said to have composed five books that are highly spoken of by the ancients, but are not now ex tant. Eudoxus and Menechemus were also
disciples of Plato, and distinguished them selves, the former in geometry as well as as tronomy, the latter by, his application of conic sections to many problems. After an interval of ninety years from their time, that is, about three hundred years before Christ, flourished Euclid, who, by, collecting and methodizing all the principles of geometry then known into a regular system, called his Elements of Geometry, secured to himself a celebrity which, in point of extent, has never been sur passed, and perhaps scarcely ever equalled, his work having ever since been considered as I the standard of all geometrical knowledge. Euclid was quickly followed by Archimedes, a mathematical genius, who added many dia 1 coveries to the sciences of geometry, mechanics, optics., and hydrodynamics. In geometry he discovered the ratio between the sphere and the circumscribing cylinder, found the quadra ture of the parabola, and the solidity of its co noid ; he invented the spiral which bears his name, and discovered its rectification besides a variety of other important geometrical propo sitions, many of which are extant, and attest the skill and ingenuity of the author.
Apollonins, of Perga, who, from his wri tings, acquired the name of the Great Geome trician, flourished about thirty years after Ar chimedes. His work on the Conic Section; which is the principal piece of his extant, was in all probability the hest of its kind in that day, and has since been the groundwork of all. works published on that subject Of those who after Apollonius distinguished in their time in the cultivation of the geome trical science, there are but few who added any thing worthy of particular notice. Era tosthenes attempted to measure the circumfe rence of the earth ; Ctesibius invented water pumps ; Hero of Alexandria, clepsydrae; Theodosius, who lived in the first century of the Christian era, wrote a treatise on the sphere, which was one of the first on spherical trigonometry.