Euclid (Gr.Euclid 0600605 the most celebrated of ancient geometers, flourished at Alexandria in the reign of the first Ptolemy, about 300 B. C. The Arabic historians give many unauthenticated particulars of his life ;. but it is only certain that he dwelt first in Greece and then in Egypt; and it is probable that he studied at Athens under the successors of Plato, and afterward passed over to Alexandria. There he founded the mathematical school, and was remarkable for his zeal in science, his affection for learned men, and his gentle and modest deportment. Ptolemy having asked him if geometry could not be made easier, he made the celebrated answer that there was no royal road to geometry. To appreciate the merit of Euclid, the state of geometry before him should be considered. Proclus gives the improbable legend that the Egyptians were obliged to invent geometry in order to find again the boundaries of their fields, effaced by the inundations of the Nile. Thence it was brought to Greece by Thales, but it was first raised to a liberal science, and applied to the solution of speculative and theoretical problems, by Pythagoras. Hippocrates was the first to write on elements.

Plato, without writing particularly upon geometry, contributed much to its progress by his use of the analytic method, and by the mathematical stylo of his books; and new theorems were added by numerous lesser philosophers. At the advent of Euclid something had been written on proportion, incommensurables, loci, solids, and perhaps conic sections ; and the important property of the right-angled triangle had been discovered. It was the glory of Euclid to unite in a single book all the discoveries of his predecessors, and to add several new ones of his own. He surpassed all other geometers of antiquity in the clear exposition of his theorems and the rigid order of his demonstrations. The "Elements" of Euclid belong both to geometry and arithmetic. They consist of 13 books written by Euclid, and two others written probably by Hypsicles ; and they may be divided into four parts, of which the first, comprising the first six books, treats of the properties of plane figures, and presents the theory of proportions; the second gives, in the three following books, the general properties of numbers; the third, consisting of the tenth book, is the development of all the power of the preceding ones, and is occupied with a curious and profound theory of incommensurable quantities; and the remaining books are on the elements of solid geometry, and were so much studied among the Platonists as to receive the name of the Platonic. The best known of the treatises of Euclid, after the "Elements," is the "Data." By this name are designated certain known quantities which by means of analysis lead to the discovery of other quantities before unknown.

One hundred propositions are here collected which are the most curious examples of geometrical analysis among the ancients. Newton highly valued them, and Montucla styles them the first step toward transcendental geometry. - The history of the works of Euclid is the history of geometry itself, both in Christian and Mohammedan countries, until after the revival of learning. They were commented upon by Theon and Proclus, and became the foundation of mathematical instruction in the school of Alexandria. Of the numerous editions and commentaries among the Orientals, that of Nasir ed-Din, a Persian astronomer of the 13th century, was the best. The "Elements" were restored to Europe by translation from the Arabic, the first European who translated them being Adelard of Bath, who was alive in 1130, and who found his original among the Moors of Spain. Campanus, under whose name this translation was printed, was for a long time thought to be its author. The Greek text was first published in 1533 by Simon Grynaeus at Basel, and in subsequent editions was corrected by comparison of manuscripts. Since then the work has been published in a great variety of editions, and translated into all the European and many oriental languages.

The English adaptations by Sim-son and Playfair have been widely received as text books in geometry,