Euclid is known to us almost exclusively from those of his works which have survived. Proclus in his commentaries on the first book of the Elements mentions that Euclid lived in the time of Ptolemy I. of Egypt, that he was younger than Plato, but older than Archimedes and Eratosthenes. Hence 300 B.C. may be taken as an approximate date for the middle of his career. He taught in
Alexandria, and probably was the founder of its illustrious mathematical school. His chief extant work is the Elements in thirteen books. Books i.-iv. and vi. treat of plane geometry; v. of proportion in general; vii.-ix. of the properties of numbers; x. of incommensurable magnitudes; xi.-xiii. of solid geometry. Besides the Elements, there are the Data, a collection of geometrical theorems, and the Phenomena, or appearances of the heavens. Regarding the genuineness of the Section of the Scale, Introduction to Harmony, Optics, Catoptrics, and Divisions of Superficies, commentators are divided in opinion, though they lean rather to the view that most if not all of these writings are spurious. Some other works not now extant are attributed to Euclid. The only one of any importance was the treatise on Porisms. Euclid's Elements has been translated into many languages, and is probably better known than any other mathematical book. With many of its blemishes removed and its deficiencies supplied, it is still widely used in Britain as a text-book of geometry, though attempts have been made for the last 150 years to supersede it. On the Continent it has been almost universally given up, as in America; and after a few years, should secondary education come under state control, it will probably share the same fate in Britain also. Already one united attempt to supplant Euclid was made by the Association for the Improvement of Geometrical Teaching, but their syllabus of geometry and corresponding handbook have as yet failed to command any wide respect. See C. L. Dodgson's Euclid and his Modern Rivals (1879). The first printed edition of Euclid was a translation from Arabic into Latin, which appeared at Venice in 1482. The first printed Greek text was published at Basel in 1533. The most recent edition is that of Heiberg in five volumes (1883-88). The only edition which contains all the works attributed to Euclid is that by David Gregory, which appeared at Oxford in 1703. For an account of what the Greeks had done in geometry before Euclid's time, see Allman's Greek Geometry from Thales to Euclid (1889).