EUCLID OF ALEXANDRIA, Greek mathematician : fl. about 300 a.c., taught geometry at Alexandria in the reign of Ptolemy (323-285 ac.), and extended the boundaries of mathematical science. The severity and ac curacy of his method have never been surpassed. There is very little known regarding his life, Proclus (412-485 A.D.) forming the chief source for our information. His chief work, rarroixeia, is known as and has formed for many generations the principal introduction to the study of geometry. It consists of 13 books, though some editions contain two additional books, which, however, are almost without doubt not the work cf Euclid. There also have been preserved six other works : 'Intro duction to Harmony,' 'Section of the Scale,' 'Phenomena,) 'Optics) and Catoptrics.' Con cerning some of these, however, it is doubtful whether Euclid was the author or not. Even more doubtful is the authorship of some frag ments sometimes ascribed to him. From quo tations, etc., it has been well established that he wrote four other works of which, however, nothing is in existence now : three books on 'Porism,> two books on 'Curves,) four books on 'Conic and one book on 'Fallacies.) The 'Elements) have come to us indirectly through the Arabs who made a number of trans lations of which, however, only one, made in the 13th century has been printed (Rome 1594). It is claimed that the first retranslation into Greek from Arabic was made by Adelard of Bath in the 12th century. On this there was based the first printed Greek edition edited with comments by Campanus of Novara (Venice 1482), which, however, is not very reliable. The
first translation into Latin, made by B. Zam berti, was published in Venice (1505). The first reliable Greek text was printed in Basel (1533) and edited by S. Grynaeus. Other editions were brought out by D. Gregory (Greek and Latin, Oxford 1703) ; F. Peyrard (3 vols., Paris 1814-18) ; E. F. August (two parts, Berlin 1826-29) ; T. L. Heath (3 vols., Cambridge 1908). His complete works have been edited by M. Curtze (Leipzig 1899) and by J. L. Heiberg and H. Menge (Leipzig 1883 96). There have also been many translations into almost all the modern languages. The first English translation was made by H. Bil lingsley (London 1570) ; the first French by D. Henrion (Paris 1615) ; the first German by J. Scheybl (Augsburg 1555). There are also a large number of commentaries, almost every new editor for many years feeling it his duty to attempt a new and original, and, therefore, in many cases useless commentary. Consult Anon., 'The Elements of Euclid) (in Dublin Review, Vol. XI, p. 330, London 1841) ; Dodg son, C. L., 'Euclid and His Modern Rivals' (London 1879) ; Heiberg, J. L., 'Litteratur geschichtliche Studien fiber Euklid> (Leipzig 1882) ; Hultsch, F., (in Pauly Wissowa, 'Real-Encyclopadie der classischen Altertumswissenschaft,' Vol. VI, Stuttgart 1907) ; Riccardi, P., di una Biblio grafia Euclidea> (four parts, Bologna 1887-90) ; Smith, T., 'Euclid: His Life and System) (New York 1902).