Euclid

Euclid (Eukleidēs), Greek mathematician, who lived in Alexandria c.300 BC, but of whose birthplace and life nothing reliable is known. His fame rests on his great textbook, Stoicheia (‘elements’): books 1–4 and 6 on plane geometry, 5 on proportion, 7–9 on arithmetic and the theory of rational numbers, 10 on irrationals, 11–13 on solid geometry; books 14 and 15 are not by Euclid. This work caused the name ‘Euclid’ to become almost synonymous with ‘geometry’. One of the few anecdotes told about him says that when Ptolemy I of Alexandria asked him if there was a shorter way to understand geometry than that of the Elements, he replied that there was no ‘royal road’ to geometry. His work drew extensively on the discoveries of his predecessors, but its great value lies in its rigorous exposition of the geometrical knowledge acquired by the Greeks from the time of Pythagoras, arranged systematically and in logical sequence. As soon as it was published Euclid's textbook became the subject for study and comment, and the edition (or reworking) of Theon (fourth century AD) was widely used; most valuable is the commentary of Proclus (fifth century AD) on book 1.

In western Europe Euclid's work suffered the common fate of Greek science and mathematics, being known only to the Arabs until in the first half of the twelfth century an Englishman, Adelard of Bath, translated the Arabic version of the Elements into Latin. (See TEXTS, TRANSMISSION OF ANCIENT 7). The original Greek was not generally known until a text was printed at Basle in 1533. The vernacular translations date from the middle of the sixteenth century; although in Europe geometrical textbooks gradually incorporated modern advances in the subject, in Britain the Elements held their ground more or less unadulterated until the end of the nineteenth century. Euclid seems to have been the source of the words put at the end of mathematical proofs, in Greek, hŏper edei deixai, ‘which was to be proved’, but usually known in the Latin version, q (uod) e(rat) d(emonstrandum). He wrote a number of other mathematical works, some of which survive in Greek and others in the Arabic translations only. He also wrote a treatise on music, still extant.