VIETA. (otherwise given VIET, VIETTE, Or DE VIETTE, and by himself Latinized into VIET/ELIO, FRANcoiS, the most eminent French mathematician of the 16th c., was b. at Fontenai-le-Comte, near La Rochelle, in 1540. Of his early life and education we know nothing, and almost all our acquaintance with the details, meager as they are, of his personal history, is derived from the records of his friend, De Thou (q.v.). Vieta was employed throughout his whole life in the service of the state under Henry III. and Henry IV., and devoted only his hours of leisure to the study of mathematica and other subjects—affording an excellent illustrative argument against the belief that abundant leisure is essential to high eminence, and in favor of the contradictory theory that mental work of whatever sort tends to prepare the mind for any other species of thought-labor. Vieta was a zealous Roman Catholic, and a strenuous supporter of the doctrine of the divine right of kings. His genius and persevering industry broughthim prominently into notice on various occasions. During the war against the Spaniards, the latter, to preserve as much as possible their oeinmunications with their numerous outlying possessions, and prevent the French from profiting by information from inter cepted letters, adopted a species of cipher (see CRYPTOGRAPITY) of more than 500 charac ters, each varying from time to time in its signification. Some specimens being inter cepted, were submitted to Vieta, who after a time discovered a key to the cipher, to the great diScomfiture of the Spaniards, who, incapable of accounting for the discovery otherwise, attributed it to magic; though the story that Vieta was summoned to Rome to defend himself before the pope against the charge of having dealings with the devil may safely be regarded as untrue. V iota's next prominent appearance was an as assailant of the Gregorian calendar, in opposition to which he published (1600) a " true Gregorian calendar," which was with justice consiAered by his contemporaries as inferior to that which obtained the papal sanction. However, V ieta did not, or would not, see his error, and attacked the Jesuit Clavius, to whom the pope had intrusted the compilation of the calendar, in a bitterly abusive manner; displaying, however, such a mastery of knowl edge, that one of Clavius's defenders was led to sympathize with the unfortunate Jesuit who had to withstand the assault of one who was at once a lawyer, theologian, mathe matician, orator, and poet. Vieta, however, is almost exclusively recognized by pos
terity as a mathematician; yet, though worthy to rank among the highest of this class, immediately after such men as Newton and Lagrange, the incessant state of politico religious turmoil in which France was kept during his life, and the fact that all his works printed during his life were set up at his own expense, and distributed among his friends, have hitherto hindered a general recognition of his high merit. The Italian tabulators of the progress of mathematical science have thus had a good opportunity of decking out their national idols (Cardan, especially) with plumes stolen from the obscure French investigator. The claims of Vieta, however, are now becoming more and more generally recognized. He is indisputably entitled tobe considered as the creator of modern algebra, which he established on the footing of a purely symbolical science; lie applied his algebra to the extension of trigonometry, discovered the relations of multiple angles; and he extended the ancient process of extracting square and cube roots to the solution of all equations, an extension which has been since modernized and modified, and now appears as Ikrner's method. Besides, he proved his superior mathematical powers, by solving problems which had puzzled Apollouius, Regiomontanus, etc. ; and was acknowl edged by the mathematicians of Belgium and Italy as their master. Yet, strange to say, his own countrymen, the French, have so little knowledge of the surpassing talents and achievements of Vieta, that, omitting all intelligent mention of his peculiar successes, they ascribe to him praises due to his Italian predecessors, and to his great English suc cessor, Newton. Most of Vieta's works were collected by Schooten, and published by the Elzevirs, at Leyden, in 1646. Two other works of his have been recently discovered, the Harmon icon Cceleste and the Canon 31athematicus, the latter the first table in which the trigonometrical functions of an angle are cr,mpletely given. Of the first, two MSS. exist; while the second was printed and circulated according to Vieta's usual fashion, and has long been a bibliographical curiosity; but neither has yet been published. See Knight's Eng. Cyc. art. "Vieta."