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VIETA (or VIETE), FRANCOIS, SEIGNEUR ...

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Originally appearing in Volume V28, Page 58 of the 1911 Encyclopedia Britannica.
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VIETA (or VIETE), See also:FRANCOIS, SEIGNEUR DE LA BIGOTIERE (1540-1603)  , more generally known as FRANCISCUS See also:VIETA, See also:French mathematician, was See also:born in 1540 at Fontenay-le-See also:Comte, in See also:Poitou . According to F . See also:Ritter,' Vieta was brought up as a See also:Catholic, and died in the same creed; but there can be no doubt that he belonged to the See also:Huguenots for several years . On the completion of his studies in Iaw at See also:Poitiers Vieta began his career as an See also:advocate in his native See also:town . This he See also:left about 1567, and somewhat later we find him at See also:Rennes as a councillor of the See also:parlement of See also:Brittany . The religious troubles drove him thence, and See also:Rohan, the well-known See also:chief of the Huguenots, took him under his See also:special See also:protection . He recommended him in 158o as a " maitre See also:des requetes " (See also:master of See also:requests) ; and See also:Henry of See also:Navarre, at the instance of Rohan, addressed two letters to Henry III. of See also:France on the 3rd of See also:March and the 26th of See also:April 1585, to obtain Vieta's restoration to his former See also:office, but without result . After the See also:accession of Henry of Navarre to the See also:throne of France, Vieta filled in 1588 the position of councillor of the parlement at See also:Tours . He afterwards became a royal privy councillor, and remained so till his See also:death, which took See also:place suddenly at See also:Paris in See also:February 1603, but in what manner we do not know; See also:Anderson, the editor of his scientific writings, speaks only of a " praeceps et immaturum autoris fatum." ' Bolletino Boncompagni (See also:Rome, 1868), vol. i. p . 227, n . 1 . We know of one important service rendered by Vieta as a royal officer .

While at Tours he discovered the See also:

key to a See also:Spanish See also:cipher, consisting of more than 5oo characters, and thenceforward all the despatches in that See also:language which See also:fell into the hands of the French could be easily read . His fame now rests, however, entirely upon his achievements in See also:mathematics . Being a See also:man of See also:wealth, he printed at his own expense the numerous papers which he wrote on various branches of this See also:science, and communicated them to scholars in almost every See also:country of See also:Europe . An See also:evidence of the See also:good use he made of his means, as well as of the kindliness of his See also:character, is furnished by the fact that he entertained as a See also:guest for a whole See also:month a scientific adversary, Adriaan See also:van Roomen, and then paid the expenses of his See also:journey See also:home . Vieta's writings thus became very quickly known; but, when Franciscus van Schooten issued a See also:general edition of his See also:works in 1646, he failed to make a See also:complete collection, although probably nothing of very See also:great value has perished . The See also:form of Vieta's writings is their weak See also:side . He indulged freely in flourishes; and in devising technical terms derived from the See also:Greek he seems to have aimed at making them as unintelligible as possible . None of them, in point of fact, has held its ground, and even his proposal to denote unknown quantities by the vowels A, E, I, 0, U, Y—the consonants s, C, &c., being reserved for general known quantities—has not been taken up . In this See also:denotation he followed, perhaps, some older contemporaries, as See also:Ramus, who designated the points in geometrical figures by vowels, making use of consonants, R, S, T, &c., only when these were exhausted . Vieta is wont to be called the See also:father of See also:modern See also:algebra . This does not mean, what is often alleged, that nobody before him had ever thought of choosing symbols different from numerals, such as the letters of the See also:alphabet, to denote the quantities of See also:arithmetic, but that he made a general See also:custom of what until his See also:time had been only an exceptional See also:attempt . All that is wanting in his writings, especially in his Isagoge in artem analyticam (1591), in See also:order to make them look like a modern school algebra, is merely the sign of equality—a want which is the more striking because See also:Robert See also:Recorde had made use of our See also:present See also:symbol for this purpose since 1557, and See also:Xylander had employed See also:vertical parallel lines since 1575 .

On the other See also:

hand, Vieta was well skilled in most modern artifices, aiming at a simplification of equations by the substitution of new quantities having a certain connexion with the See also:primitive unknown quantities . Another of his works, Recensio canonica effectionum geometricarum, bears a See also:stamp not less modern, being what we now See also:call an algebraic See also:geometry—in other words, a collection of precepts how to construct algebraic expressions with the use of See also:rule and See also:compass only . 'While these writings were generally intelligible, and therefore of the greatest didactic importance, the principle of homogeneity, first enunciated by Vieta, was so far in advance of his times that most readers seem to have passed it over without adverting to its value . That principle had been made use of by the Greek authors of the classic See also:age; but of later mathematicians only See also:Hero, See also:Diophantus, &c., ventured to regard lines and surfaces as See also:mere See also:numbers that could be joined to give a new number, their sum . It may be that the study of such sums, which he found in the works of Diophantus, prompted him to See also:lay it down as a principle that quantities occurring in an See also:equation ought to be homogeneous, all of them lines, or surfaces, or solids, or supersolidsan equation between mere numbers being inadmissible . During the three centuries that have elapsed between Vieta's See also:day and our own several changes of See also:opinion have taken place on this subject, till the principle has at last proved so far victorious that modern mathematicians like to make homogeneous such equations as are not so from the beginning, in order to get values of a symmetrical shape . Vieta himself, of course, did,not see so far as that; nevertheless the merit cannot be denied him of having indirectly suggested the thought . Nor are his. writings lacking in actual inventions . He conceived methods for the general See also:resolution of equations of the second, third and See also:fourth degrees different from those of Ferro and See also:Ferrari, with which, however, it is difficult to believe him to have been unacquainted . He devised an approximate numerical See also:solution of equations of the second and third degrees, wherein Leonardo of See also:Pisa must have preceded him, but by a method every vestige of which is completely lost . He knew the connexion existing between the See also:positive roots of an equation (which, by the way, were alone thought of as roots) and the coefficients of the different See also:powers of the unknown quantity . He found out the See also:formula for deriving the sine of a multiple See also:angle, knowing that of the See also:simple angle with due regard to the periodicity of sines .

This formula must have been known to Vieta in 1593 . In that See also:

year Adriaan van Roomen gave out as a problem to all mathematicians an equation of the 45th degree, which, being recognized by Vieta as depending on the equation between See also:sin 4 and sin x/45, was resolved by him at once, all the twenty three positive roots of which the said equation VIGEE-See also:LEBRUN was capable being given at the same time (see See also:TRIGONOMETRY) . Such was the first encounter of the two scholars . A second took place when Vieta pointed to See also:Apollonius's problem of taction as not yet being mastered, and Adriaan van Roomen gave a solution by the See also:hyperbola . Vieta, however, did not accept it, as there existed a solution by means of the rule and the compass only, which he published himself in his Apollonius See also:Gallus (1600) . In this See also:paper Vieta made use of the centre of similitude of two circles . Lastly he gave an See also:infinite product for the number r (see CIRCLE, SQUARING OF) Vieta's collected works were issued under the See also:title of See also:Opera Mathematica by F. van Schooten at See also:Leiden in 1646 . (M . CA.) VIEU%TEMPS, See also:HENRI (182o-1881), Belgian violinist and composer, was born at See also:Verviers, on the loth of February 182o . Until his seventh year he was a See also:pupil of Lecloux, but when De See also:Beriot heard him he adopted him as his pupil, taking him to appear in Paris in 1828 . From 1833 onwards he spent the greater See also:part of his See also:life in See also:concert tours, visiting all parts of the See also:world with See also:uniform success . He first appeared in See also:London at a Philharmonic concert on the 2nd of See also:June 1834, and in the following year studied See also:composition with See also:Reicha in Paris, and began to produce a See also:long See also:series of works, full of formidably difficult passages, though. also of pleasing themes and See also:fine musical ideas, which are consequently highly appreciated by violinists .

From 1846 to 1852 he was See also:

solo violinist to .the See also:tsar, and See also:professor in the conservatorium in St See also:Petersburg . From 1871 to 1873 he was teacher of the See also:violin class in the See also:Brussels See also:Conservatoire, but was disabled by an attack of See also:paralysis in the latter year, and from that time could only superintend the studies of favourite pupils . He died at Mustapha, in See also:Algiers, on the 6th of June 1881 . He had a perfect command of technique, faultless intonation and a marvellous command of the See also:bow . His staccato was famous all over the world, and his See also:tone was exceptionally See also:rich and full .

End of Article: VIETA (or VIETE), FRANCOIS, SEIGNEUR DE LA BIGOTIERE (1540-1603)
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