See also:

• VIETA (or VIETE), FRANCOIS, SEIGNEUR DE LA BIGOTIERE (1540-1603)

VIETA (or VIETE), See also:

• FRANCOIS (1558-1614)

FRANCOIS, SEIGNEUR DE LA BIGOTIERE (1540-1603)  , more generally known as FRANCISCUS See also:

• VIETA (or VIETE), FRANCOIS, SEIGNEUR DE LA BIGOTIERE (1540-1603)

VIETA, See also:

• FRENCH
• FRENCH, DANIEL CHESTER (1850– )
• FRENCH, NICHOLAS (1604-1678)

French mathematician, was See also:

• BORN, IGNAZ, EDLER VON (1742–1791)

born in 1540 at Fontenay-le-See also:

• COMTE, AUGUSTE [ISIDORE AUGUSTE MARIE FRANCOIS XAVIER] (1798-1857)

Comte, in See also:

• POITOU

Poitou . According to F . See also:

• RITTER, HEINRICH (1791-1869)
• RITTER, KARL (1779–1859)

Ritter,' Vieta was brought up as a See also:

• CATHOLIC (Gr. KcaBoXuK6s, general, universal)

Catholic, and died in the same creed; but there can be no doubt that he belonged to the See also:

• HUGUENOTS

Huguenots for several years . On the completion of his studies in Iaw at See also:

• POITIERS

Poitiers Vieta began his career as an See also:

• ADVOCATE (Lat. advocatus, from advocare, to summon, especially in law to call in the aid of a counsel or witness, and so generally to summon to one's assistance)

advocate in his native See also:

• TOWN

town . This he See also:

• LEFT

left about 1567, and somewhat later we find him at See also:

• RENNES

Rennes as a councillor of the See also:

• PARLEMENT (see PARLIAMENT)

parlement of See also:

• BRITTANY

Brittany . The religious troubles drove him thence, and See also:

• ROHAN
• ROHAN, HENRI
• ROHAN, LOUIS RENE EDOUARD, CARDINAL DE (1734-1803)

Rohan, the well-known See also:

• CHIEF (from Fr. chef, head, Lat. caput)

chief of the Huguenots, took him under his See also:

• SPECIAL

special See also:

• PROTECTION

protection . He recommended him in 158o as a " maitre See also:

• DES

des requetes " (See also:

• MASTER (Lat. magister, related to tnagis, more, as the corresponding minister is to minus, less; the English form is due partly to the O. Eng. maegister, and partly to O. Fr. maistre, mod. maitre; cf. Du. meester, Ger. Meister, Ital. maestro)

master of See also:

• REQUESTS, COURT OF

requests) ; and See also:

• HENRY
• HENRY (1129-1195)
• HENRY (c. 1108-1139)
• HENRY (c. 1174–1216)
• HENRY (Fr. Henri; Span. Enrique; Ger. Heinrich; Mid. H. Ger. Heinrich and Heimrich; O.H.G. Haimi- or Heimirih, i.e. " prince, or chief of the house," from O.H.G. heim, the Eng. home, and rih, Goth. reiks; compare Lat. rex " king "—" rich," therefore " mig
• HENRY, EDWARD LAMSON (1841– )
• HENRY, JAMES (1798-1876)
• HENRY, JOSEPH (1797-1878)
• HENRY, MATTHEW (1662-1714)
• HENRY, PATRICK (1736–1799)
• HENRY, PRINCE OF BATTENBERG (1858-1896)
• HENRY, ROBERT (1718-1790)
• HENRY, VICTOR (1850– )
• HENRY, WILLIAM (1795-1836)

Henry of See also:

• NAVARRE (Span. Navarra)

Navarre, at the instance of Rohan, addressed two letters to Henry III. of See also:

• FRANCE
• FRANCE, ANATOLE (1844– )

France on the 3rd of See also:

• MARCH
• MARCH (1) (from Fr. marcher, to walk; the earliest sense in French appears to be " to trample," and the origin has usually been found in the Lat. marcus, hammer; Low Lat. marcare, to hammer; hence to beat the road with the regular tread of a soldier: cf.
• MARCH, AUZIAS (c. "1395-1458)
• MARCH, EARLS OF
• MARCH, FRANCIS ANDREW (1825– )

March and the 26th of See also:

• APRIL

April 1585, to obtain Vieta's restoration to his former See also:

• OFFICE (from Lat. officium, " duty," " service," a shortened form of opifacium, from facere, " to do," and either the stem of opes, " wealth," " aid," or opus, " work ")

office, but without result . After the See also:

• ACCESSION (from Lat. accedere, to go to, to approach)

accession of Henry of Navarre to the See also:

• THRONE

throne of France, Vieta filled in 1588 the position of councillor of the parlement at See also:

• TOURS

Tours . He afterwards became a royal privy councillor, and remained so till his See also:

• DEATH

death, which took See also:

• PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place suddenly at See also:

• PARIS
• PARIS (also called ALEXANDROS)
• PARIS, ALEXIS PAULIN (1800-x881)
• PARIS, BRUNO PAULIN GASTON (1839-1903)
• PARIS, FRANCOIS DE (169o-1727)
• PARIS, LOUIS PHILIPPE ALBERT
• PARIS, TREATIES OF (1814-1815)

Paris in See also:

• FEBRUARY

February 1603, but in what manner we do not know; See also:

• ANDERSON
• ANDERSON, ADAM (1692—1765)
• ANDERSON, ALEXANDER (c. 1582-1620?)
• ANDERSON, ELIZABETH GARRETT (1836— )
• ANDERSON, JAMES (1662—1728)
• ANDERSON, JAMES (1739-1808)
• ANDERSON, JOHN (1726-1796)
• ANDERSON, MARY (1859– )
• ANDERSON, RICHARD HENRY (1821–1879)
• ANDERSON, ROBERT (1750–1830)
• ANDERSON, SIR EDMUND (1530-1605)

Anderson, the editor of his scientific writings, speaks only of a " praeceps et immaturum autoris fatum." ' Bolletino Boncompagni (See also:

• ROME
• ROME (Roma)

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
• KEY (in O. Eng. tang; the ultimate origin of the word is unknown; it appears only in Old Frisian kei of other Teutonic languages; until the end of the 17th century the pronunciation was kay, as in other words in O. Eng. ending in aeg; cf. daeg, day; clang
• KEY (the phraseograms being indicated by hyphens)
• KEY, SIR ASTLEY COOPER (1821-1888)
• KEY, THOMAS HEWITT (1799-1875)

key to a See also:

• SPANISH

Spanish See also:

• CIPHER, or CYPHER (from Arab. sifr, void)

cipher, consisting of more than 5oo characters, and thenceforward all the despatches in that See also:

• LANGUAGE (adapted from the Fr. langage, from langue, tongue, Lat. lingua)

language which See also:

• FELL
• FELL, JOHN (1625-1686)

fell into the hands of the French could be easily read . His fame now rests, however, entirely upon his achievements in See also:

• MATHEMATICS (Gr. /saBnµar1Kil, Sc. vOcvn or E7rlQTt'µn; from p iN.La, "learning" or "science ")

mathematics . Being a See also:

• MAN
• MAN, ISLE OF (anc. Mona)

man of See also:

• WEALTH

wealth, he printed at his own expense the numerous papers which he wrote on various branches of this See also:

• SCIENCE (Lat. scientia, from scire; to learn, know)

science, and communicated them to scholars in almost every See also:

• COUNTRY (from the Mid. Eng. contre or contrie, and O. Fr. cuntree; Late Lat. contrata, showing the derivation from contra, opposite, over against, thus the tract of land which fronts the sight, cf. Ger. Gegend, neighbourhood)

country of See also:

• EUROPE

Europe . An See also:

• EVIDENCE (Lat. evidentia, evideri, to appear clearly)

evidence of the See also:

• GOOD, JOHN MASON (1764-1827)

good use he made of his means, as well as of the kindliness of his See also:

• CHARACTER (Gr. xapareri7p, from xap&crew, to scratch)

character, is furnished by the fact that he entertained as a See also:

• GUEST (a word common to Teutonic languages; cf. Ger. Gast, and Swed. gust; cognate with Lat. hostis, originally a stranger, hence enemy; cf. " host " )
• GUEST, EDWIN (1800–188o)

guest for a whole See also:

• MONTH
• MONTH (a common Teutonic word, cf. Ger. Mond, Du. maand, Dan. maaned, &c., and cognate with Lat. mensis, Gr. µi7v, &c., in other branches of the Indo-Germanic family; all ultimately from the root seen in the word for the moon in nearly all those languages

month a scientific adversary, Adriaan See also:

• VAN

van Roomen, and then paid the expenses of his See also:

• JOURNEY (through O. Fr. jornee or journee, mod. Fr. journee, from med. Lat. diurnata, Lat. diurnus, of or belonging to dies, day)

journey See also:

• HOME
• HOME, DANIEL DUNGLAS (1833-1886)
• HOME, EARLS OF

home . Vieta's writings thus became very quickly known; but, when Franciscus van Schooten issued a See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

general edition of his See also:

• WORKS

works in 1646, he failed to make a See also:

• COMPLETE

complete collection, although probably nothing of very See also:

• GREAT

great value has perished . The See also:

• FORM (Lat. forma)

form of Vieta's writings is their weak See also:

• SIDE
• SIDE (mod. Eski Adalia)

side . He indulged freely in flourishes; and in devising technical terms derived from the See also:

• GREEK
• GREEK, ETRUSCAN AND

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 (from Lat. denotare, to mark out, specify)

denotation he followed, perhaps, some older contemporaries, as See also:

• RAMUS, PETRUS, or PIERRE DE LA RAMEE (1515-1572)

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

father of See also:

• MODERN

modern See also:

• ALGEBRA (from the Arab. al-jebr wa'l-mugabala, transposition and removal [of terms of an equation], the name of a treatise by Mahommed ben Musa al-Khwarizmi)

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 (see also WRITING)

alphabet, to denote the quantities of See also:

• ARITHMETIC (Gr. apeOµ7run7, sc. TEXVn, the art of counting, from (ipLBµos, number)

arithmetic, but that he made a general See also:

• CUSTOM (from O. Fr. costume, costume or coustume; Low Lat. costuma, a shortened form of consuetudo)

custom of what until his See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

time had been only an exceptional See also:

• ATTEMPT (Lat. adtemptare, attentare, to try)

attempt . All that is wanting in his writings, especially in his Isagoge in artem analyticam (1591), in See also:

• ORDER
• ORDER (through Fr. ordre, for earlier ordene, from Lat. ordo, ordinis, rank, service, arrangement; the ultimate source is generally taken to be the root seen in Lat. oriri, rise, arise, begin; cf. " origin ")
• ORDER, HOLY

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
• ROBERT (1275—1343)
• ROBERT, HUBERT (1753-1808)
• ROBERT, LOUIS LEOPOLD (1794-1835)

Robert See also:

• RECORDE, ROBERT (c. 1510-1558)

Recorde had made use of our See also:

• PRESENT

present See also:

• SYMBOL (Gr. o-uµ(3oXov, a sign)

symbol for this purpose since 1557, and See also:

• XYLANDER, GUILIELMUS (WILHELM HOLTZMAN, according to his own spelling) (1532-1576)

Xylander had employed See also:

• VERTICAL (from Lat. vertex, highest point)

vertical parallel lines since 1575 .

On the other See also:

• HAND
• HAND (a word common to Teutonic languages; cf. Ger. Hand, Goth. handus)
• HAND, FERDINAND GOTTHELF (1786-185r)

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

primitive unknown quantities . Another of his works, Recensio canonica effectionum geometricarum, bears a See also:

• STAMP (from " to stamp," to strike or tread heavily, hence to impress, O. Eng. stempen, Du. stampen, Ger. stampfen, whence, O. Fr. estamper, mod. etamper)

stamp not less modern, being what we now See also:

• CALL (from Anglo-Saxon ceallian, a common Teutonic word, cf. Dutch kallen, to talk or chatter)

call an algebraic See also:

• GEOMETRY

geometry—in other words, a collection of precepts how to construct algebraic expressions with the use of See also:

• RULE

rule and See also:

• COMPASS (Fr. corn pas, ultimately from Lat. cum, with, and passus, step)

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 (Fr. age, through late Lat. aetaticum, from aetas)

age; but of later mathematicians only See also:

• HERO (Gr. open)
• HERO, THE YOUNGER

Hero, See also:

• DIOPHANTUS

Diophantus, &c., ventured to regard lines and surfaces as See also:

• MERE
• MERE, ADALBERT (1838-1909)

mere See also:

• NUMBERS, BOOK OF
• NUMBERS, PARTITION OF

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

lay it down as a principle that quantities occurring in an See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

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 (O. Eng. dreg, Ger. Tag; according to the New English Dictionary, " in no way related to the Lat. dies")
• DAY, JOHN (1574-1640?)
• DAY, THOMAS (1748-1789)

day and our own several changes of See also:

• OPINION (Lat. opinio, from opinari, to think)

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

resolution of equations of the second, third and See also:

• FOURTH

fourth degrees different from those of Ferro and See also:

• FERRARI, GAUDENZIO (1484-1549)
• FERRARI, GIUSEPPE (1812–1876)
• FERRARI, PAOLO (1822–1889)

Ferrari, with which, however, it is difficult to believe him to have been unacquainted . He devised an approximate numerical See also:

• SOLUTION (from Lat. solvere, to loosen, dissolve)

solution of equations of the second and third degrees, wherein Leonardo of See also:

• PISA
• PISA, COUNCIL OF (1409)

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 (or PORTABLE) ORGAN

positive roots of an equation (which, by the way, were alone thought of as roots) and the coefficients of the different See also:

• POWERS, HIRAM (1805-1873)

powers of the unknown quantity . He found out the See also:

• FORMULA
• FORMULA (Lat. diminutive of forma, shape, pattern, &c., especially used of rules of judicial procedure)

formula for deriving the sine of a multiple See also:

• ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

angle, knowing that of the See also:

• SIMPLE

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

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
• SIN (O. Eng. syn: a common Teutonic word, cf. Dutch zonde, Ger. Siinde)

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, CHARLES FRANCCOIS
• LEBRUN, PIERRE ANTOINE (1785–1873)
• LEBRUN, PONCE DENIS ECOUCHARD (1729-1807)

LEBRUN was capable being given at the same time (see See also:

• TRIGONOMETRY (from Gr. rpiywvov, a triangle, /ATpov, measure)

TRIGONOMETRY) . Such was the first encounter of the two scholars . A second took place when Vieta pointed to See also:

• APOLLONIUS

Apollonius's problem of taction as not yet being mastered, and Adriaan van Roomen gave a solution by the See also:

• HYPERBOLA

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, C
• GALLUS, CORNELIUS (c. 70-26 B.C.)
• GALLUS, GAIUS AELIUS
• GALLUS, GAIUS CESTIUS
• GALLUS, GAIUS SULPICIUS

Gallus (1600) . In this See also:

• PAPER
• PAPER (Fr. papier, from Lat. papyrus)

paper Vieta made use of the centre of similitude of two circles . Lastly he gave an See also:

• INFINITE (from Lat. in, not, finis, end or limit; cf. findere, to deave)

infinite product for the number r (see CIRCLE, SQUARING OF) Vieta's collected works were issued under the See also:

• TITLE (0. Fr. title, mod. titre, from Lat. titulus)

title of See also:

• OPERA (Italian for " work ")

Opera Mathematica by F. van Schooten at See also:

• LEIDEN

Leiden in 1646 . (M . CA.) VIEU%TEMPS, See also:

• HENRI

HENRI (182o-1881), Belgian violinist and composer, was born at See also:

• VERVIERS

Verviers, on the loth of February 182o . Until his seventh year he was a See also:

• PUPIL (Lat. pupillus, orphan, minor, dim. of pupus, boy, allied to puer, from root pm- or peu-, to beget, cf. "pupa," Lat. for " doll," the name given to the stage intervening between the larval and imaginal stages in certain insects)

pupil of Lecloux, but when De See also:

• BERIOT, CHARLES AUGUSTE DE (18cn-187o)

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

part of his See also:

• LIFE

life in See also:

• CONCERT (through the French from Lat. con-, with, and certare, to strive)

concert tours, visiting all parts of the See also:

• WORLD

world with See also:

• UNIFORM

uniform success . He first appeared in See also:

• LONDON

London at a Philharmonic concert on the 2nd of See also:

• JUNE

June 1834, and in the following year studied See also:

• COMPOSITION
• COMPOSITION (Lat. compositio, from componere, to put together)

composition with See also:

• REICHA, ANTON JOSEPH (1770-1836)

Reicha in Paris, and began to produce a See also:

• LONG, GEORGE (1800-1879)
• LONG, JOHN DAVIS (1838– )

long See also:

• SERIES (a Latin word from serere, to join)

series of works, full of formidably difficult passages, though. also of pleasing themes and See also:

• FINE

fine musical ideas, which are consequently highly appreciated by violinists .

From 1846 to 1852 he was See also:

• SOLO, OR SOLO WHIST

solo violinist to .the See also:

• TSAR, or CZAR

tsar, and See also:

• PROFESSOR (the Latin noun formed from the verb profiteri, to declare publicly, to acknowledge, profess)

professor in the conservatorium in St See also:

• PETERSBURG

Petersburg . From 1871 to 1873 he was teacher of the See also:

• VIOLIN

violin class in the See also:

• BRUSSELS (Fr. Bruxelles, Flem. Brussel)

Brussels See also:

• CONSERVATOIRE (the Fr. equivalent of Ital. Conservatorio, Ger. Conservatorium, from Med. Lat. conservatorium, a place where anything is preserved, Lat. conservare, to preserve)

Conservatoire, but was disabled by an attack of See also:

• PARALYSIS, or PALSY (from Gr. aapal,6a , to relax; Wycliffe has palesy, and another old form of the word is parlesy)

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 (Fr. Alger, Arab. Jezair, i.e. The Islands)

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 (pronounced " bo ")

bow . His staccato was famous all over the world, and his See also:

• TONE, THEOBALD WOLFE (1763-1798)

tone was exceptionally See also:

• RICH, BARNABE (c. 1540-1617)
• RICH, CLAUDIUS JAMES (1787-1821)
• RICH, JOHN (1692-1761)
• RICH, PENELOPE, LADY (c. 1562–1607)
• RICH, RICHARD, 1ST BARON RICH (1490?-1567)

rich and full .