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ordinances respecting the clergy. The council closed with the third formal session, 6 May, 1312.

Mansi. Conciliorum collectio, XXV, 367 sqq.; Ehble, Bin BruchslQrk der Akten des Konzils von Vienne in Archiv fUr Lit- eratur-und Kirchengeschichte des Miltelalters, IV (1888), 361 sqq.: Idem, Vorgeschich'e des KoJizils von Vienne, loc. cit., II, 353 sqq.. Ill, 1 sqq., 1409 aqq.: Hefele, Komiliengeschichte, VI (2nd ed, Freiburg im Br., 1890), 436 sqq.. 515 sqq.; Hebeb, GiUachten und Reformvorschlage fiir das Vienner Gencralconcil (Leipzig, 1S98) ; Goller. Die Gravamina auf dem Korizil von Vienne in Feslgabe far H. Finke (Mflnster, 1904), 197 sqq.; MoLLAT, hes doUances du clergS de la province de Sens au concile de Vienne in Revue d'hisl. eccUs., VI (1905), 319 sqq.

J. P. KlRSCH.

Vierthaler, Fr.\nz Michael, a distinguished ■\ustrian pedagogue, b. at Mauerkirchen, Upper Aus- tria, 25 September, 1758; d. at Vienna, 3 October, 1827. As his parents were poor, he was a choir-boy at the Benedictine .-Vbbey of Michaclbeuren and at Salzburg. \t Salzburg he also attended the gj'mna- eiuni and from 1770-77, he took the law course at the university, though his favourite study was classic languages. In 1783 he became instructor at the Virgilian college for nobles at Salzburg. By teaching history he was led to WTite his"Phil- osophische Geschichte der Menschheit" (7 vols., 1787-1S19). The first volume attracted attention and gained for Vierthaler, in 1790, the position of di- rector of the seminary for teachers at Salzburg, which the archbishop had estabhshed for the betterment of the primary schools. In the same year he began a course of catechetical instruction for the students of the seminary for boys, and in 1791 pedagogical lectures at the university. In 1796 he was made court hbra- rian. During 1800-02 he edited the "Salzburger Literaturzeitung" and from 1799-1806 the "Salz- burger Staatszcitung". He married in 1802; in 1803 he w.as appointed supervisor of the pubhc schools in the Duchy of Salzburg, and in 1804 supervisor of the two orphan asylums. Three years later, when Salz- burg was made part of Austria, the Austrian Govern- ment called him to Vienna, where he took charge of the orphan asylum.

Vierthaler was a strong advocate of practical training in teaching. Ho kept up a correspondence with the young teachers from the seminary and encouraged their zeal. He prepared a unified plan of studies for schools that he visited, sought to provide good and cheap school-books and other aids to study, and suc- ceeded in arousing pubhc interest infthe cause of the schools. His three chief pedagogical works are: "Elemente der Methodik und Piidagogik" (1791); "Gei.st der Sokratik" (1793); "Entwurf der Schuler- ziehungskunde" (1794). He was a master in his call- ing, distinguished by the clearness, simphcity, and practicalness of his teachings. He laid more em- pliasis than other teachers of his era on the principle that instruction should subserve education. The aim of his pedagogical method was a "noble humanity tr.ansfigured by God". The basis of all his efforts was the Catholic P'aith which he placed above everything else. Like Overberg he regarded the personality of the teacher as the most important thing in education. In many respects he was ahead of his times, c. g. in his high estimation of the teaching of the natural sciences and of physical training; also in his opposition to corporal punishment. Besides his pedagogical writings Vierthaler wrote a large number of school-books and books for children; among the.se are an edition of the Gospels and Epistles and a geography of Salzburg.

.^NTnALLER. Franz Mirhael Vierthaler, der Salzburger Padegoge (Salzl)urg, 1880); Vierthaler, Padagogische Hauplschriflen, cd. VON DER FcHR (Pwlcrbom. 1904): VON DER FuHB, Michael Vierthaler u. seine Zeil (Berlin, 1909).

Klemens Loffler. Viesti. See Manfredonia, Archdiocese op. Vieta (VifcTE), Francois, Seigneur de La Bigotti&re, father of modern algebra, b. at Fontenay-le-Comte

(Poitou), 1540; d. in Paris, Feb., 1603. The son of a solicitor, he made his early studies under the Fran- ciscans of his native place. He studied law in the University of Poitiers, returned to Fontenay at nine- teen, and soon took rank with the leading barristers of the province, numbering Mary Stuart among his cli- ents. Indifferent in religion, and with his legal prac- tice ruined by the religious wars, he accepted the position of tutor to Catherine, the eleven-year-old daughter of Jean de Parthenay, Sieur de Soubise, a militant Huguenot. Three years later, at the mar- riage of his pupil, ho left the Chateau du Pare and went to La Rochelle. Here ho gained as chents and friends the Huguenots, Coligny, Conde, the Queen of Navarre, Henry of Navarre, and Fran^oise de Rohan, who, hke his former pupil, Catherine, Viscountess de Rohan by a second marriage, remained his benefactress for life. Of his wife little beyond the name is known. The title of Sieur de La Bigottiero lie ]irobably as- sumed. He became a barrister in Paris and later a councillor of the Parlement in Rennes. For some years he was in disfavour with Henry III, despite the efforts in 1585 of his friend Henry of Navarre. To the lat- ter, as king, Viota^ while councillor of the Parlement in Tours, rendered signal service by discovering the key to the Si)anish cipher. During his last years, spent mainly in Paris, he was maitre des requites (ma-ster of requests) and royal privy councillor. He was a Catholic at his death. His kindly treatment of Adri- anus Romanus, a rival scholar, indicates a generous nature.

To Vieta as a mathematician Huygens, Halley, Cha.sles, and Fourier have given high rank. He made the use of letters as symbols of quantity a general cus- tom. He was higfily skilful in the treatment of equa- tions, knew the relations between the po.sitive roots and the coefficient!?, and devised solutions for the equations of the second, third, and fourth degrees by methods different from the existing ones. He enun- ciated the principle of homogeneity. He extended the tables of Rheticus, gave formulse for the sine and co- sine of a multi])le angle, and attempted to find the value of TT by moans of infinite series. To a consider- able extent ho ajiplied algebra to geometry and trig- onometry and geometry and trigonometry to algebra. His collected works were ]niblishod by Van Schooten, "Opera Matheniatica", Leyden, 1646.

Bertrand in Revue des Deux Mondes (15 May, 1897), or Eloges Academiques, new series, 143-76 (Paris, 1902); Cha.sle8, Camples rcndus de I'Acad. des Sci., XII, XIII (1841); Fillon et Ritter, Notice sur la vie et les ouvrages de Francois Viite (Nantes, 1850); GaMBIER. Le nuithimaticien Fraji^ois Viite, GSn^logie de sa famille (La Rochelle, 1911); Hittton, Tracts on Math, and Phil. Subjects, II, (London, 1812), 260-74; Ritter. BulU ettino di Hibliografia e di Storia delte Sci. mat. e fis., I (Rome. 1868), 223-27.

Paul H. Linehan.

Viger, Denis-Benjamin, French-Canadian states- man and writer, b. at Montreal, 19 .Vug., 1774; d. 1861. After studying classics and philosophy at the Sulpician college of his native city, he joined the bar, was elected (1808) member of Parliament for Montreal, and re-elected for other constituencies in ISIO, 1SI4, and 1827. He was sent (1828) to repre- sent French Canadian interests against Lord Dal- housie's .administration before the English Parhament. In 1830, though a member of the Upper House, he returned to London, where he spent two years refuting .\ttorney-General .Stuart's memoir. His patriot- ism did not impair his loyalty. Yet, in 1838, he was imprisoned for nineteen months, refusing bail, and demanding a trial. After the union of the Canadas, he was twice returned to Parliament (1841 .and 184.5). His knowledge of constitutional law urged him to side with Governor Metcalfe, and accept Lafontaine's heritage as premier; wliereby he assumed the respon- sibility of dividing the Liberal party. His friends misunderstood him and suspected him of inclining