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* TRIGONOMETRY. •164 TRILLIUM. for simplifying and classifying the treatment of the whole subject. Lagrange, Legendre, Carnot, Gauss, and others expanded the theory of polygonometry and polyhedrometry. The nine- teenth century has contributed the so-called pro- jective formulas, and made further generaliza- tion of fornuilas known before. A few leading works on the subject are: Casey, A Treatise on Plane Trigonometry (Dublin, 1888) ; id., Treatise on Spherical Trigonometry (ib., 1889) ; Mc- Clelland and Preston, Spherical Trigonometry (London, ISnO) ; Helmes, Die Trigonometric (Hanover, 1881); Wittstein, Trigonometrie (ib., 1887) ; Hobson, Plane Trigonometry (Cambridge, 1891); Chauvenet, Plane and Spherical Trig- onometry (New York, various editions). For the history of the subject, consult Braunmiihl, Bcitriige zur Geschiehte der Trigonometrie (Halle, 1897), and his Yorlesungen iiher Ge- schiehte der Trigonometrie (Leipzig, vol. i., 1900; vol. ii., 1903). For reference to valuable tables, see the article on Log.ritiims. TRIISODON, trl'I'so-don (Neo-Lat., from Cik. rpeii. trcis, three + f<ros, isos, equal + idom, odoKS, tooth). A fossil creodont mammal from the Puerco beds of New Mexico. The .skull is the oldest known mammalian skull. Consult !Matthew, "Additional Observations on the Creo- donta." in Bulletin of American. Museum of 'Nat- ural History, vol. xiv. (New York, 1901). See Creodonta; Mammalia. . TRIKALA, tre-kii'la, or TRIKKALA. A town of (Jreece, capital of the Nomarchy of Tri- kala. situated on the Trikkalinos River, 37 miles northwest of Larissa and on the Volos-Kalabaka Railway (Map: Greece, C 2). It manufactures cotton, woolen stuffs, leather, and dye products. Its population in 1889 was 14.820, mostly Wal- lachs. Trikala is the ancient Trikka, which was celebrated for its temple of ^Esculapius. TRIKOUPIS, tre-koo'pis, Charilaos (1832- 96) . A Greek statesman, son of Spiridon Trikou- pis, born at Nauplia, .July 23, 1832. He stud- ied jurisprudence in Athens and Paris and in 1852 entered the diplomatic service as attache to the legation at London, where in 1863 he became charge d'affaires. In 18C.5 he conducted the ne- gotiations with Great Britain regarding the ces- sion of the Ionian Islands. Elected to the BoulS in the same year, he became an adherent of the radical party, was in 1866 appointed Minister of Foreign Affairs, became Premier in 1875, was once more Minister of Foreign Affairs under Canaris, in the coalition Mini-stry of 1877, and Premier agixin in 1880, 1882-85," 1886-90, 1891-93, and 1893-95, when, owing to the financial embarrass- ment of the Government, he met with a crushing defeat, losing even the seat in the Boule, which he had held for thirty years. While on his deathbed he was reelected by the District of Valtos. He died at Cannes, France, April 11, 1890. His endeavors to raise the economic con- ditions of the country, by the enactment of agrarian and tariff legislation and the building of railways, met with little success. For a num- ber of years his party continued to hear the name of Trikoupists. A volume of his speeches, Ai7oi TToXiTiKoi, appeared at Athens in 1888. Compare Tsokopoulos, Bio7poi^(a XapiXdou TpiKoi/irT) (Athens, 1896). TRIKOUPIS, Spiridon (1788-1873). A Greek author and statesman. He was the son of a primate of Missolonghi, where he was born, April 20, 1788. He studied in France and Eng- land, became secretary of the Karl of Guilford during his occupancy of the position of Governor of the Ionian Islands, and played an important part in the war for independence. After 1821 he was employed in administrative and diplomatic business, being a member of the provisional Gov- ernment in 1826, and of the National Conven- tion at Trffizen in the following year. He was president of the Council and Minister of Foreign Affairs in 1832; was thrice sent to London ( 1835- 38, 1841-43, and 18.50-01) as Ambas.sador; was Jlinister of Foreign Affairs and of Public Instruc- tion in 1843; vice-president of the Senate (1844- 49) ; and Envoy Extraordinary to Paris (1850) on the occasion of the blockade of the ports of Greece by England. He died February 24, 1873, at Athens. His funeral oration on Lord Byron (whose friend and comrade he had been), deliv- ered in the Cathedral of Missolonghi, some days after the poet's death, was translated into sev- eral European languages. Many other orations, partly religious and partly political, were col- lected and published (Paris. 1836). His master- piece is the history of the Greek revolution, "IcTTopla T77S 'EXXt/kk^s 'Biraxao-Tdo-cus (London, 1853-57). TRIL'BY. ( 1 ) A romance by Charles Nodier (1822). (2) A novel by George du Jlaurier (1895) and its chief character, a beau- tiful artists' model, wdiose love for 'Little Billee' and domination by the hypnotic powers of Sven- gali form the plot of the story. The novel is full of reminiscences of Parisian artist life and gained a wide popularity. TRILL (Fr. triller. It., ML. trillare, to trill, probably onomatopoetic in origin). In music, an embellishment produced by the continued and rapid repetition of one note alternately with another, either a whole tone of semitone above it. Its sign is tr placed over or under the princi- pal note. The trill was known and used at the end of the sixteenth century, but its name was added considerably later. TRILLIUM (Neo-Lat., from Lat. tres, three, so called from the symmetrical arrangement of the three outer and three inner segments). A COMMON WAEE-BOBiN {Trillium erectum). genus of about a dozen species of North Ameri- can perennial herbs of the lily family growing in moist and shady (not marshy) grounds from