Page:The New International Encyclopædia 1st ed. v. 19.djvu/544

* TRISECTION OF AN ANGLE. 474 TEIST. the angle to be trisected, C any point on OB, CM i OA and CP || OA, it is easily seen that if P can be found so that PN=2C0 then PO is a tiisection line of angle AOB. But the trammel of the conchoid with its directrix rest- ing on CM. parameter AM = CB=2C0, its pole at O, will describe a curve cutting CP in the required point. Jlam* other methods have been devised for the solution of this problem. ViMe (1,501) showed its relation to the solution of the cubic equation. Gauss (1801) showed its relation to c.yclotoniic equations. Other mathe- maticians of the nineteenth century have de- clared its solution impossible by means of the straight edge and compasses (that is, by the postulates of Euclidean geometry). But the real reason for the failure of this method to solve the proljlem and also its associates was set forth by Klein. The argument may be briefly stated as follows: (1) According to the formula of De Moivre (q.v.) the roots of the equation a;'=cos -(- /sin (^ .0  + 4ir (2) These roots are represented geometrically by the vertices of an equilateral triangle inscribed in the unit circle with its centre at the origin. The figure shows that to the root Xj corresponds the argument „• Hence the equa- tion a:' = COS0 + isin (p is the analytic expres- sion of the problem of the trisection of the angle. No root of the equation can be expressed as a rational function of cos0 and sin0. That is, the equation is irreducible and can be solved by the aid of a finite number of square roots only for special values of <p. Hence the trisection of an arbitrary angle cannot be ef- fected with straight edge and compasses. Con- sult: Klein. Fainoits Frohlcms of Elementary Geomctrii (18!l(i, Eng. ed., Boston, 1897). TBISMEGISTUS. See Hermetic. TBIS'MUS NASCEN'TIUM (Neo-Lat., lock- jaw of the now bi.rn). A form of lockjaw occur- ring in newly born children a few days after birth. In consequence of it the children cannot nurse or cry, and they usually die in forty-eight hours. In some cases the attack comes in eight or ten days after birth. The cause is infection with the tetanus poison, probably always through the wound in the umbilical cord. See Tetanus. TRISSINO, tres-se'nd, Giovanni Giorgio (-1550). An Italian author, born at Vieenza. Excluded from his native territory by the Signoria of 'S'enice, he spent some time in Germany, at Ferrara, and at Florence, and in 1.514 went to Kome, where he was received with favor by Pope Leo X., who sent him on missions to the Em- peror Maximilian and to the Signoria of Venice. At the instance of Leo X., the ban of proscrip- tion was taken olf. He enjoyed the esteem of Popes Clement VII. and Paul III., and passed some time at Venice as nuncio of the former pontiff. He died in Rome December 8, 1550. Trissino sought to revive the epic in his mother tongue; he gave to the Italian stage its first regular tragedy, and he made the first large use of the hendeca.syllable in blank verse. His at- temi)t to produce an epic poem resulted in the Italia libcrata dai Goti, a work of twenty-seven cantos in eleven-syllabled blank verse, completed in 1548. Blank verse and the hendecasyllable are used also in Trissino's Sofoiiishn (1515), which, although it has not the conventional division into acts, is regarded as the first regular tragedy in the modern languages of Europe. In a comedy, / Siinillinti, which is a free imitation of the Menwrlmii of Plautus, Trissino adopted his fa- vorite eleven-syllabled blank verse and introduced certain lyrical strophes like those employed in the Greek comedy. Some Latin poems, a Canzone a Clemcntc 17/., and various Rime make up the rest of his compositions in verse. Trissino gave new life to the already mooted question of the proper Italian tongue with his edition of the De Vulgari Eloqiiio of Dante in 1529; and his treatise, II CdstcUano, advocated the doctrine of a general Italian tongue as opposed to a merely Tuscan standard. Of his remaining ^yorks there may be mentioned the Poetica. Consult: Morsolin, Gianqiorgio Trissino, monografia di un letterato del s'eeolo XVI. (2d ed.. Florence, 1894) ; Ciam- polini. La prima tragcdia regolare nella lettera- ttira italiana (Lucca, 1884). TRISSOTIN, trJ'so'taN'. A poet in Moli&re's Feminra .iiirantcs, satirizing a gallant preacher, Ablie Cotin. TRIST, Nicholas Philip (1800-74). An American lawyer and diplomatic agent, born at Charlottesville, Va. He was educated at the United States Military Academy, but did not graduate. He studied law under the direction of Thomas Jefi'erson, whose granddaughter lie mar- ried, and of whose household he was a member, but became a clerk in the United States Treas- ury Department in 1824. and was private secre- tary to President Jackson in 1829. In 18.34-36 he was L'nited States Consul at Havana, and in 1845 he was chief clerk in the Department of State. During the Mexican War, after the American successes at Buena Vista and Vera Cruz. President Polk, on April 15, 1847, ap- pointed Trist a special agent to negotiate for peace, Init without notifying General Scott. On the arrival of Trist a violent quarrel ensued be- tween him and Seott. Negotiations, however, were fruitless until after the capture of the City of Jlexico and the resignation of Santa Anna as President. The succeeding Government wished to make terms and Trist, though his powers had been withdrawn, feeling that the strong desire for peace in the United States would excuse the ir- regularity, proceeded with the negotiations, by the advice of General Scott, who had now become his friend. The Treaty of Guadalupe Hi-