TRANSVERSAL. 426 TRANSYLVANIA. transversal are such that the product of three not having a common extremity will equal the product of the other three; that each diagonal is cut harmonically by the other two; and that when a hexagon has three of its vertices collinear, and the other three also collinear, the intersec- tions of the opposite sides are collinear also — a special case of Pascal's theorem on a hexagon inscribed in a conic. Desargues (q.v.) in his Essai pour tes coniques generalized the theorem of Pappus with respect to the quadrilateral. He showed that if a transversal cuts a conic and a quadrilateral inscribed therein, the product of the segments between either point of the conic and two opposite sides of the quadrilateral will have to the product of the segments between this point and the other two opposite sides, the same ratio as between the corresponding products when the other point of the conic is taken. The the- ory was extended by Pascal, who was a friend of Desargues, and later by Newton, Cotes, and Maclaurin. In more recent times Carnot and Poncelet have been among the foremost to elabo- rate the theory. To Carnot is due the introduc- tion of negative lines in the theory of transver- sals, and the treatment of the subject as related to modem geometry. See Concdkrence and CoLLiNE.RiTy, Ceva's and Menelaus's theorems being important examples of the theory of trans- versals. TRAN'SYLVA'NIA (Hung. Erdily, from erdo, forest, the name corresponding to the Latin, Tran.siJvnnia. beyond the forest; Ger. Siebenhiir- gen) . A former grand ducliy and crownland of Austria, since 1807 an integral part of the lands of the Hungarian crown. It occupies the south- eastern corner of the Hungarian Kingdom, and is bounded by Rumania on the east and soutli. Area, 21.518 square miles (Map: Hungary, H 3). It is inclosed on the east and south by the great range of the Carpathian Mountains, which bends round at a riglit angle, the part extending east and west being known as the Transylvanian Alps. The interior is crossed b.v numerous spurs of the border chains, and lias an elevated surface. Some of the valleys are remarkably fertile. The chief river, the Maros, an affluent of the Theiss. crosses the country from northeast to southwest. The southern part is traversed by the Aluta, an af- fluent of the Danube, which breaks through the Transylvanian Alps in the Red Tower Pass, while the northern part is drained by the Szamos, an affluent of the Theiss. Transylvania has a number of small mountain lakes and is rich in mineral springs. The region is famous for its scenery, and the mixture of nationalities, with the various costumes, adds greatly tq its pic- turesqueness. The climate is generally mild in the interior, especially along the rivers, while in the mountain regions the winters are long and severe. In spite of its mountainous surface, Transylvania has a very productive soil. The chief crops are wheat, barley, rye, oats, flax, tol)acco, and some industrial plants. Fruits and especially grapes are cultivated extensively. Stock-breeding is favored by the abundance of meadow land, and is carried on on a large scale. The local breed of horses is superior and many are exported. Wool is an important product. The mineral products in 1900 included 2200 kilograms of gold, 2574 kilograms of silver, and nearly 1,000,000 tons of coal. The total value of the mineral output was over .$7,000,000, of which salt alone amounted to over $2,000,000. Wild game still abounds in the mountains and large forests, including bears, wolves, foxes, and boars. Transylvania is well provided with transporta- tion facilities. The population was 2.251.216 in 1890 and 2,450,838 in 1900. About 50 per cent, of the inhabitants are Wallachs (Rumans), about 33 per cent. Magj'ars (Hungarians) and Szeklers (close kin to the Magj'ars) , and about 9 per cent. Germans. The Germans represent mainl.v de- scendants of colonists brought into the country from the region of the Lower Rhine by King Gejza II. of Hungary about the middle of the twelfth century. They dwell mainl.v in the south- ern part of the country, the district inhabited by them being known as Saxon Land. Their chief town is Hermannstadt. The great bulk of the inhabitants of Transylvania belong to the peas- ant class. The nobility and gentry are Magyars. ■ Of the population 30 per cent, are Greek Ortho- dox, 28 per cent. Greek Catholic, 24 per cent. Protestant, 13 per cent. Roman Catholic, 2^2 per cent, tinitarians (Transylvania having be- come the cradle of modern Unitarianism in the sixteenth century), and 2 per cent. Jewish. History. The largest cities of Transylvania are Klausenburg, which possesses a university, Krondstadt. Hermannstadt, and Maros-Vilsar- liel,v. Trans.vlvania formed part of the Roman province of Dacia. When the groat migration of nations took place it Avas for a time occupied by Germanic peoples. They were followed by the Avars, after whom came the Petehene,gs. In the eleventh century the country was brought under the sway of the Magyars. The advent of Ger- man colonists in the twelfth century improved the condition of the country. It was probably not long after this that the immigration of Wallachs set in from the region now called Rumania. Un- der the Hungarian kings Transylvania was ruled by voivodes. In 1520, after the battle of Jloliacs, in which Louis II. of Hungary was overwlu'lmed by Soh^man the Magnificent, the national party among the Hungarians chose John Zapolya, Voi- vode of Transylvania, King. He had a rival in Ferdinand I. of Hapsburg. Part of Hungary re- mained in possession of John Zapolya, who was upheld by the Turks. Transylvania was severed from the Kingdom of Hungary, the roval crown remaining in the' possession of the Hapsburgs. From 1571 to 1570 the country had an able prince in Stephen Bflthory, who in 1575 was elected King of Poland. Other princes of the Biithory (q.v.) family followed. At the beginning of the seventeenth century Transylvania was for a short time in the power of Austria, but in 1004 a great
