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* CARTESIANS. 265 CARTHAGE. and those which reduce to eardioids are of tlic third class. A curve in space defined as the locus of a point whose distances from three fixed points (1) It p > m. the origin is a dnuble point. (2) It p = 111, the origin is a eusp. (3) If p < m, the origin is a conjugate point. are connected liy two linear relations is called a twisted Cartesian. See also Cassini and Cas- si.MAX Oval. CARTHAGE (Lat. Carthago, Gk.KapxvS'ii', KarchCdOii ). The greatest city of antiquity on the north coast of Africa, situated in about latitude 36° .50' N. and longitude 10° 20' E., near the modern Tunis, on a peninsula extending into a small bay of the jSIediterranean Sea. It was founded, according to legend, by Dido (q.v.), a Phtcnician queen, who had fled from Tyre after the murder of her husband; but more probably it originated in an emporium or factory estab- lished by the colonial merchants of Vtica, and the capitalists of the mother city Tyre, on ac- count of the conveiiience of its situation. The native name of the city seems to have been Kart Iladisha, the 'new town,' probably with refer- ence to Tyre, which was always recognized by the Carthaginians as their mother city. Unfor- tunately, we know very little of its growth. Our information only begins after Carthage had be- come one of the greatest coinniercial cities of the world, and we have but very scanty and one- sided accounts of it even then. The number of inhabitants in B.C. 149, just before the Third Punic War, is said to have been about 700,000. The population was partly of Pha>nician, partly of Libyan descent. The territory which the Carthaginians acquired by the subjugation of the Libyan tribes, and by the ultimate annexa- tion of other older Phoenician colonics, with which they had at first been simply in alliance, such as Utiea, Ihidrumetum, Hippo, the two Leptes, etc., extended in the middle of the Fifth Century B.C. southward to Lake Triton, east- ward to the Great Syrtis, and westward to the Atlantic. At first, Carthage was essentially n mercantile city, and even paid a ground- rent to the Libyan tribes until the Fifth Cen- tury. It was the maritime power of the Car- thaginians which enabled them to extend their settlements and conquests to the other coasts of the ilediterranean. At the beginning of the Sixth Century B.C., Carthage appears as the ally of the Phrcnicians in Sicily, now crowded by the Greeks into the western part of the island. After cliccking the Greek advance and founding colonies of their own, the Carthaginians reduced the coasts of Sardinia. Ilanno (q.v.) founded col- onies on the west coast of Africa heyimd the Straits of Gibraltar, and Himilco visited the coasts of Spain and Gaul. With the establishment of this control over the western ^Mediterranean, Carthage also estab- lished her trading policy. No foreign traders were allowed at any of her western colonies, and only the harbors of Carthage were open to foreign ships. All trailers found elsewhere were drowned. This policy led the Cartha- ginians to form an alliance with the Etrus- cans, and in B.C. 540, in the battle of Alalia, they checked the attempts of the Greeks to en- croach upon their territory, ^fassilia (Marseilles) alone held its position on the coast of Gaul. The first treaty with the Romans was concluded in B.C. son, the second in B.C. .348. the third in B.C. 306. The connected history of Carthage begins with the Fifth Century B.C., a ))eriod of wars between the Carthaginians and the Greeks in Sicily. The Carthiiginian army under Ilamilcar was destroyed by Gelon, at Ilimcra. in B.C. 480, and for a time the Greeks were free from attack. In B.C. 410 wars broke out anew, and the Greek cities of the southern coast of Sicily were plun- dered and destroyed. At Syracuse the pestilence comjiellcd the Carthaginians to raise the siege, and under the leadership of Dionysius I., the tyrant of Syracuse, the Greeks recovered much of their lost territory. After several unsuccessful attempts to drive the Carthaginians from the island, Dionysius, in B.C. 383, made a treaty which gave them the land west of the river Haly- cus. A later invasion of the Carthaginians was repelled by Timoleon (q.v.), in B.C. 343, but tliirty years later, when Agathocles was tyrant of Syracuse, the war began again, and Syracuse was once more besieged. Deserting his city, Agathocles crossed to Africa, and for three years ravaged the almost defenseless territory of Car- thage, though not strong enough to attack the city. After his death the Carthaginians again increased their dominions in Sicily, and although Pyrrhus contended successfully against them at first, he left that island entirely in B.C. 275. The subjugation of southern Italy by the Ro- mans brought the two great conquering nations into collision, and the First Punic War arose ( n.c. 264). ami after a great naval victory of the Romans, terminated in B.C. 241, the Carthagin- ians giving up Sicily, and paying to the Romans a large sum of money. Soon after this a mutiny of the hired troops of Carthage, cotnbined with an insurrection of the Libyan trilies, the ancient inhabitants of the country, who were ke|)t down by the arbitrai'y rule of the Carthaginian colo- nists, threatened the entire ruin of the city. Ilam- ilcar Barca brought this bloody war to a success- ful termination, but Carthage, crippled by the struggle, was unable to prevent the Romans from seizing Sardinia and Corsica. Abiuit B.C. 236 Hamilcar Barca led an army to Spain, where he, and, after him, his son-in-law, Ilasdrubal, obtained great successes. Here was founded New Carthage, now Cartagena (q.v.). After Hasdru- bal's death (n.C. 221), Hannibal (q.v.). burning to revenge the defeat which his native city had sustained from the Romans, attacked and took Saguntum, a city on the Ebro. allied with Rome (B.C. 219). Thus began the Second Punic War,