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248 CONIC SECTIONS CONINGTON luzzo. II. A city, capital of the province, situ- ated 1,500 ft. above the sea, near the junction of the Gesso and Stura torrents, 46 m. S. of Turin, with which it is connected by railway ; pop. in 1872, 22,882. Coni was originally a city of refuge. About the year 1100 Boniface, marquis of Savoy, conquered the region and established there the marquisate of Susa, but was not able to repress the outrages of the neighboring barons. The people soon rose against them, razed their strongholds, and built a town upon the site of the present city, which they called the "new city of Cuneo." In the 16th century the place was strongly fortified, and afterward underwent many sieges. In 1800, after the battle of Marengo, the French dismantled the fortress, and converted its site into promenades, and the town is now defended only by a wall. The cathedral is the ancient sanctuary of the "Madonna del Bosco," but has otherwise little interest. The church of San Francisco, belonging to a Capuchin con- vent, dates from the 12th century. There is also a handsome town hall, and other public buildings, and a pleasant public walk at the junction of the Gesso and Stura. There are considerable manufactures of silk and cotton, and the city is an agricultural mart for the sur- rounding region. About 10 m. S. W., in the the Val di Gesso, are the mineral baths of Val- dieri, a place of much resort. CONIC SECTIONS, the name given to the sec- tions formed by cutting a right cone by a plane. The term is also constantly used to denote the curves formed by the intersection of the cut- ting plane with the surface of the cone. If the plane be parallel to the base of the cone, the section is a circle, or through the vertex a point. If the angle between the cutting plane and the plane of the base is less than the angle between the side of the cone and the base, the section is an ellipse, or through the vertex a point. If the angle between the cutting plane and the plane of the base is equal to that be- tween the side of the cone and the base, the section is a parabola, or through the vertex a straight line. If the angle between the cutting plane and the plane of the base is greater than that between the side of the cone and the base, the section is a hyperbola, or through the ver- tex a triangle. If we suppose two similar cones to be so placed that they touch each other only at their vertices, and their axes form one straight line, then in the case of the hyperbola the cutting plane will cut both cones, giving two curves, which however are generally re- garded as two branches of one curve. The properties of the conic sections were investi- gated with great thoroughness by the ancient Greek mathematicians of the school of Plato. Four books by Apollonius of Perga on conic sections have come down to us in the original Greek, and three more in Arabic transla- tions. They are wonderfully full and accu- rate, and have left comparatively little for modern geometers to do in the investigation of the properties of these curves. Conic sec- tions were in his day merely speculative theo- ries; but after the lapse of 18 centuries it was discovered by Kepler that the orbits of the planets are ellipses, and from that time nearly all the most brilliant applications of mathematics to natural science and to the practical arts have been possible only through the use of conic sections. What was pure geometrical speculation among the Greeks, has proved of much practical advantage to us, the inheritors of their knowledge. The curves are now generally treated by the methods of ana- lytical geometry. Every conic section may be represented by an equation of the second de- gree, and conversely every equation of the second degree may be represented by a conic section. One of the best purely geometrical treatises on the subject is the " Conic Sec- tions " of Prof. Jackson of Union college ; and the most elaborate and at the same time clear and practical analytical treatise is the " Conic Sections" of Prof. Salmon of Dublin. CONINGTON, John, an English author, born at Fishtoft, near Boston, Aug. 10, 1825, died there, Oct. 25, 1869. He knew his letters when he was fourteen months old, and could read for his own amusement at three and a half years. Before he was six years old he was well acquainted with the historical parts of the Bible, and at eight he could repeat a considerable portion of the uEneid. In 1836 he was sent to the Beverley grammar school, where he remained two years, and at the age of 13 he entered the school at Rugby under Dr. Arnold. He was here distinguished for his re- markable memory and excellent scholarship, and after a course of five years was matriculated at Oxford in 1843. In 1847 he became a fellow of the university, and devoted himself chiefly to the study of the classics. He left Oxford in the following year, and established himself in London as a student of law. But he could not transfer his interest in the ancient poets to jurisprudence, and the experiment proved a failure. After six months' trial he returned to Oxford, and resumed his favorite pursuits. During his stay in London he formed a con- nection with the "Morning Chronicle," and for a time became a regular contributor to that journal. In 1857 he published an edition of the " ChoephoroB " of ^Eschylus, having previ- ously edited the " Agamemnon," with a trans- lation into English verse which he afterward suppressed. He had also collected the mate- rials for an edition of the "Supplices," which he was prevented from compiling by the plan for editing Virgil in conjunction with Mr. Goldwin Smith, and his subsequent appoint- ment to the chair of Latin. The first volume of the edition of Virgil, containing the Eclogues and Georgics, was published in 1858, Mr. Smith having retired from the joint editorship. In 1863 he published a translation of the Odes of Horace, which was followed by the ^Eneid in 1866, by the last 12 books of the Iliad in 1868,