solid figure formed by the revolution of a right-angled triangle about one of the sides containing the right angle. The axis of the cone is the side about which the triangle revolves; the circle traced by the other side containing the right angle is the “base”; the hypotenuse in any one of its positions is a generator or generating line; and the intersection of the axis and a generator is termed the vertex. The Euclidean definition may be modified, so as to avoid the limits thereby placed on the figure, viz. the notion that the solid is between the vertex and the base. A general definition is as follows:—If two intersecting straight lines be given, and one of the lines is made to revolve about the other, which is fixed in such a manner that the angle between the lines is everywhere the same, then the surface (or solid) traced out by the moving line (or generator) is a cone, having the fixed line for axis, the point of intersection of the lines for vertex, and the angle between the lines for the semi-vertical angle of the cone.
An “oblique cone” is the solid or surface traced out by a line which passes through a fixed point and through the circumference of a circle, the fixed point not being on the line through the centre of the circle perpendicular to its plane. A “quadric cone” is a cone having any conic for its base. The plane containing the vertex, centre of the base, and perpendicular to the base is called the principal section; and the section of a cone by a plane containing the vertex is a triangle if the solid be considered, and two intersecting lines if the surface be considered. The “subcontrary section” of an oblique cone is made by a plane not parallel to the base, but perpendicular to the principal section, and inclined to the generating lines in that section at the same angles as the base; this section is a circle. The planes parallel to the base or subcontrary section are called “cyclic planes.”
The Greeks distinguished three types of right cones, named “acute,” “right-angled” and “obtuse,” according to the magnitude of the vertical angle; and Menaechmus showed that the sections of these cones by planes perpendicular to a generator were the ellipse, parabola and hyperbola respectively. Apollonius went further when he derived these curves by varying the inclination of the section of any right or oblique cone (see Conic Section). It is to be noted that the Greeks investigated these curves in solido, and consequently the geometry of the cone received much attention. The mensuration of the cone was established by Archimedes. He showed that the volume of the cone was one-third of that of the circumscribing cylinder, and that this was true for any type of cone. Therefore the volume is one-third of the product area of base ✕ vertical height. The surface of a right circular cone is equal to one-half of the circumference of the base multiplied by the slant height of the cone.
Analytically, the equation to a right cone formed by the revolution of the line 𝑦＝𝑚𝑥 about the axis of 𝑥 is 𝑧＝𝑚(𝑥2+𝑦2). Obviously every tangent plane passes through the vertex; this is the characteristic property of conical surfaces. Conical surfaces are also “developable” surfaces, i.e. the surface can be applied to a plane without wrinkling or rending. Connected with quadric cones is the interesting curve termed the “spheroconic,” which is the curve of intersection of any quadric cone and a sphere having its centre at the vertex of the cone.
References should be made to the articles Geometry and Surface for further discussion; and to the bibliographies of these articles for sources where the subject can be further studied. The geometrical construction of the curves of intersection of the cone with other solids is given in treatises on descriptive solid geometry, e.g. T. H. Eagles, Constructive Geometry.
CONECTE, THOMAS (d. 1434), French Carmelite monk and preacher, was born at Rennes. He travelled through Flanders and Picardy, denouncing the vices of the clergy and the extravagant dress of the women, especially their lofty head-dresses, or hennins. He ventured to teach that he who is a true servant of God need fear no papal curse, that the Roman hierarchy is corrupt, and that marriage is permissible to the clergy, of whom only some have the gift of continence. He was listened to by immense congregations, and in Italy, despite the opposition of Nicolas Kenton (d. 1468), provincial of the English Carmelites, he introduced several changes into the rules of that order. He was finally apprehended by order of Pope Eugenius IV., condemned and burnt for heresy.
An account of Friar Thomas’s preaching and its effect is given by Enguerrand de Monstrelet, provost of Cambrai (d. 1453), in his continuation of Froissart’s chronicles.
CONEGLIANO, a town and episcopal see of Venetia, Italy, in the province of Treviso, 17 m. N. by rail from the town of Treviso, 230 ft. above sea-level. Pop. (1901) town, 5880; commune, 10,252. It is commanded by a large castle. It was the birthplace of the painter Cima da Conegliano, a fine altarpiece by whom is in the cathedral (1492). The place is noted for its wine, chiefly sweet champagne.
CONESTOGA (said to mean “people of the immersed or forked poles”), a tribe of North American Indians of Iroquoian stock. Their country was Pennsylvania and Maryland on the lower Susquehanna river and at the head of Chesapeake bay. They were sometimes known as Susquehannas. They were formerly a powerful people, able to resist the attacks of the Iroquois. In 1675, however, the latter overwhelmed and scattered them. After nearly a century of wandering, the tribe suffered final extinction in the Indian wars of 1763.
CONEY ISLAND, an island about 9 m. S.E. of the S. end of Manhattan Island, U.S.A., on the S. shore of Long Island, from which it is separated by Gravesend Bay, Sheepshead Bay, Coney Island Creek, a tidal inlet, and a broad stretch of low salt marshes. It lies within the limits of the Borough of Brooklyn, New York city. The island is the westernmost of a chain of outlying sandbars that extends along the southern shore of Long Island for almost 100 m.; it is about 5 m. long and varies from 14 m. to 1 m. in width. It is served by the Long Island railway, by several lines of electric railway, and (in summer) by steamboat lines. The island is the most popular seashore resort of the United States. There are four quite distinctly marked districts. At the extreme western extremity, Norton’s Point, is the district known as Sea Gate, lying between Gravesend Bay and Lower New York Bay. It is an exclusively residential section, has a fine light-house, a large number of summer homes and the handsome club-house of the Atlantic Yacht Club. A broad shore drive connects it on the E. with West Brighton, the most popular amusement centre, to which the name Coney Island has come to be more especially applied. Its great scenic and spectacular features, “side-shows,” booths, cafés and dancing halls, have made “Coney Island” a well-known resort. There are bathing beaches, two immense iron piers, observation towers, scenic railways, “Ferris” wheels, and the two amusement reservations known as “Luna Park” and “Dreamland.” From West Brighton a broad parkway known as “the Concourse” connects with Brighton Beach, 34 m. to the E., passing the large bathing establishments maintained by the city of New York. At Brighton Beach there are a large hotel, a theatre and the Brighton Race Track. Still farther to the E., and extending to the eastern extremity of the island, lies Manhattan Beach, with hotels, a theatre and baths, and patronized more largely by a wealthier class of visitors. Adjacent to Manhattan Beach on the mainland, and separated from it by a narrow neck of Sheepshead Bay, lies the village of Sheepshead Bay, in which is the famous race track of the Coney Island Jockey Club.
CONFALONIERI, FEDERICO, Count (1785–1846), Italian revolutionist, was born at Milan, descended from a noble Lombard family. In 1806 he married Teresa Casati. During the Napoleonic period Confalonieri was among the opponents of the French régime, and was regarded as one of the leaders of the Italiani puri, or Italian national party. At the time of the Milan riots of 1814, when the minister Prina was assassinated, Confalonieri was unjustly accused of complicity in the deed. After the fall of Napoleon he went to Paris with the other Lombard delegates to plead his country’s cause, advocating the formation of a separate Lombard state under an independent prince. But he received no encouragement, for Lombardy was destined for Austria, and Lord Castlereagh consoled him by
