Page:Collier's New Encyclopedia v. 09.djvu/571

TBEWIA 501 TRIANGLE TREWIA, in botany, the typical ge- nus of Trewiacese. Leaves opposite, en- tire, without stipules; flowers dioecious, males in long, racemes, females axillary, solitary; males, sepals three to four, sta- mens many; females, calyx three to four- cleft, style four-cleft; drupe five-celled, each cell with a single seed. Known spe- cies one, T. nudi-flora, an Indian decidu- ous tree, growing in the sub-Himalayas. The wood is used for drums and agricul- tural implements. TRIACANTHINA, in ichthyology, a &roup of Sclerodermi, with three genera, having the range of the family. The skin is covered with small, rough, scalelike scutes; dorsal, with from four to six spines; a pair of strong movable ventral spines joined to the pelvic bone. TRIACANTHUS, in ichthyology, a genus of Triacanthina, with five species ranging from the Australian seas to the N. of China. T. brevirostris, from the Indian Ocean, is the most common. TRI.fflNOPS, in zoology, a genus of Phyllorhininse, with one species from Persia and another from East Africa. Noseleaf, horse-shoe-shaped in front, tri- dentate behind; ears without a distinct antitragus, the outer margin of the ear conch arising from the posteriors of the eyelids. TRIANGLE, in building, a gin formed by three spars; a staging of three spars. In draughting, a three-cornered straight- edge, used in conjunction with the T- square for drawing parallel, perpendicu- lar, or diagonal lines. It has one right angle, the two others being each of 45°, or one of 30° and the other of 60°. In ecclesiology, a symbol of the Holy Trin- ity represented by an equilateral tri- angle. In geometry, a portion of a surface bounded by three lines, and consequently having three angles. Triangles are either plane, spherical, or curvilinear. A plane triangle is a portion of a plane bounded by three straight lines called sides, and their points of intersection are the vertices of the triangle. Plane tri- angles may be classified either with ref- erence to their sides or their angles. When classified with reference to their sides, there are two classes: (1) Scalene triangles, which have no two sides equal. (2) Isosceles triangles, which have two sides equal. The isosceles triangle has a particular case, called the equilateral tri- angle, all of whose sides are equal. When classified with reference to their angles, there are two classes: (1) Right-angled triangles, which have one right angle. (2) Oblique-angled triangles, all of whose angles are oblique; subdivided into (a) acute-angled triangles, which have all their angles acute; and (&) obtuse- angled triangles, which have one obtuae angle. The sides and angles of a tri- angle are called its elements; the side on which it is supposed to stand is called the base, and the vertex of the opposite angle is called the vertex of the triangle ; the distance from the vertex to the base is the altitude. Any side of a triangle may be regarded as a base, though in the right-angled triangle one of the sides about the right angle is usually taken. The three angles of a plane triangle are together equal to two right angles, or 180°; its area is equal to half that of a rectangle or parallelogram having the same base and altitude; in a right-an- gled plane triangle the square of the side opposite the right angle is equal to the sum of the squares of the other two sides. In music, a bar of steel bent into the form of a triangle. It is su^ended by one angle and struck with a small rod. In pottery, a small piece of pottery placed between pieces of biscuit ware in the seggar to prevent the adherence of the pieces when fired. In surveying, since every plane figure may be regarded as composed of a certain number of tri- angles, and as the area of a triangle is easily computed, the whole practice of land surveying is nothing more than the measurement of a series of plane tri- angles. Arithmetical triangle, a name given to a table of numbers arranged in a triangular manner, and formerly em- ployed in arithmetical computation. It is equivalent to a multiplication table. 1 1 1 12 1 13 3 1 14 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 Curvilinear triangle, a triangle whose sides are curved lines of any kind what- ever; as, a spheroidal triangle, lying on the surface of an ellipsoid, etc. Mixtilinear triangle, a triangle in which some of the lines are straight and others curved. Spherical triangles take the names, right-angled, obtuse-angled, acute- angled, scalene, isosceles, and equilateral, in the same cases as plane triangles. Two spherical triangles are polar, when the angles of the one are supplements of the sides of the other, taken in the same order. A spherical triangle is quadrantal, when one of its sides is equal to 90°.