n. A triangular box-fish, as Sectophrys trigonus, of the family Ostraciidæ of the West Indies.n. In angling, an arrangement of three fish-hooks bound together with the points outward, forming a triangle.Three-cornered; three-angled; triangular.n. In geometry, a figure composed of three lines which meet two by two in three points, called the vertiees of the triangle; especially, a rectilinear figure of this description.n. Any three-cornered or three-sided figure, body, or arrangement; anything having a triangular form or bounding a three-sided space.n. A musical instrument of percussion, made of a rod of polished steel bent into the form of a triangle, and open at one of its angles.n. [capitalized] In astron, same as Triangulum.n. Eccles., a symbol of the Trinity.n. A chest made in triangular form to hold a priest's cope.n. A three-cornered straight-edge, with one right angle and the other angles more or less acute, used in conjunction with the T-square for drawing parallel, perpendicular, or diagonal lines.n. A kind of gin for raising heavy weights, formed by three spars joined at top. See gin, 2 .n. Milit., formerly, in the British army, a sort of frame formed of three halberds stuck in the ground and united at the top, to which soldiers were bound to be flogged: generally in the plural.n. In ceramics, a form of the stilt consisting of three metal pins held together in the form of a triangle. See stilt, 5.n. One of certain tortricid moths: an English collectors' name. Tortrix rufana is the red triangle.n. In entomology, a large three-sided cell found in the wings of many dragon-flies.n. See conjugate triangles, under conjugate.n. A triangle whose sides are rectilinear.n. the circumscribed circle;n. the inscribed and the three escribed circles;n. the Feuerback or nine-point circle;n. the Brocard or seven-point circle;n. the Tucker or triplicate-ratio cirde;n. the sine triple-angle circle (constructed as follows: on the sides of the triangle ABC take D and D' on BC, E and E' on AC, F and F' on AB such that the angle AEF =AF'E' =A, BFD =BD'F' =B, CDE =CE'D' =C; then the circle in question passes through D, D', E, E', F, F', and DD': EE': FF'=sin 3A: sin 3B: sin 3C)n. the Taylor or six-point circle, which passes through the six feet of perpendiculars drawn to the sides from feet of perpendiculars on the sides from the vertices of the trianglen. the Spieker circle, or circle inscribed in the triangle whose vertices are the mid-points of the sides of the primitive triangle. See circle.n. the centroid, or intersection of median linesn. the orthocenter, or intersection of perpendiculars from the angles upon the opposite sidesn. the circumcenter, or center of the circumscribed circlen. the center of the Feuerbach circle;n. the incenter, or center of the inscribed circlen. the radical center of the escribed circles;n. the symmedian, Grebe, or Lemoine point, the intersection of the three lines each bisecting a side and bisecting a perpendicular from an angle upon a siden. the Spieker point, or mid-point between the circumcenter and incentern. the Brocard points, two points of the Brocard circle (which see, under circle) (through the symmedian point S of any triangle ABC lines are drawn parallel to the sides of the latter, meeting these sides in D and D' on BC, E and E' on AC, F and F' on AB, so that D, S. E' are collinear, as well as E, S, F' and F, S, D'; then the three lines through A parallel to FD, through B parallel to DE, and through C parallel to EF meet in one Brocard point P, while the lines through A parallel to D' E', through B parallel to E'F', and through C parallel to F' D' meet in the other Brocard point P')n. (10) the center of the triplicate-ratio circle; besides others.
