AB'C, ABC

are annex triangles. - Anterior triangle of the neck, a triangle on the surface of the neck bounded by the ventral midline, the sternoclidomastoid, and the lower margin of the mandible. It is divided into the submaxillary and superior and inferior carotid triangles. See cut under muscle 1. - Arithmetical triangle. See arith triangle metical, and figurate number (under figurate ). - Characteristic triangle spherical triangle having side angles an aliquot of 180°, its relation to the spherical net each face of which is composed of two or four such triangles. - Circular triangle, a plane figure formed by three arcs of circles intersecting two by two in three angles.- Conjugate tri angleen (a) triangle whose sides are mean proportionals dron. (b) See conjugate triangles, under conjugate. - Copolar triangles, diagonal triangle. See the adjectives. -Digastric triangle. Same as submaxillary triangle. -Equiangular triangle, a triangle all whose angles are equal: it is also equilateral. - Equilateral triangle, a triangle all whose sides are equal: it is also equiangular. - Fundamental triangle, the triangle which serves to define homogeneous coördinates in a plane.- Harmonic triangle, a triangular table of the reciprocals of succe ive numbers and their succe ive differences.He elbachian triangle. See He elbachian. - Homologous triangles, triangles placed projectively, so that the lines through corresponding angles meet in a point, and the intersections of corresponding sides (produced when nece ary) lie on a straight line. When two tri an between the of opposite gles ABC and UVW are homologous when A is considered as corresponding to U, B to V, and C to W, and also when A is considered as corresponding to V, B to W, and C to U, they are said to be doubly homologous; and they are then homologous also when A is considered as corresponding to W, B to U, and C to V.-In-and-circumscribed triangle, a triangle whose angles lie on a given curve or curves, and whose sides are tangent to a given curve or curves. - Inferior carotid triangle, a triangle on the surface of the neck bounded by the median line, the sternomastoid, and the anterior belly of the omohyoid. Also called the triangle of nece ity, as the place for tying the carotid, if it cannot be tied in the superior carotid triangle. See cut under musclel. - Inflexional triangle, an imaginary triangle upon whose sides lie, three by three, the nine points of inflexion of a plane cubic curve. - Infra clavicular, internal triangle. See the adjectives. In triangle, in her., arranged in the form of a triangle: said of bearings usually more than three in number. When three in number, they are generally blazoned as two and one; when six in number, they are blazoned three, two and one; and the term in triangle is used for a larger or indefinite number. - Isosceles triangle, a triangle two of whose sides are equal: the angles opposite those sides are also equal. - Medial line of a triangle, a straight line joining a vertex to the midpoint of the opposite side. Null-line of a triangle, a straight line the locus of points the sum of whose distances from two of the sides of a triangle is equal to the distance from the third side. Every null-line pa es through three intersections of sides with bisectors of internal or external angles of the triangle. - Oblique triangle, a triangle having no angle equal to 90°. - Occipital, ocellar, Pythagorean, quadrantal triangle. See the adjectives. - Plane triangle. (a) A triangle whose sides lie in one plane. (b) A triangle whose sides are rectilinear. Polar triangle, a triangle each vertex of which is in any sense a pole of a side of a primitive tri angle.-Posterior triangle of the neck, a triangle on the surface of the neck bounded by the anterior border of the trapezius, the sternoclidomastoid, and the clavicle. It is divided into the suboccipital and subclavian triangles by the omohyoid. See cut under musclel. - Rational prime triangle, a triangle whose sides are relatively prime multiples of a linear unit, while its area is commensurable with the square of that unit: thus, the sides may measure 10, 17, 21, this giving the area 84.- Remarkable circle of a triangle, a circle having a peculiar relation to any triangle. Such circles are particularly (1) the circumscribed circle; (2) the inscribed and the three escribed circles; (3) the Feuerbach or nine - point circle; (4) the Brocard or seven - point circle; (5) the Tucker or tripli. cate - ratio circle; (6) the sine triple - angle circle (constructed as follows: on the sides of the triangle ABC take Dand D' on BC, E and E' on AC, F and F on AB such that the angle AEF = AFE' = A, BFD = BD'F' = B, CDE = CE'D' = C; then the circle in question pa es through D, D', E, E', F, F', and DD': EE': FF = sin 3A: sin 3B: sin 3C); (7) the Taylor or six -point circle, which pa es through the six feet of perpendiculars drawn to the sides from feet of perpendicu lars on the sides from the vertices of the triangle; (8) the Spieker circle, or circle inscribed in the triangle whose vertices are the mid-points of the sides of the triangle. See circle. Remarkable point of a triangle, a point having unique metrical relations to the triangle. The remarkable points usually considered are-(1) the centroid, or intersection of median lines; (2) the orthocen ter, or intersection of perpendiculars from the angles upon the opposite sides; (3) the circumcenter, or center of the circumscribed circle; (4) the center of the Feuerbach circle; (5) the incenter, or center of the inscribed circle; (6) the Grebe, or Lemoine point, the intersection of the three lines radical center of the escribed the symmedian, each bisecting a side and bisecting a perpendicular from an angle upon a side; (8) the Spieker point, or mid-point between the circumcenter and incenter; (9) the Brocard points, two points of the Brocard circle (which see, under circle ) (through the symmedian point 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 Fon 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'); (10) the center of the triplicate - ratio circle; besides others.Respectant in triangle. See respectant. - Scarpa's triangle, a space on the anterior and inner aspect of the thigh just below the groin, through which the femoral artery pa es. - Self-conjugate triangle. See self - con fugate.- Sib i conjugate triangle. See sib i conjugate. Spherical triangle, a triangle formed on the surface of a sphere by the mutual intersection of three great circles. Spherical triangles are divided into right - angled, oblique angled, equilateral, isosceles, etc., as plane triangles are. Subclavian triangle, a triangle of the neck bounded by the omohyoid, sternoclidomastoid, and clavicle.- Submaxillary triangle, a triangle on the surface of the neck triangle bounded above by the lower margin of the lower jaw, and on its other two sides by the digastric muscle. See cut under muscle 1. - Suboccipital triangle, a triangle on the surface of the neck bounded by the anterior border of the trapezius, the sternoclidomastoid, and the omohyoid muscle. See cut under - Superior carotid triangle, a triangle on the surface of the neck bounded by the sternoclidomastoid, omohyoid, and digastric muscles. Also called triangle of election, with reference to facilities afforded for tying the carotid. See cut under muscle1. Supplemental triangle, a spherical triangle formed by joining the poles of three great circles. Surgical triangle, a triangular space, area, or region containing important ve els and nerves which may require to be operated upon: chiefly said of several such regions of the neck. - Triangle of election, in surg., same as superior carotid triangle. - Triangle of forces, a name given to the proposition in statics which a erts that, if three forces meeting at a point in one plane be in equilibrium, and if on that plane any three mutually intersecting lines be drawn parallel to the directions of the three forces, a triangle will be formed the lengths of whose sides will be proportional to the magnitudes of the forces. Triangle of He elbach. See He elbachian triangle . -Triangle of nece ity, in surg . , the inferior carotid triangle, where the artery must be tied, if there be no room for choice or election. - Triangle of Petit, a triangular space in the lateral wall of the abdomen, bounded below by the crest of the ilium and laterally by the obliquus extern us and lat is sim us dors i muscles. - Triangle of reference. Same as fundamental triangle . - Triangles in cro , in her . , a bearing consisting of a number of triangles arranged in a cro , the number being specified in the blazon. Also called cro of triangles. - Triangles of the neck, certain triangular spaces or areas on each side of the neck, bounded by several muscles, notably the sternoclidomastoid, omohyoid, and digastric us, and by the collar bone and lower jaw-bone, and containing important ve els and nerves which may require to be operated upon. The sides of all these triangles are the natural landmarks in the topographical anatomy of the neck.-Triangle spider, a spider, as Hyptiotes cavatus, which spins a triangu Triangle Spider ( Hyptiotes cavatus). (Spider five times natural size, web one third natural size.) 6464 having three legs, two opening in the usual manner, and the third turning round an extension of the central pin of the other two, besides having a motion on its own central joint. By means of this instrument any triangle or any three points may be taken off at once.- Triangular coördinates. See coördinate. - Triangular crab, any maioid, whose carapace is more or le triangular. 'See The Century Dictionary and Cyclopedia: The Century dictionary A Tri an gula res.-Triangular fascia, a thin triangular fibrous band reflected upward and inward beneath the spermatic cord from the attachment of Gimbernat's ligament on the line a iliopectinæa to the line a alba. Also called triangular ligament. - Triangular fibrocartilage, file, fret. See the nouns. - Triangular level, a light frame in the shape of the letter A, and having a plumb-line which determines verticality. - Triangular ligament. (a) Same as triangular fascia. (b) A dense fibrous membrane stretched acro the subpubic arch on the deep surface of the crura of the penis and the bulb of the urethra. Also called deep Triangular Level. perineal or subpubic fascia.- Triangular numbers, the series of figurate numbers which consists of the succe ive sums of the terms of an arithmetical series whose first term is 1 and the common difference 1. Thus, 1, 3, 6, 10, 15, 21, 28, etc., are re triangular numbers. They are so called because the number of points expre ed by any one of them may be arranged in the form of an equilateral triangle. - Triangular plexus. See plexus. -Triangular pyramid, a pyramid whose base is a triangle, its sides consisting of three triangles which meet in a point called its vertex. - Triangular scale. See scale3. tri an gul are (tri-ang-gu-lā'rē), n.; pl. triangu lari a (-ri-ä). [NL. (sc. os, bone), neut. of L. triangular is: see triangular.] A peculiar bone of the tarsus of some animals, as Cryptoprocta ferox: more fully called tri an gul are tarsi. Bar deleben.