Also 5 tri-, tryangyl, 5–7 tryangle, 6 triangil, tryanghel, 6–7 triangill; 5–6 treangle, 6 treeangle, treangell. [a. F. triangle (13th c. in Godef., Compl.), or ad. its source, L. triangulum, sb. neut. from triangulus adj. three-cornered, f. tri-, TRI- + angulus ANGLE.]
1. Geom., etc. A figure (usually, a plane rectilineal figure) having three angles and three sides.
In mod. Geom. a triangle is regarded as a system of three points not collinear, together with the three straight lines joining them; or as a system of three straight lines each intersecting the two others at different points.
Circular triangle, a plane triangle formed by three intersecting circular arcs. Spherical triangle, a triangle formed by three arcs upon the surface of a sphere: see SPHERICAL. Triangle of forces, the theorem in statics that if three forces in one plane, acting at one point, be in equilibrium, three straight lines in that plane parallel to their directions will form a triangle whose sides are proportional to their magnitudes.
1398. Trevisa, Barth. De P. R., XVII. cviii. (Tollem. MS.). Some [nuts] ben distinguid in þe cop as it were with þe schap of a triangle [orig. per formam trianguli].
c. 1400. Lanfranc’s Cirurg., 258. Þe nose is maad of .ij. boones in þe maner of a triangle in þis maner. Δ Δ.
1551. Recorde, Pathw. Knowl., I. Defin., A triangle is nothinge els to say, but a figure of three corners.
1560. Daus, trans. Sleidane’s Comm., 451. Betwyxt Caleis, Arde and Grauelyn, Townes … set as it were a treangle.
1646. Sir T. Browne, Pseud. Ep., 25. In every triangle, two sides which soever be taken are greater then the side remaining.
1781. Gibbon, Decl. & F., xvii. II. 3. The figure of the imperial city [Constantinople] may be represented under that of an unequal triangle.
1885. Leudesdorf, Cremona’s Proj. Geom., 145. A series of theorems … relating to the inscribed pentagon, quadrangle, and triangle … a series of correlative theorems relating to the circumscribed pentagon, quadrilateral, and triangle.
b. A figure of this form used symbolically (e.g., an equilateral triangle as a symbol of the Trinity), or in magic or necromancy. In Her. a figure of this form as a bearing; in triangle, said of three or more bearings arranged in the form of a triangle.
1584. R. Scot, Discov. Witchcr., XV. ii. (1886), 322. He is a lier, except he be brought into a triangle, and there he speaketh divinelie.
1766. Porny, Heraldry (1787), 175. Azure, three Trouts fretty in Triangle Argent.
1810. Southey, Kehama, XIX. viii. The sacred Triangle … Holding the Emblem which no tongue may tell.
c. 1828. Berry, Encycl. Her., I. Gloss., Triangle, this sometimes occurs as a bearing in coat-armour. See Cross of Triangles, or twelve triangles in cross.
1864. Boutell, Her. Hist. & Pop., xix. § 5 (ed. 3), 311. A nail in every point thereof, in triangle.
1894. Parker’s Gloss. Her., s.v., Charges may be described as fretted in triangle, e.g. in the arms of Troutbeck (under Salmon)…. The insignia of the Isle of Man are sometimes blazoned as flexed in triangle.
c. fig. A group or set of three, a triad.
1621. T. Williamson, trans. Goulart’s Wise Vieillard, 129. In this sacred triangle is included the renouncing of our selues.
1659. Whiting (title), Old Jacob’s Altar, newly repaired; or, the Saints Triangle of Dangers, Deliverances, and Duties.
1907. Daily Chron., 5 Dec., 3/4. Mrs. Dudeney’s novel … deals with the eternal triangle, which, in this case, consists of two men and one woman.
2. Something having the form of a triangle; any three-cornered body, object, or space.
a. 1618. Sylvester, Mem. Mortalitie, II. lx. Th’ Earth cannot fill thy heart’s unequall Angles, Thy heart’s a Triangle, the earth’s a Round.
1788. Gibbon, Decl. & F., l. (1846), V. 2. The Arabian peninsula may be conceived as a triangle of spacious but irregular dimensions.
1791. Newte, Tour Eng. & Scot., 120. The present fort, which is a triangle, has two bastions.
1843. Carlyle, Past & Pr., II. i. In what wig and black triangle dost thou walk abroad?
1847. Mrs. A. Kerr, trans. Ranke’s Hist. Servia, i. 13. The Servians … in the first half of the 14th century … formed the strongest power of the Illyrian triangle.
1895. R. W. Chambers, King in Yellow, Demoiselle D’Ys, i. A long wavering triangle of water-fowl drifted southward over our heads.
spec. *natural objects.
b. Palmistry. A triangular figure made by three of the lines of the hand: see quot. 1653.
c. 1460. Metham, Wks. (E.E.T.S.), 86. A tryangyl that ys off one length, evyn on alle partys … betokynnyth bodyly strengh and bold off herte. Ibid. The fyrste lyne ys the fyrst parte off the tryangyl, and yt gothe aboute the hylle of the thombe.
1653. R. Sanders, Physiogn., 58. This Triangle is made in the hand by three Lines, that of Life, the middle natural Line, and that of the Head.
c. Astron. The constellation Triangulum, north of Aries, characterized by three stars in the positions of the angular points of an isosceles triangle.
Also, Triangulum minus, the Lesser Triangle, a constellation immediately south of this, introduced by Hevelius in 1690, but now disused; Triangulum australe, the Southern Triangle, a modern constellation near the South Pole.
1551. Recorde, Cast. Knowl. (1556), 265. By hir [Andromeda’s] lefte foot is ther a small constellation … commonly called the Triangle.
1868. Lockyer, Guillemin’s Heavens (ed. 3), 334. The Altar and the Southern Triangle, which lie along the Milky Way in looking towards the pole.
d. Anat. Applied, with defining words, to the triangular areas bounded by certain muscles: as
Triangles of the neck, anterior (subdivided into the submaxillary triangle and the superior and inferior carotid triangles) and posterior (subdivided into the occipital and subclavian triangles); Triangle of Petit, above the crest of the ilium; Scarpa’s tr., in the upper part of the thigh.
1846. Brittan, trans. Malgaigne’s Man. Oper. Surg., 147. The inferior triangle of the popliteal space is bounded on each side by the heads of the gastrocnemius.
1876. Clin. Soc. Trans., IX. 41. I removed all the enlarged glands in front of the sterno-mastoid, and thus cleared the anterior triangle of the neck.
1897. Allbutt’s Syst. Med., IV. 418. [An abscess] may open superficially in the loin through the triangle of Petit.
e. Entom. A triangular marking or space on an insect’s wing.
1832. [see 4].
1891. Cent. Dict., Triangle.… In entom. a large three-sided cell found in the wings of many dragonflies … often called the discoidal triangle, to distinguish it from the internal triangle, which adjoins it on the inner side, and the anal triangle, which lies close to the anal border of the wing.
f. A species of box-fish of triangular form, as Ostracion trigonum.
** artificial objects.
g. A small ornament or piece of jewelery of a triangular form.
1528. Will of W. Mores (Somerset Ho.). A triangill of siluer and gilte.
1529. Will of Leigh (ibid.). My corsse gurdell wt the Treeangle of flowres of silver and golde.
1531. Rec. St. Mary at Hill, 48. A demysent [girdle] with … a pendantte a treangell of selver and gelt.
1632. J. Hayward, trans. Biondi’s Eromena, 120. This Iewell … a triangle of three rich diamonds, each angle … enriched with a great pearle.
† h. Eccl. A stand or frame on which copes were hung up. Obs.
1532. in Archæol. Cant. (1872), VIII. 124. Item a treangle for copys, a presse [Editor’s Note, a crane or stand for hanging copes].
1538. in Archæologia, XLIII. 226. ij chestes and the tryangle for the same ornaments to be hengyd.
1849. Rock, Ch. of Fathers, II. vi. 43. [A doubtful statement].
† i. (More fully triangle virginal), an early kind of keyboard stringed instrument. Obs.
[1661. Pepys, Diary, 14 June. I sent to my house by my Lord’s order his shipp and triangle virginall.] Ibid. (1662–3), 18 March. This day my tryangle which was put in tune yesterday, did please me very well.
j. A musical instrument of percussion, consisting of a steel rod bent into a triangular form, but open at one corner; it is struck with a small straight steel rod. Also transf. = TRIANGLER.
1801. in Busby, Dict. Mus.
1811. Lady Granville, Lett. (1898), I. 21. We play upon the … guitar, triangle, and castagnettes.
1878. F. Hueffer, in Grove, Dict. Mus., I. 28/1. He is said to have accepted the appointment of supernumerary triangle at the Gymnase.
1913. Times, 14 May, 8/5. The only percussion (even the usual drums are excluded) consists of triangle and cymbals.
k. Name for a kind of large tripod composed of three poles or spars joined at the top, bearing a pulley for hoisting heavy weights, or for weighing: see also quot. 1867.
1699. Evelyn, Kal. Hort. (ed. 9), 63. If the Tree be too ponderous to be lifted perpendicular by the Hand alone, by applying a Triangle and Pully … draw out the Tree.
1707. Mortimer, Husb. (1721), I. 187. Set up three Poles (like unto a Triangle wherewith they usually weigh heavy Ware) spreading at the Bottom.
1867. Smyth, Sailor’s Word-bk., Triangle,… a machine formed by spars for lifting weights, water-casks, &c. Also, a stage hung round a mast, to scrape, paint, or grease it.
1873. in 5th Rep. Dep. Kpr. Irel., 26. The Records were lowered through the aperture in the centre of the floor by means of a rope, supported by a triangle raised over the opening.
l. Mil. (Usually pl.) A tripod, orig. formed of three halberds stuck in the ground and joined at the top, to which soldiers were formerly bound to be flogged; a structure resembling this.
[1796. Grose, Dict. Vulg. T., s.v. Halbert, Soldiers of the infantry, when flogged, being commonly tied to three halberts, set up in a triangle, with a fourth fastened across them.]
1847. in Webster.
1853. Stocqueler, Milit. Encycl., Triangles, a wooden instrument consisting of three poles so fastened at top that they may spread at bottom in a triangular form…. An iron bar, breast high, goes across one side of the triangle. The triangles were used in some regiments for … inflicting military punishments.
1871. G. Lawrence, Anteros, i. (1872), 11. He was unsparing both of his tongue and of the lash—the triangles were an honoured institution in those days.
1897. P. Warung, Tales Old Regime, 29. Already, at Molong [Australia], there is one military-post and a triangles, and at Wellington Valley there is another military-post and another triangles.
m. Pottery. A triangular piece of baked ware, with points projecting from the angles, placed between pieces of biscuit ware to prevent their adhering to each other when baking.
1877. in Knight, Dict. Mech.
n. Angling. A set of three hooks fastened together so that their barbs are at the angular points of a triangle.
1867. F. Francis, Angling, iv. (1880), 116. I had used a single flight of small brazed triangles.
1904. Gallichan, Fishing Spain, 145. The flying triangles are to blame. It is not often that one loses a fish hooked on the tail triangle.
o. A drawing-instrument in the form of a right-angled triangle of wood, vulcanite, etc.; a set square.
1877. Knight, Dict. Mech., Triangle.… A three-cornered straight-edge,… for drawing parallel, perpendicular, or diagonal lines. It has one right angle, the two others being each of 45°, or one of 30° and the other of 60°.
3. Collectors’ name for certain moths. See also 4.
1832. Rennie, Conspect. Butterfl. & Moths, 55. The Triangle (Gr[aphiphora] Triangulum, Ochsenheimer) appears the end of July. Ibid., 164. The Triangle (P[seudotamia] trigonana, Stephens). Near London.
4. Comb., as triangle-marked adj.; triangle moth, Limacodes asellus; triangle-ways adv. (rare) = TRIANGLEWISE.
1689. Lond. Gaz., No. 2485/4. 16 silver Trencher-Plates;… marked with a Cypher triangle-ways.
1832. Rennie, Conspect. Butterfl. & Moths, 228. The Triangle-marked Purple (G[racillaria] purpurea, Haworth). Wings … purple, with a three-cornered central halfband…. The Triangle-marked Red (G. stigmatella, Stephens)…. The Triangle Marked Buff (G. ochracca, Haworth).
