a. (sb.). Also 6–7 -er, -are, (7 triangler). [ad. late L. triangulār-is: see TRIANGLE and -AR1. Cf. OF. triang(u)lier (13th c. in Godef.).]
1. Having, or arranged in, the form of a triangle; contained by three sides and angles; three-cornered, three-sided.
1541. R. Copland, Guydon’s Quest. Chirurg., E iv. The bony substaunce [of the nose] hath two trianguler bones wherwith the brydge is reysed vp.
1590. Spenser, F. Q., II. ix. 22. The frame thereof seemd partly circulare, And part triangulare.
1644. Evelyn, Diary, 3 Feb. A triangular brick building.
1776. Withering, Brit. Plants (1796), II. 375. Populus … Leaves nearly triangular, toothed and angular.
1825. Scott, Talism., i. His triangular shield suspended round his neck.
b. Situated at the angular points of a triangle. (In quots. quasi-adv.) ? Obs.
1622. Drayton, Poly-olb., xxii. 1152. Three … hils that stand Trianguler.
1707. Mortimer, Husb. (1721), II. 74. 3 or 4 quarter Stakes set triangular or quadrangular.
c. Having three edges, as a prism or pyramid; three-edged, trihedral, triquetrous.
1644. Digby, Nat. Bodies, xxix. § 1. 257. Those … cunning in Optikes … by refractions … make all sortes of colours out of pure light: as we see … in … triangular glasses, or prismes.
1665. Sir T. Herbert, Trav. (1677), 384. Other strange Fish we had … some were globous, others triangular.
1727–41. Chambers, Cycl., s.v. Pyramid, The pyramid is said to be triangular, quadrangular, &c. as the base is triangular, quadrangular, &c.
1807. Hutton, Course Math., II. 262. To find the Number of Balls in a Triangular Pile.
1852. Mrs. Stowe, Uncle Tom’s C., vi. The small, sharp, triangular beech-nuts lay scattered thickly on the ground.
1873. E. Spon, Workshop Receipts, Ser. I. 330/2. Triangular glovers’ needles for sewing up skins.
d. Contained by triangles, as a solid figure; of which the faces are triangles. rare.
1805–17. R. Jameson, Char. Min. (ed. 3), 144. Triangular Dodecahedron … consists of two six-sided pyramids, joined base to base.
2. Pertaining or relating to a triangle: as triangular compasses, a kind of compasses with three legs, used for taking off triangles; triangular co-ordinates (Geom.), a kind of trilinear co-ordinates. Triangular quadrant: see quot. 1706.
1701. Moxon, Math. Instr., 21. Triangular Compasses, containing 3 Legs or Feet, to take off at once any Triangle used on Maps, Globes, etc.
1706. Phillips (ed. Kersey), Triangular Quadrant, is a Sector with a loose Piece to make it an Equilateral Triangle; having the Calendar graduated on it, with the Sun’s Place, Declination, &c. It is an Instrument of great Use in the Arts of Dialling, Navigation, and Surveying.
1807. T. Young, Lect. Nat. Philos., etc., I. x. 102. Triangular compasses are sometimes used for laying down a triangle equal to a given triangle.
b. Arith. Triangular numbers (also ellipt. as sb. pl. triangulars), the first series of POLYGONAL numbers (1, 3, 6, 10, 15, 21, etc.), obtained by continued summation of the natural numbers 1, 2, 3, 4, 5, 6, etc.: see quot. 1837.
1706. W. Jones, Syn. Palmar. Matheseos, 165. In a Rank of Triangulars their Sums are called Triangulars or Figurates of the 3d Order.
1796. Hutton, Math. Dict., I. 468/2. The triangular numbers 1, 3, 6, 10, 15, &c. Ibid. (1806), Course Math. (1810), I. 214. The sides or faces in either the triangular or square piles, are called arithmetical triangles; and the numbers … in these, are called triangular numbers.
1837. Babbage, Bridgew. Treat., 37. They are called triangular numbers because a number of points corresponding to any term can always be placed in the form of a triangle.
3. fig. Relating to or taking place between three persons or parties, three-sided; also, constituting a triad or set of three, threefold, triple.
1812. T. Jefferson, Writ. (1830), IV. 175. The triangular war must be an idea of the Anglomen and malcontents.
1816. T. L. Peacock, Headlong Hall, xv. Avarice, luxury, and disease constitute the triangular harmony of the life of man.
1871. W. White, Jrnls. (1898), 243–4. Mrs. Linton and Mr. Congreve to dine; we had an interesting triangular talk.
Mod. In these elections there will be several triangular contests.
4. Comb.: a. parasynthetic, as triangular-bodied, -headed, -leaved, -pointed, -spotted; also triangular-wise adv. b. Bot. in combination with other adjs. of form, as triangular-cordate, -crenate, -dentate, -hastate, -ovate, -rhomboid, -subulate.
1707. Mortimer, Husb. (1721), I. 189. Placing another Row at the Ends where the forked Sticks meet Triangular-wise.
1731. Miller, Gard. Dict., s.v. Aloe, The upright triangular-leav’d viscous Aloe.
1768. Parsons, in Phil. Trans., LVIII. 194. The triangular-headed Cameleons.
1804. Shaw, Gen. Zool., V. 420. Triangular-bodied, unarmed Trunk-Fish.
1823–5. Sir J. E. Smith, Eng. Flora (1828), II. 9. Mercury Goose-foot. Leaves triangular-arrow-shaped, entire.
1870. Hooker, Stud. Flora, 264. Scrophularia nodosa … leaves ovate or triangular-cordate.
1887. W. Phillips, Brit. Discomycetes, 99. Margin triangular-dentate.
