a. (sb.) [ad. L. trigōnāl-is, f. trigōn-um: see prec. and -AL.]
1. Of, pertaining or relating to, a trigon or triangle; of the form of a triangle, having three angles, triangular. (In quot. 1570 = TRIANGULAR 2 b.)
Trigonal co-ordinates (Geom.), a system of co-ordinates related in a particular way to trilinear co-ordinates, invented by S. Levi in 1876.
1570. Billingsley, Euclid, VII. def. x. 186. 6 in diuers respectes is a lineall number … and also a trigonall or trianguler number.
1571. Digges, Pantom., iv. def. viii. T j b. When any equiangle triangle … is … described within a circle, [its] sides are called the trigonal … Cordes of that circle.
1849. Freeman, Archit., II. v. 170. A fine lofty pile, with … three trigonal apses.
1891. Cent. Dict., s.v., A linear equation in trigonal coördinates of the first class represents a cubic [curve].
b. Geom. and Cryst. Applied to a solid figure with triangular faces, or having some other relation to a triangle. Also, Having a relation to three angles: as trigonal quoin, a solid angle contained by three plane angles; trigonal symmetry, the symmetry of a figure or body which coincides with its original position after rotation about an axis through an angle of 120° or 240°.
1878. Gurney, Crystallogr., 38. If three symmetral planes and no more intersect in the same straight line, it is called an axis of trigonal symmetry.
1891. Cent. Dict., s.v. Trisoctahedron, The trigonal trisoctahedron has each face an isosceles triangle.
1895. Story-Maskelyne, Crystallogr., iv. § 79. 98. A plane figure may … be symmetrical with regard to a point within it as a pole of symmetry…. Where n = 2, or = 3, 4, or 6, the symmetry may be defined as being diagonal, trigonal, tetragonal, or hexagonal. Ibid., vii. § 180. 211. The trigonal dodecahedron,… a tetrahedron with a three-faced pyramid on each of its faces. Ibid., § 257. 302. The trigonal trapezohedron … has trapezoids for its faces, which meet in two trigonal quoins.
2. Triangular in section, triquetrous: now esp. in Zool. and Bot.
1571. Digges, Pantom., IV. xi. Y iij b. The solide of Tetraedron may … be parted into 4 equal Trigonal Pyramides.
a. 1728. Woodward, Nat. Hist. Fossils (1729), I. 158. Spar of a yellow Hue, shot into numerous trigonal pointed Shoots.
1753. Chambers, Cycl. Supp., s.v. Leaf, Trigonal Leaf, one much like the triquetrous, only that … the several faces are each hollowed in form of channels. Ibid., Lilium, the lilly … The pistil … finally becomes an oblong and trigonal fruit.
1854. Woodward, Mollusca, II. 225. Shell impunctate, oblong, or trigonal.
1895. W. M. Macpherson, Monymusk, v. 76. A plain roundheaded door with a trigonal hood.
3. Astrol. Relating to, or of the nature of, a trigon (in either sense): see prec. 2.
1603. Sir C. Heydon, Jud. Astrol., xxi. 470. All trigonall aspects doe accord.
1635. Swan, Spec. M., v. § 2 (1643), 105. The Trigonall revolution … of the Planets [cf. TRIGON 2 quot. 1704].
† 4. Of or pertaining to a trigon (TRIGON 3 a). Also as sb. short for trigonal instrument. Obs. rare.
1593. Fale, Dialling, 39. Your Diall being made, and the Stile placed therein: take your Trigonall Instrument, and set it upon the Stile, so that the whole Diameter thereof may stand plaine upon the edge or upper part, the centre A, of your Instrument…. Then fasten a thread at the uppermost end of your Trigonall in every line of the signes so yt you may direct downeward by the centre A, to the plat of your Diall: and … then moving the Trigonall on the right hand, so that the thread may be stretched on the left hand, make there likewise a prick upon the plat.
B. sb. 1. See A. 4.
2. Anat. TRIGONE, TRIGONUM 2 (Cent. Dict.).
Hence Trigonally adv. (rare–0), triangularly (Cent. Dict., 1891).
