a. and sb. Also 7 quadrilaterall. [ad. L. type *quadrilaterālis, f. quadrilater-us + -AL. See prec. and cf. F. quadrilatéral.]
A. adj. Four-sided; having a four-sided base or section.
1656. Stanley, Hist. Philos., v. (1701), 162/2. The Altar … was no longer a Cube, but … a quadrilateral Pillar.
1674. trans. Scheffer’s Lapland, xvi. 83. The whole form seems to be like a quadrilaterall house.
1718. Quincy, Compl. Disp., 33. In common Salt we plainly discover Quadrilateral Pyramids, with square Bases.
1836–41. Brande, Chem. (ed. 5), 1125. Carbazotate of Potassa crystallizes in long yellow quadrilateral needles.
1876. Duhring, Dis. Skin, 38. Nails are rounded or quadrilateral bodies.
b. Bot. Of a stem: (see quot.).
1875. Bennett & Dyer, trans. Sachs’ Bot., 184. The principal sections of all the leaves … may lie in two planes, crossing one another at right angles, when the shoot is quadrilateral.
B. sb. A figure bounded by four straight lines; a space or area having four sides.
In mod. Geom. A figure formed by four straight lines, no three of which pass through the same point, and by the six points (vertices) forming the intersections of these lines, taken two by two (Cf. QUADRANGLE).
1650. T. Rudd, Euclide, 45. To forme a … Quadrilaterall, about which a circle may be circumscribed.
1827. Hutton, Course Math., I. 282. A Diagonal is a line joining any two opposite angles of a quadrilateral.
1866. R. A. Proctor, Handbk. Stars, 16. The intermediate figures are quadrilaterals of varying form.
1893. E. H. Barker, Wanderings by Southern Waters, 301. Four … towers occupying the angles of a small quadrilateral.
b. The space lying between, and defended by, four fortresses; spec. that in North Italy formed by the fortresses of Mantua, Verona, Peschiera and Legnano.
1859. Times, 1 July, 8/5. But no one believes that such fortresses as compose the famous ‘Quadrilateral’ can be taken in a day.
1866. Sat. Rev., 21 July, 66/1. The Quadrilateral and Venice still remain in the hands of the Austrians.
1870. Pall Mall Gaz., 2 Sept., 2/1. He has four fortresses around him…; but upon twelve square miles of territory,… he cannot play at quadrilaterals.
fig. 1888. Ld. Rosebery, in Daily News, 20 Feb., 5/5. Am overjoyed … that Edinburgh is once more the quadrilateral of Liberalism.
Hence Quadrilateralness, ‘the property of having four sides’ (Bailey, vol. II. 1727).
1896. H. Holman, Educ., vi. 303. It is an idea which involves the ideas of rectilinealness, quadrilateralness, equilateralness, and equiangularity.
