[f. mod.L. vers-us (sc. sinus), pa. pple. of L. vertĕre to turn.]
1. Versed sine. a. Trig. Originally, the segment of the diameter intercepted between the foot of the sine and the extremity of the arc; in mod. use, the ratio of this line to the radius, or (equivalently, as a function of an angle) the quantity obtained by subtracting the cosine from unity.
In mod. use also in the contracted form VERSIN.
1596. W. B[urrough], Variation of Compasse, B 5 b. The versed signe of the semidiurnall arke.
a. 1652. S. Foster, Descr. Ruler. A large Scale of Versed-Sines.
1690. Leybourn, Curs. Math., 397. The Line VS … is the Line of Versed Sines.
1732. Hadley, in Phil. Trans., XXXVII. 353. Draw b D the Sine, and b r the Sine complement of the Arch B b : BD is the versed Sine of the same.
1763. Emerson, Meth. Increments, 91. Hence we have the following series of versed sines.
1828. J. M. Spearman, Brit. Gunner (ed. 2), 319. The arcs being similar, the versed sines are proportional to the arcs or to their radii.
1853. Sir H. Douglas, Milit. Bridges (ed. 3), 43. A segment of a sphere whose radius is r, the sagitta, or versed sine, being d.
b. Bridge-building. The rise of an arch.
1838. Civil Eng. & Arch. Jrnl., I. 127/1. The Dover road is carried over the railway by a flat segmental arch, 30 feet span, the rise or versed sine [printed line] is only two feet. Ibid. (1839), II. 191/2. Span of the arch … 58 feet—the rise or versed sine being ten feet.
1879. Cassell’s Techn. Educ., IV. 384/1. It forms the strongest arch;… but in consequence of the height of the versed sine … it becomes necessary … to limit the span.
† 2. Versed scale, a scale of versed sines. Obs.
a. 1652. S. Foster, Descr. Ruler, viii. 31. The Versed Scale is in length four times the same Radius. Ibid., 32. Let the Tangents … be measured out of the Versed Scale.
