[f. as prec.: see -ENCY.]
1. The quality or state of being congruent; congruity. Of a congruency: see prec. 2 b.
1494. Fabyan, Chron., VII. 370. They agreed to reste there styll, and that of a congruency, for they myght dwell in no lande where they shulde more suerly be defended.
1577. Fenton, Gold. Epist. (1582), 81. It appertaines to reason and congruencie, to exhibite a few remedies.
1686. Goad, Celest. Bodies, III. iii. 470. The presence of the Planets aforesaid with the Sun, or their Conjunction, or if you will, Congruency.
b. with pl.
1615. Bp. Andrewes, Serm. Nativity, x. Though there want not divers other good congruencies why Christ should come from Bethlehem.
1681. H. More, Exp. Dan., iv. 129, note. Many congruencies with historical passages … do notably confirm this Hypothesis.
2. Geom. A system of lines in which the parameters have a two-fold relation, such as a system of lines each of which twice touches a given surface.
1864. Plücker, New Geom. of Space, in Phil. Trans. (1865), 727. A ‘congruency’ contains all congruent rays of two complexes, it may be regarded as their mutual intersection. Ibid., 748. Such rays as belong to both linear complexes … constitute a linear congruency of rays represented by the system of the two equations.
1874. G. Salmon, Analytic Geom. (ed. 3), § 468. Every congruency of lines may be regarded as the system of the bitangents of a certain surface, viz. each line of the congruency is in general met by two consecutive lines, and the locus of the points of intersection is the surface in question.
