Also 6 -gruens, -grewence. [ad. L. congruentia agreement, harmony, congruity, f. congruent- pr. pple.: see CONGRUENT and -ENCE. (Also in mod.F.)]
1. The fact or condition of according or agreeing; accordance, correspondence, harmony. Const. with.
1533. Tindale, Lords Supp., Wks. (1573), 468. That analogie and proper congruence of the figures with their verities.
1606. Holland, Sueton., 223 (R.). Such was the congruence of their humours and dispositions.
1641. H. Ainsworth, Orthod. Found. Relig., 59. As sinne is a difference from Gods Law, so justice is a congruence with the Law.
1805. W. Herschel, in Phil. Trans., XCV. 243. Our idea of the congruence or harmony of the celestial motions.
1882. Farrar, Early Chr., I. 337. Even in minor matters we trace the same congruence between Apollos and the writer of this Epistle [Hebrews].
2. Accordance with what is right, fitting, or reasonable; = CONGRUITY 3.
c. 1430. trans. T. à Kempis’ Imit., I. xix. Also for congruence [of tyme] diuersite of exercises plesiþ.
1572. Bossewell, Armorie, III. 11 b. This fishe maye with more congruence be borne in armes, then many others.
1656. Jeanes, Mixt. Schol. Div., 73. This is farre short of a demonstration … It is, at the best, but a philosophical congruence.
† b. esp. in Of congruence, of good congruence (of due or very c., by good c., in good c., etc.): by right or propriety; as is fitting or reasonable.
1447. Bokenham, Seyntys (Roxb.), 117. Agna is a lamb, a best ful meke And sympyl also … Wych tuo to Anneys by good congruence Longyn.
c. 1485. Digby Myst. (1882), IV. 1088. Who then aught of verrey congruence To be mor glad than I?
1532. More, Confut. Tindale, Wks. 352/1. Not in reason onely and good congrewence, but also by plaine ordinaunce and statute.
1533. Tindale, Lord’s Supp., Wks. (1573), 460. It was expedient and of good congruence that he should dye.
1619. Dalton, Countr. Just., lxx. (1630), 170. This Recognisance … is rather of congruence than by any expresse authority.
3. Gram. Agreement or concord: grammatical correctness. See CONGRUITY 4.
† 4. Theol. = CONGRUITY 5.
a. 1541. Barnes, Tract, viii. Freewill, Wks. (1573), 273. M. Duns sayth, that man may performe his attrition, of his naturall power, yea, and this attrition of congruence, is a disposition to take away mortall sinne, without any speciall grace.
1554. T. Sampson, in Strype, Eccl. Mem., III. App. xviii. 48. Herein they so enwrap themselves with their terms of the first grace … with merit of congruence and merit of condignity.
1635. Pagitt, Christianogr., I. iii. (1636), 179. They admit not of the merit of Congruence, condignity, nor works of Supererogation.
5. Geom. = CONGRUENCY 2.
1879. Henrici, Geometry, in Encycl. Brit., X. 407/1. A double infinite number of lines, that is, all lines which satisfy two conditions, or which are common to two complexes, are said to form a congruence of lines, e. g. all lines in a plane, or all lines cutting two curves, or all lines cutting a given curve twice … It follows that all lines in which corresponding planes in two projective pencils meet form a congruence.
6. Theory of Numbers. The relation between two numbers which being divided by a third number, called the modulus, give the same remainder; also an expression exhibiting two congruous quantities in the form of an equation; thus, A=B (mod. P). See CONGRUENT 5.
A congruence may be of any order, linear, quadratic, or other. The general type of a linear congruence is ax+b=0 (mod. P), where a, b, and P are given numbers, and x a number to be determined.
[1801. C. F. Gauss, Disq. Arithmet. (Lipsiae), § 25. Expressionem duas quantitates congruas exhibentem ad instar aequationum, congruentiam vocamus.]
1889. Chrystal, Algebra. Gauss … made the notion of Congruence the fundamental idea in his famous Disquisitiones Arithmeticæ.
