sb. Also 6–7 -eme. [ad. late L. theōrēma (Gellius), a. Gr. θεώρημα, -ματ-, spectacle, speculation, theory, (in Euclid) a proposition to be proved, f. θεωρεῖν to be a spectator (θεωρός), to look at, inspect. Perh. directly a. F. théorème (téorème in Rabelais).]
A universal or general proposition or statement, not self-evident (thus distinguished from an AXIOM), but demonstrable by argument (in the strict sense, by necessary reasoning); ‘a demonstrable theoretical judgement’ (Abp. Thomson).
a. In Mathematics and Physics; spec. in Geometry, a proposition embodying merely something to be proved, as distinguished from a PROBLEM (sense 4), which embodies something to be done.
Particular theorems are usually named after their discoverers or investigators, as Boole’s, Carnot’s, Cauchy’s, Cayley’s, Clifford’s, Euler’s, Fermat’s, Feuerbach’s, Galilio’s, Lagrange’s, Lambert’s, Maclaurin’s, Newton’s, Pappus’s, Pascal’s, Ptolemy’s, Riemann’s, Sylvester’s, Taylor’s, Wallis’s, Wilson’s (etc.) theorem; sometimes by defining adjectives, as the BINOMIAL, EXPONENTIAL, MULTINOMIAL theorem.
1551. Recorde, Pathw. Knowl., Argts. The Theoremes, (whiche maye be called approued truthes) seruinge for the due knowledge and sure proofe of all conclusions … in Geometrye.
1570. Billingsley, Euclid, I. Introd. 8. A Theoreme, is a proposition, which requireth the searching out and demonstration of some propertie … of some figure.
1612. Selden, in Drayton, Poly-olb., A iij, His Geometricall Theorem in finding the squares of an Orthogonal triangles sides.
1752. Franklin, Lett., Wks. 1887, II. 253. I thank you for communicating the illustration of the theorem concerning light.
1806. Hutton, Course Math., I. 2. A Theorem is a demonstrative proposition: in which some property is asserted, and the truth of it required to be proved…. A set or collection of such Theorems constitutes a Theory.
1816. trans. Lacroix’s Diff. & Int. Calculus, 22. This formula is called Taylor’s Theorem, from the English geometer by whom it was discovered.
1862. H. Spencer, First Princ., II. xvi. § 136. Geometrical theorems grew out of empirical methods.
b. In general sense, or in reference to any particular science or technical subject. (In quot. 1697 applied to an axiom.)
1597. Hooker, Eccl. Pol., V. lxxvi. § 2. The first being a Theoreme both vnderstood and confest of all, to labour in proofe thereof were superfluous.
1615. Crooke, Body of Man, 27. I call it a Science, because it hath vniuersall or generall Theoremes or Maximes, and common Notions.
1649. Jer. Taylor, Gt. Exemp., I. Ad Sect. vi. 105. Christian Princes cannot be restrained [from war] with the engagements and peaceful Theoremes of … a holy Religion.
1676. Coley, Astrol., 143. Note that by the word Theorem is understood a Speculation or an undoubted Rule or Principle in any Science or Art, and is that which respects Contemplation more than Practice.
1697. trans. Burgersdicius his Logic, I. xxii. 90. Ax[iom] 10…. Ax. 11…. These Theorems … the Sense of them is manifest enough.
1766. Beccaria, Ess. Crimes, xiv. (1793), 51. The following general theorem is of great use in determining the certainty of facts.
1835. I. Taylor, Spir. Despot., iii. 101. In working the abstract theorem of a church polity.
1864. Bowen, Logic, xi. 374. A demonstrable judgment, or one which is announced as needing proof, if theoretical, is called a Theorem.
Hence Theorem v., trans. to express in or by means of a theorem.
1840. Carlyle, Heroes, i. (1872), 23. They are matters which refuse to be theoremed and diagramed.
1891. G. Meredith, One of our Conq., I. vii. 121. Euclid would have theorem’d it out for you at a glance.
