theorem, n.
(ˈθiːərɪm)
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).]
1. 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, Galileo'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 tr. 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 can⁓not 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 tr. 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. |
2. A stencil. Also transf., a design executed by means of a stencil. Obs. exc. Hist.
| 1824 Federal Gaz. 29 Apr. 1/5 Theorem painting on velvet..varnished theorems or theorems cut from any design..may be had. 1832 L. M. Child Girl's Own Book (ed. 4) 137 After all the parts are in readiness, lay your theorem upon your drawing paper, take a stiff brush of bristles..fill it with the colour you want. 1968 Canad. Antiques Collector June 21/1 Theorem Painting, designs painted on white cotton velvet, was an art introduced to America from England. Also known as Formula or, if on silk, Poonah painting. 1973 New Yorker 3 Feb. 40/3 Old theorems (stencilled paintings or watercolors done on velvet or paper by genteel housebound girls in the nineteenth century). |
Hence ˈtheorem 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. |