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porism Math.|ˈpɔərɪz(ə)m, ˈpɒr-|
[ad. L. porisma, a. Gr. πόρισµα a deduction from a previous demonstration, a corollary, also a problem, f. πορίζειν to carry, deduce, f. πόρος way. So F. porisme.]
With the ancient Greek mathematicians, a kind of geometrical proposition, the nature of which has been much disputed; app. one arising during the investigation of some other proposition, either by immediate deduction from it (= corollary n. 1), or by consideration of some special case in which it becomes indeterminate.
The sense indicated by Playfair's definition (quot. 1792) is that now most generally accepted and used; but other widely different definitions have been given.
c1374Chaucer Boeth. iii. pr. x. 71 (Camb. MS.) Ryht as thyse geometryens whan they han shewyd hyr proposiciouns ben wont to bryngen in thinges þat they clepyn porysmes or declaraciouns of forseyde thinges. Ryht so wole I yeue the heere as a corolarye or a mede of coroune. [c1645Enquiry, etc. in Harl. Misc. (Malh.) V. 499 It may be proposed a problem, or porisma, to be considered, whether the souls of brutes are not more than rarefied, or inflamed matter.] 1704J. Harris Lex. Techn. I, Porisme. Proclus and Pappus define this Geometrical Term to signifie a kind of Theorem, in the form of a Corollary, which is dependant upon, or deduced from some other Theorem already demonstrated. And 'tis commonly used to signifie some General Theorem, which is discovered from finding out some Geometrical Place. 1792Playfair in Trans. Roy. Soc. Edinb. III. ii. 156 There was another subject, that of Porisms, the most intricate and enigmatical of any thing in the ancient geometry. Ibid. 170 From this account of the origin of Porisms, it follows, that a Porism may be defined, A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate, or capable of innumerable solutions. 1795Hutton Math. Dict. s.v., Pappus says, a Porism is that in which something was proposed to be investigated. 1798H. Brougham in Phil. Trans. LXXXVIII. 383 This is a case of a most general enunciation, which gives rise to an infinite variety of the most curious porisms. 1853Cayley Coll. Math. Papers II. 56 Researches on the Porism of the in- and circumscribed triangle. 1855J. Martineau Ess. (1890) I. 434 An epic or song..may have a human power greater than the Porisms or the Principia. 1887H. Delevingne in N. & Q. 7th Ser. IV. 424/2 Between i. 15 and 16 occurs the first porism or corollary, to the effect that the angles formed by two straight lines at their point of intersection are together equal to four right angles. |