porism

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  1. A form of mathematical proposition among the Greeks, concerning the nature of which there continues to be much dispute. The corollaries to Euclid's elements — that is, extra propositions, inserted by commentators and readily deducible from his theorems —are called by this name. But the word had a more general meaning, which Chasles defines as follows: A porism is an incomplete theorem expressing a relation between things variable according to a common law, the statement being left incomplete in regard to some magnitude which would be stated in the theorem properly so called. For example, to say that there is within every triangle a point every line through which has for the sum of its distances from the two vertices which lie on one side of it its distance from the third vertex, is a porism in substance. But the porism was further distinguished by a peculiar mode of enunciation, namely, that which in modern language is made to be constant, is called in the porism “given.” The definition of Playfair, which has had great currency, is as follows: A porism is a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate, or capable of innumerable solutions. This is the sense in which the word would ordinarily be understood to-day. Other widely different definitions have been given. Ryht as thyse geometryens, whan they have shewyd hyr proposiciouns, ben wont to bryngen in thinges that they clepen porysmes, or declaraciouns of forseyde thinges. Chaucer, Boëthius, iii. prose 10.
  2. Synonyms See inference.

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  1. Middle English porysme, from Old French (and F.) porisme = Spanish porisma = Italian porisma, porismate, porismato; from Greek πόρισμα(τ-), a corollary, from πορίζειν, bring about, procure, deduce, from πόρος, a way, passage: see pore, n.
 

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