Last modified on 18 June 2013, at 12:28

porism

EnglishEdit

EtymologyEdit

Ancient Greek πόρισμα (pórisma, a deduction from a previous demonstration).

NounEdit

porism (plural porisms)

  1. (geometry) A proposition affirming the possibility of finding such conditions as will render a certain determinate problem indeterminate or capable of innumerable solutions.
    Porism: A proposition affirming the possibility of finding one or more of the conditions of an indeterminate theorem. Dugald Stewart
    Porism: A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions. - John Playfair
  2. A corollary.
    Porism: something between a problem and a theorem or that in which something is proposed to be investigated. - Pappus
    A Porism is a proposition in which it is proposed to demonstrate that some one thing, or more things than one, are given, to which, as also to each of innumerable other things, not given indeed, but which have the same relation to those which are given, it is to be shewn that there belongs some common affection described in the proposition. - Robert Simson
    In the original Greek of Euclid's Elements the corollaries to the propositions are called porisms. - Robert Potts
    The term porism is vague in meaning. The aim of a porism is not to state some property or truth, like a theorem, nor to effect a construction, like a problem, but to find and bring to view a thing which necessarily exists with given numbers or a given construction, as, to find the centre of a given circle, or to find the G.C.D. of two given numbers. - Florian Cajori, A History of Mathematics

Part or all of this entry has been imported from the 1913 edition of Webster’s Dictionary, which is now free of copyright and hence in the public domain. The imported definitions may be significantly out of date, and any more recent senses may be completely missing.