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Webster 1913 Edition
Porism
Po′rism
,Noun.
[Gr. [GREEK] a thing procured, a deduction from a demonstration, fr. [GREEK] to bring, provide: cf. F.
porisme
.] 1.
(Geom.)
A proposition affirming the possibility of finding such conditions as will render a certain determinate problem indeterminate or capable of innumerable solutions.
Playfair.
2.
(Gr. Geom.)
A corollary.
Brande & C.
☞ Three books of porisms of Euclid have been lost, but several attempts to determine the nature of these propositions and to restore them have been made by modern geometers.
Webster 1828 Edition
Porism
PO'RISM
,Noun.
In geometry, a name given by ancient geometers to two classes of propositions. Euclid gave this name to propositions involved in others which he was investigating, and obtained without a direct view to their discovery. These he called acquisitions, but such propositions are now called corollaries. A porism is defined, 'a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions.' It is not a theorem, nor a problem, or rather it includes both. It asserts that a certain problem may become indeterminate, and so far it partakes of the nature of a theorem, and in seeking to discover the conditions by which this may be effected, it partakes of the nature of a problem.
Definition 2024
porism
porism
English
Noun
porism (plural porisms)
- (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
- 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