# porism

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## Contents

## English[edit]

### Etymology[edit]

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

### Noun[edit]

**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*- Robert Simson**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.*In the original Greek of Euclid's Elements the corollaries to the propositions are called*- Robert Potts**porisms**.*The term*- Florian Cajori,**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.*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 The imported definitions may be significantly out of date, and any more recent senses may be completely missing.(See the entry for porism in *Webster’s Revised Unabridged Dictionary

*, G. & C. Merriam, 1913.)*