Definition:Porism

Definition

The porism is a term whose precise definition is difficult to pin down.

It arises from the works of Euclid, and appears to have two different meanings:

1. A result which follows directly, or in passing, during the course of proving something else; that is, a corollary.
2. A proposition that asserts that there may be conditions under which a particular problem has either no solutions or an indeterminate number of them.

Linguistic Note

The word porism derives ultimately from the Greek $\pi \omicron \rho \omicron \varsigma$ (poros) meaning a thing brought, or a thing deduced.

Sources

• 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 1 (2nd ed.) ... (previous) ... (next): Introduction: Chapter $\text{II}$. Euclid's Other Works
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): porism