Porism

Porism is defined by Simson as a proposition to demonstrate that some one thing or more things are given, to which, as also to each of innumerable other things, not indeed given, but having the same relation to those which are given, it is to be shown that there belongs some common affection described in the proposition. Playfair defined a porism to be a proposition affirming the possibility of finding such conditions as will render a certain problem capable of innumerable solutions. Owing to the loss of Euclid's three books on porisms, and the obscurity of the account given by Pappus of their contents, there has been much discussion among geometers as to the nature of a porism. The two most important books on the subject are Simson's De Porismatibus in his Opera Reliqua (1776), and Chasles's Les trois livres de Porismes d'Euclide (1860). Chasles is of opinion that the porisms were closely allied to the modern theories of anharmonic ratio, homographic division, and involution.