PORISM. The subject of porisms is perplexed by the multitude of different views which have been held by famous geometers as to what a porism really was and is. 'This article must therefore be limited to a short historical account (1) of the principal works of the Greek mathe-maticians which we know to have been called Forams, and (2) of some of the principal contributions to the elucidation of these works, and conjectures as to the true signification of the term.

The treatise which has given rise to the controversies on this subject is the Porisms of Euclid, the author of the Elements. For as much as we know of this lost treatise we are indebted to the Collection of Pappus of Alexandria, who mentions it along with other geometrical treatises, and gives a number of lenunas necessary for understanding it. Pappus state,s that the porisms of Euclid are neither theorems nor problems, but are in some sort intermediate, so that they may be presented either as theorems or as problems ; and they were regarded accordingly by many geometers, who looked merely at the form of the enuncia-tion, as being actually theorems or problems, though the definitions given by the older writers showed that they better understood the distinction between the three classes of propositions. The older geometers, namely, defined a theorem as ;1 T _ 71-pOTEIAI.LEVOV EIS darcISECELY CLiYr013 iiiroBgtrit Torn/col; Oeoviiioaros.

Proclus gives a definition of a porism which agrees very well with the fact that Euclid used the same word rOpurpu. in his Elements for what is now called by the Latin name " corollary." Proclus's definition is T?) miptu'ita A.4yercu