152 SIMSON. 



Indeed it must be confessed that Pappus's account 

 of it, our only source of knowledge, is exceedingly 

 obscure, all but the panegyric which in a somewhat 

 tantalizing manner, he pronounces upon it. " Collec- 

 tio," says he, " curiosissima multarum rerum spectan- 

 tium ad resolutionem difficiliorum et generaliorum 

 problem atum " (lib. vii. Proem). His definition al- 

 ready cited is, as he himself admits, very inaccurate ; 

 because the connexion with a locus is not necessary to 

 the porismatic nature, although it will very often exist, 

 inasmuch as each point in the curve having the same 

 relation to certain lines, its description will, in most 

 cases, furnish the solution of a problem, whence a 

 porism may be deduced. Nor does Pappus, while 

 admitting the inaccuracy of the definition, give us one 

 of his own. Perhaps \ve may accurately enough de- 

 fine a porism to be the enunciation of the possibility 

 of finding that case in which a determinate problem 

 becomes indeterminate, and admits of an infinity of 

 solutions, all of which are given by the statement of 

 the case. 



For it appears essential to the nature of a porism 

 that it should have some connection with an indeter- 

 minate problem and its solution. I apprehend that 

 the poristic case is always one in which the data be- 

 come such that a transition is made from the deter- 

 minate to the indeterminate, from the problem being 

 capable of one or two solutions, to its being capable of 

 an infinite number. Thus it would be no porism to 

 affirm that an ellipse being given, two lines may be 

 found at right angles to each other, cutting the curve, 

 and being in a proportion to each other which may be 



aryjl most able geometrician, is not to be questioned. He was, indeed, one 

 of the first mathematicians of the age in which he flourished, along with 

 the Robervals, the Harriots, the Descartes. How near he approached the 

 differential calculus is well known. His correspondence with Roberval, 

 Gassendi, Pascal, and others, occupies ninet}" folio pages of his posthumous 

 works, and contains many most ingenious, original, and profound observa- 

 tions on various branches of science. 



