502 SIMSON. 



connexion with a locus is not necessary to the poris- 

 matic nature, although it will very often exist, inas- 

 much as each point in the curve having the same re- 

 lation 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 ad- 

 mitting the inaccuracy of the definition, give us one of 

 his own. Perhaps we may accurately enough define 

 a porism to be the enunciation of the possibility of 

 finding that case in which a determinate problem be- 

 comes 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 connexion with an indetermi- 

 nate problem and its solution. I apprehend that the 

 poristic case is always one in which the data become 

 such that a transition is made from the determinate 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 found : the two 

 lines are the perpendiculars at the centre, and are of 

 course the two axes of the ellipse ; and though this 

 enunciation is in the outward form of a porism, the 

 proposition is no more a porism than any ordinary pro- 

 blem ; as that a circle being given a point may be found 

 from whence all the lines drawn to the circumference 

 are equal, which is merely the finding of the centre. 

 But suppose there be given the problem to inflect two 



