156 SIMSON. 



given their works to the world had they become 

 possessed of such a treasure as Dr. Simson had found I 

 Yet though ready for the press, and with its preface 

 composed, and its title given in minute particularity, 

 he never could think that he had so far elaborated and 

 finished it as to warrant him in finally resolving on its 

 publication. 



There needs no panegyric of this most admirable 

 performance. Its great merit is best estimated by the 

 view which has been taken of the extraordinary 

 difficulties overcome by it. The difficulty of some 

 investigations the singular beauty of the propositions, 

 a beauty peculiar to the porism from the wonderfully 

 general relations which it discloses the simplicity of 

 the combinations the perfect elegance of the demon- 

 strations render this a treatise in which the lovers of 

 geometrical science must ever find the purest delight. 



Beside the general discussions in the preface, and 

 in a long and valuable scholium after the sixth propo- 

 sition, and an example of algebraical porisms, Dr. 

 Simson has given in all ninety-one propositions. Of 

 these four are problems, ten are loci, forty-three are 

 theorems, and the remaining thirty-four are porisms, 

 including four suggested by Matthew Stewart, and 

 the five of Fermat improved and generalized ; there 

 are, besides, four lemmas and one porism suggested 

 by Dr. Traill, when studying under the Professor. 

 There may thus be said to be in all ninety-eight pro- 

 positions. The four lemmas are propositions ancillary 

 to the author's own investigations ; for many of his 

 theorems are the lemmas preserved by Pappus as an- 

 cillary to the porisms of Euclid. 



In all these investigations the strictness of the Greek 

 geometry is preserved almost to an excess; and there 

 cannot well be given a more remarkable illustration 

 of its extreme rigour than the very outset of this 

 great work presents. The porism is, that a point 

 may be found in any given circle through which all 



