506 SIMSON. 



published among his papers when he died. Nothing 

 can be more unlike those who freely boasted of having 

 discovered the secret, and promised to restore the 

 whole of Euclid's lost books. It is as certain that 

 the secret was never revealed to them as it is that 

 neither they nor any man could restore the books. 

 But how speedily would the Castillons, the Alberts, 

 even the Fermats, have given their works to the 

 world had they become possessed of such a treasure as 

 Dr. Simson had found ! 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. Sim- 

 son 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 



