80 GBEEK GEOMETRY. 



logic from its generality ; it is, as the lawyers say, void for 

 uncertainty. The modern one objected to by Pappus is not 

 uncertain ; it is quite accurate as far as it goes ; but it is too 

 confined, and errs against the rules of logic by not being 

 coextensive with the thing proposed to be defined. 



The difficulty of the subject has been sufficiently shown 

 from the extreme conciseness and the many omissions, the 

 almost studied obscurity, of the only account of it which 

 remains ; and to this must certainly be added the corruption 

 of the Greek text. The success which attended Dr. Simson's 

 labours in restoring the lost work, as far as that was possible, 

 and, at any rate, in giving a full elucidation of the nature of 

 porisms, now, for the first time, disclosed to mathematicians, 

 is, on account of those great difficulties by which his pre- 

 decessors had been baffled, the more to be admired. But 

 there is one thing yet more justly a matter of wonder, when 

 we contrast his proceedings with theirs. The greater part of 

 his life, a life exclusively devoted to mathematical study, had 

 been passed in these researches. He had very early become 

 possessed of the whole mystery, from other eyes so long con- 

 cealed. He had obtained a number of the most curious solu- 

 tions of problems connected with porisms, and was constantly 

 adding to his store of porisms and of lemmas subservient to 

 their investigation. For many years before his death, his 

 work had attained, certainly the form, if not the size, in 

 which we now possess it. Yet he never could so far satisfy 

 himself with what has abundantly satisfied every one else, as 

 to make it public, and he left it unpublished among his papers 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 Girards, even the Ferrnats, 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 



