156 On the ORIGIN and 



the lemmata of Pappus pointed out to him, as the tract which 

 Apollonius had purfued. 



3. There was another fubject, that of Porifms, the molt 

 intricate and enigmatical of any thing in the ancient geometry, 

 which was dill referved to exercife the genius of Dr Sim son, 

 and to call forth that enthufiaftic admiration of antiquity, and 

 that unwearied perfeverance in refearch, for which he was fo 

 peculiarly diflinguifhed. A treatife in three books, which 

 Euclid had compofed on Porifms, was loft, and all that re- 

 mained concerning them was an abftract of that treatife, in- 

 ferted by Pappus Alexandrinus in his Mathematical Col- 

 letlions. in which, had it been entire, the geometers of later 

 times would doubtlefs have found wherewithal to confole them- 

 felves for the lofs of the original work. But unfortunately it 

 has fufFered fo much from the injuries of time, that all which 

 we can immediately learn from it is, that the ancients put a high 

 value on the propofitions which they called porifms, and re- 

 garded them as a very important part of their analyfis. The 

 Porifms of Euclid are there faid to be, " Colleclio artificio- 

 " fifftma multarum rerum quse fpectant ad analyfin diffici- 

 " liorum et generalium problematum *." The curiofity, how- 

 ever, which is excited by this encomium is quickly difappoint- 

 ed ; for when Pappus proceeds to explain what a Porifm is, he 

 lays down two definitions of it, one of which is rejected by 

 him as imperfect, while the other, which is ftated as correct, is 

 too vague and indefinite to convey any ufeful information. 



These defects might neverthelefs have been fupplied, if the 

 enumeration which he next gives of Euclid's propofitions had 

 been entire ; but on account of the extreme brevity of his 

 enunciations, and their reference to a diagram which is loft, 

 and for the conftructing of which no directions are given, they are 

 all, except one, perfectly unintelligible. For thefe reafons, the 



fragment 



* Colleftiones Math. lib. vii. iri init. 



