156 On th ORIGIN and 
the /emmata of Pappus pointed out to him, as the tract which 
Apo.tuonius had purfued. 
3. THERE was another fubjeCt, that of Pori/ms, the moft 
intricate and enigmatical of any thing in the ancient geometry, 
which was ftill referved to exercife the genius of Dr Simson, 
and to call forth that enthufiaftic admiration of antiquity, and 
that unwearied perfeverance in refearch, for which he was fo 
peculiarly diftinguifhed. A treatife in three books, which 
Euciip 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- 
leétions, 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 Eucuip are there faid to be, ‘* Colleétio artificio- 
“ fiffima multarum rerum que 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. 
Tuese defects might neverthelefs have been fupplied, if the 
enumeration which he next gives of EucLip’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 conftruéting of which no directions are given, they are 
‘all, except one, perfectly unintelligible. For thefe reafons, the 
fragment 
* ColleGiones Math. ib. vii. in init. 
