INVESTIGATION of PORISMS. 15% 
fragment in queftion is fo obfcure, that even to the learning 
and penetration of Dr Hattey, it feemed impofflible that it 
could ever be explained; and he therefore concluded, after 
giving the Greek text with all poflible correétnefs, and adding 
the Latin tranflation, ‘‘ Ha€tenus Porifmatum defcriptio nec 
** mihi intellecta, nec lectori profutura. Neque aliter fieri po- 
* tuit, tam ob defectum fchematis cujus fit mentio, quam ob 
* omiffa quedam et tranfpofita, vel aliter vitiata in propofi- 
“* tionis generalis expofitione, unde quid fibi velit PAppus haud 
‘* mihi datum eft conjicere. His adde dictionis modum nimis 
* contractum, ac in re difficili, qualis hee eft, minime ufur- 
** pandum *.” . 
4. IT is true, however, that before this time, FErnmatT had 
attempted:to explain the nature of Porifms, and not altogether 
without fuccefs +. Guiding his conjectures by the definition 
which Pappus cenfures as imperfect, becaufe it defined po- 
rifms only “ ab accidente,” viz. ‘* Porifma eft quod deficit hy- 
** pothefi a Theoremate Locali,”” he formed to himfelf a tolera- 
bly juft notion of thefe propofitions, and illuftrated his general! 
defcription by examples that are in effect Porifms. But he was 
able to proceed no farther ; and he neither proved, that his no- 
tion of a Porifm was the fame with Euciin’s, nor attempted to 
reftore, or explain any one of Evc.ip’s propofitions ; much lefs 
did he fuppofe, that they were to be inveftigated by an analyfis 
peculiar to themfelves. And fo imperfect indeed was this at- 
tempt, that the complete reftoration of the Porifms was necef- 
fary to prove, that Fermat had even approximated to the 
truth. 
5- Aut this did not, however, deter Dr Simson from turn= 
ing his thoughts to the fame fubjeét, which he appears to have 
done 
* De fedtione rations, proem. p. 37- 
+ “ Porifmatum. Evct1pzorum renovata dottrina, et fub forma Ifagoges exhibita,’” 
Fermat Opera Varia, p. 116. 
