INVESTIGATION of PORtSMS. 157 



fragment in queftion is fo obfcure, that even to the learning 

 and penetration of Dr Halley, it feemed knpoflible that it 

 could ever be explained , and he therefore concluded, after 

 giving the Greek text with all poilible correclnefs, and adding 

 the Latin tranflation, " Hactenus Porifmatum defcriptio nee 

 " mihi intellefta, nee lectori profutura. Neque aliter fieri po- 

 " tuit, tam ob defectum fchematis cujus fit mentio, quam ob 

 " omiffa qusedam et tranfpoiita, vel aliter vitiata in propoii- 

 " tionis generalis expofitione, unde quid fibivelit Pappus haud 

 " mihi datum eft conjicere. His adde dictionis modum nimis 

 " contractum, ac in re difficili, qualis haec eft, minime ufur- 

 " pandum *." 



4. It is true, however, that before this time, Fermat had 

 attempted to explain the nature of Porifms, and not altogether 

 without fuccefs *j\ 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 5 and he neither proved, that his no- 

 tion of a Porifm was the fame with Euclid's, nor attempted to 

 reftore, or explain any one of Euclid'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. All this did not, however, deter Dr Simson from turn- 

 ing his thoughts to the fame fubject, which he appears to have 



done 



* De fe£tione rationis, proem, p. 37. 



f " Porifmatum Euclid^eorum renovata do&rlna, et fub forma Ifagoges exhibits." 

 Fermat Opera Varia, p. 116. 



