siMsosr. 149 



in vain. He thus records his failure : " Hactenus 

 Porismatum descriptio nee mihi intellecta nee lectori 

 profutura." These are his words, in a preface to a 

 translation which he published of Pappus's seventh 

 book, much superior in execution to that of Comman- 

 dini. But this eminent geometrician was much more 

 honest than some, and much more safe and free from 

 mistake than others who touched upon the subject that 

 occupied all students of the ancient analysis. He was 

 far from pretending, like Girardus, to have discovered 

 that of which all were in quest. But neither did he 

 blunder like Pemberton, whom we find, the very year 

 of Simson's first publication, actually saying in his paper 

 on the Rainbow " For the greater brevity I shall de- 

 liver them (his propositions) in the form" of porisms, 

 as, in my opinion, the ancients called all propositions 

 treated by analysis only" (Philosophical Transactions, 

 1723, p. 148) ; and, truth to say, his investigation is not 

 very like ancient analysis either. The notion of D'Alem- 

 bert, somewhat later, has been alluded to already ; he 

 imagined porism to be synonymous with lemma, misled 

 by an equivocal use of the word in some passages of 

 ancient authors, if indeed he had ever studied any of 

 the writers on the Greek geometry, which, from what 

 I have stated before, seems exceedingly doubtful. But 

 the most extraordinary, and indeed inexcusable igno- 

 rance of the subject is to be seen in some who, long 

 after Simson's paper had been published, were still in 

 the dark ; and though that paper did not fully explain 

 the matter, it yet ought to have prevented such errors 

 as these fell into. Thus Castillon, in 1761, showed that 

 he conceived porisms to be merely the constructions of 

 Euclid's Data. If this were so, there might have been 

 some truth in his boast of having solved all the Porisms 

 of Euclid ; and he might have been able to perform his 

 promise of soon publishing a restoration of those lost 

 books. 



It is remarkable enough that before Halley's attempts 



