498 SIMSON. 



much more honest than some, and much more safe 

 and free from mistake than others who touched upon 

 the subject which 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 deliver them (his propositions) 

 in the form of porisms, as, in my opinion, the ancients 

 called all propositions treated by analysis only" (Philo- 

 sophical Transactions, 1723, p. 148) ; and, truth to 

 say, his investigation is not very like ancient analysis 

 either. The notion of D'Alembert, somewhat later, 

 has been alluded to already ; he imagined porisms 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 be- 

 fore, seems exceedingly doubtful. But the most extra- 

 ordinary, and indeed inexcusable ignorance of the sub- 

 ject 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 con- 

 ceived porisms to be merely the constructions of Eu- 

 clid'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. 



