74 GREEK GEOMETRY. 



author. The extreme difficulty of the subject was increased 

 by the corruptions of the text that remains in the only 

 passage of the Greek geometers which has reached us, 

 the only few sentences in which any mention whatever is 

 made of Porisms. This passage is contained in the preface 

 or introduction to the Seventh book of Pappus, which we 

 have already had occasion to cite. But this was by far the 

 least of the difficulties which met the inquirer after the 

 hidden treasure, the restorer of lost science, though Albert 

 Girard thought or said, in 1635, that he had restored the 

 Porisms of Euclid. As we have seen, no trace of his labours 

 is left ; and it seems extremely unlikely that he should have 

 really performed such a feat and given no proofs of it. 

 Halley, the most learned and able of Dr. Simson's pre- 

 decessors, had tried the subject, and tried it 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 theKainbow "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" (Philosophical 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 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 



