474 SIM60N. 



highly interesting subject of the Greek geometry. We 

 shall presently see that both Fermat and Halley, its 

 most successful students, had made but an incon- 

 siderable progress in the most difficult branches. 



How entirely the academicians of France were 

 either careless of those matters, or ignorant, or both, 

 appears by the * Encyclopedic ; ' the mathematical 

 department of which was under no less a geometrician 

 than d'Alembert. The definition there given of ana- 

 lysis makes it synonymous with algebra : and yet 

 mention is made of the ancient writers on analysis, 

 and of the introduction to the seventh book of Pappus, 

 with only this remark, that those authors differ 

 much from the modern analysts. But the article 

 ' Arithmetic' (vol. i., p. 677) demonstrates this 

 ignorance completely; and that Pappus's celebrated 

 introduction had been referred to by one who never 

 read it. We there find it said, that Plato is sup- 

 posed to have invented the ancient analysis ; that 

 Euclid, Apollonius, and others, including Pappus 

 himself, studied it, but that we are quite ignorant 

 of what it was : only that it is by some conceived to 

 have resembled our algebra, as else Archimedes could 

 never have made his great geometrical discoveries. It 

 is, certainly, quite incredible that such a name as 

 d'Alembert's should be found affixed to this statement, 

 which the mere reading of any one page of Pappus's 

 books must have shown to be wholly erroneous ; and 

 our wonder is the greater, inasmuch as Simson's ad- 

 mirable restoration of Apollonius's ' Loci Plani' had 

 been published five years before the ' Encyclopedic ' 

 appeared. 



