SIMSON. 129 



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 analysis 

 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 supposed 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'Alem- 

 bert'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 Sim son's admirable res- 

 toration of Apollonius's ' Loci Plani' had been pub- 

 lished five years before the 'Encyclopedic' appeared. 



Again, in the ' Encyclopedic,' the word Analysis, 

 as meaning the Greek method, and not algebra, is not 

 even to be found. Nor do the words synthesis, or 

 composition, inclinations, tactions or tangencies, occur 

 at all ; and though Porisms are mentioned, it is only 

 to show the same ignorance of the subject : for that 

 word is said to be synonymous with * lemma,' because 

 it is sometimes used by Pappus in the sense of sub- 

 sidiary proposition.* When Clairault wrote his ines- 

 timable work on curves of double curvature, he made 

 no reference whatever to Euclid's 'Loci ad Superficiem,' 



* Euclid uses the word Corollary in his Elements. 

 K 



