ANCIENT ANALYSIS. POBISMS. 63 



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 admirable restoration of Apollonius's ' Loci Plani ' 

 had been published five years before the ' Encyclopedie ' ap- 

 peared. 



Again, in the ' Encyclopedie,' the word Analysis, as mean- 

 ing the Greek method, and not algebra, is not even to be 

 found. Nor do the words synthesis, or composition, inclina- 

 tions, tactions or tangencies, occur at all ; and though Porism.s 

 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 subsidiary proposition.* When Clairault wrote his in- 

 estimable work on curves of double curvature, he made no 

 reference whatever to Euclid's ' Loci ad Snperficiem ;' much 

 less did he handle the subject after the same manner ; he 

 deals, indeed, with matters beyond the reach of the Greek 

 Geometry. 



Such was the state of this science when Eobert Simson 

 first applied to it his genius, equally vigorous and undaunted, 

 with the taste which he had early imbibed for the beauty, the 

 simplicity, and the closeness of the ancient analysis. 



He was appointed professor in 1711, and taught with ex- 

 traordinary success ; but his genius was bent to the diligent 

 investigation of truth, in the science of which he was so great 

 a master. The ancient geometry, that of the Greeks of which 

 I have spoken, early fixed his attention and occupied his 

 mind by its extraordinary elegance, by the lucid clearness 

 with which its investigations are conducted, by the exercise 

 which it affords to the reasoning faculties, and above all, by 

 the absolute rigour of its demonstrations. He never under- 

 valued modern analysis ; it is a great mistake to represent 



* Euclid uses the word Corollary in his Elements. See Note II. 



