SECT. 



DISSERTATION SECOND. 11 



that science had now become a distinction which the great 

 were disposed to recognise. 



Werner, who lived in the end of this century, is Ihe first 

 among the moderns who appears to have been acquainted 

 with the geometrical analysis. His writings are very rare, 

 and I have never had an opportunity of examining them. 

 What 1 here assert is on the authority of Montucla, 

 whose judgment in this matter may be safely relied on, as 

 he has shown, by many instances, that he was well ac- 

 quainted with the nature of the analysis referred to. It is 

 not a little remarkable that Werner should have understood 

 this subject, when we find many eminent mathematicians, 

 long after his time, entirely unacquainted with it, and con- 

 tinually expressing their astonishment how the ancient 

 geometers found out those simple and elegant constructions 

 and demonstrations, of which they have given so many ex- 

 amples. In the days of Werner, there was no ancient 

 book known, except the Data of Euclid, from which any 

 information concerning the geometrical analysis could be 

 collected ; and it is highly to his credit, that, without aay 

 other help, he should have come to the knowledge of a 

 method, not a little recondite in its principles, and among 

 the finest inventions either of ancient or of modern science. 

 Werner resolved, by means of it, Archimedes's problem 

 of cutting a sphere into two segments, having a given ratio 

 to one another. He proposed also to translate, from the 

 Arabick, the work of Apollonius, entitled Sectio Rationis, 

 rightly judging it to be an elementary work in that analy- 

 sis, and to come next after the Data of Euclid. ' 



Benedetto, an Italian mathematician, appears also to have 

 been very early acquainted with the principles of the same 

 ingenious method, as he published a book on the geometri 

 cal analysis at Turin in J 585. 



1 See Montucla, vol. I. p. 581. 



