PRINTED BOOKS, ETC. BEFORE 1734 51 



sent forth a new book, the first part of which was 

 a translation.^ 



The foUowing extract is from Stone's translation 

 of De l'Hospital's Preface, the words in the square 

 brackets [ ] being interpolateci by Stone : — 



" By means of this Analysis we compare the 

 infinitely small (DiiTerences or) Parts of finite 

 Magnitudes, and find their Ratio's to each other ; 

 and hereby Hkewise learn the Ratio's of finite 

 Magnitudes, those being in reality so many infinitely 

 great Magnitudes, in respect of the other infinitely 

 small ones. This Analysis may ever be said to go 

 beyond the Bounds of Infinity itself ; as not being 

 confined to infinitely small (Differences or) Parts, 

 but discovering the Ratio's of Differences of Differ- 

 ences, or of infinitely small Parts of infinitely small 

 Parts, and even the Ratio's of infinitely small Parts 

 of these again, without End. So that it not only 

 contains the Doctrine of Infinites, but that of an 

 Infinity of Infinites. It is an Analysis of this kind 

 that can alone lead us to the Knowledge of the true 

 Nature and Principles of Curves : For Curves being 

 no other than Polygons, having an Infinite Number 

 of Sides, and their Differences arising altogether 

 from the different Angles which their infinitely 

 small Sides make with each other, it is the Doctrine 

 of Infinites alone that must enable us to determine 

 the Position of these Sides, in order to get the 



^ l^he Method of Fluxions^ both Direct and Inverse. The former bein^ 

 a Translation from the Celebrated Marqiiis De PHospiiars Analyse 

 des Injinenunts Petits : And the Latter Supply'd by the Trans lator, 

 E. Stone, F.R.S. London, MDCCXXX. 



