TEXT-BOOKS, 1736-1741 I55 



or by any other Mark drawn into an Unit " (p. 228). 

 ' ' Fluxions are not Moments, but finite Quantities 

 of another kind." *'When Mr. Newton is demon- 

 strating any Proposition, he considers the Moments 

 of Time in the Sense of the Vulgar, as indefinitely 

 small, but not infinitely so ; and by that means 

 performs the whole work, in finite Figures, by the 

 Geometry of Euclid and Apollonius, exactly without 

 any Approximation : and when he has brought the 

 work to an Equation, and reduced the Equation to 

 the simplest Form, he supposes the Moments to 

 decrease and vanish ; and from the terms which 

 remain he deduces the Demonstration. But when 

 he is only investigating any Truth, or the Solution 

 of any Problem, he supposes the Moment of Time 

 to be infinitely little, in the Sense of Philosophers, 

 and Works in Figures infinitely small." 



James Hodgson, 1736 



152. James Hodgson, a mathematical teacher and 

 writer, and a fellow of the Royal Society of London, 

 is the author of a book, The Doctrine of Fluxions.^ 



Hodgson says in his Introduction that *' it is now 

 some years since the greatest Part of this Book was 

 prepared for the Press." There is no direct refer- 

 ence in the book to the Analyst controversy, but 

 the declaration is made that the principles upon 

 which fluxions rest need " fear no Opposition." 



^ The Doctrine of Fluxions, fotinded on Sir Isaac Newton s Afethod, 

 Piiblished by Himself in his Tract upon the Quadrature of Curves^ 

 By James Hodgson, London, MDCCXXXVI. 



