232 LIMITS AND FLUXIONS 



occupied a mudi higher rank as a mathematician. 

 Foreigners place him high among his English con- 

 temporaries. He wrote M atheìnatical Lucubrations^ 

 1755, and Residuai Analysis^ 1764. We shall con- 

 sider only his Discoui'se concerning Residuai Analysis^'^ 

 1758. From it we quote as follows : 



*' Yet, notwithstanding the method of fluxions is 

 so greatly applauded, I am induced to think, it is 

 not the most naturai method. . . . The operations 

 therein being chiefly performed with algebraic 

 quantities, it is, in fact, a branch of the algebraic 

 art, or an improvement thereof, made by the help 

 of some peculiar principles borrowed from the 

 doctrine of motion. . . . We may indeed very 

 naturally conceive a line to be generated by motion ; 

 but there are quantities . . . which we cannot 

 conceive to be so generated. It is only in a 

 figurative sense, that an algebraic quantity can be 

 said to increase or decrease with some velocity. 

 Fluxions therefore are not immediately applicable 

 to algebraic quantities. . . . It therefore, to me, 

 seems more proper, in the investigation of proposi- 

 tions by algebra, to proceed upon the aftciently- 

 received principles of that art. . . . That the borrow- 

 ing principles from the doctrine of motion, with a 

 view to improve the analytic art, was done, not 

 only without any necessity, but even without any 

 peculiar advantage, will appear by showing, that 

 whatever can be done by the method of computa- 



^ A Discourse Concentiug Residuai Analysis : A new Branch of the 

 Algebraic Art. By John Landen. London, 1758. 



