CRITICISMS BY BRITISH WRITERS 273 



fluxions " according to the Newtonian notation, 

 "when for u we put the function itself, which it 

 represents. " 



23 1. The attitude of some British mathematicians 

 of the early part of the nineteenth century toward 

 the discussions of the fundamental concepts of the 

 calculus carried on during the eighteenth century 

 is exhibited in the foUowmg passage from John 

 Leslie's Dissertation on the progress of mathematica! 

 and physical science : ^ 



*'The notion of flowing quantities, . . . appears 

 on the whole, very clear and satisfactory ; nor 

 should the metaphysical objection of introducing 

 ideas of motion into Geometry have much weight. 

 Maclaurin was induced, however, by such cavelling, 

 to devote half a volume to an able but superfluous 

 discussion of this question. As a refinement on the 

 ancient process of Exhaustions, the noted method 

 of Prime and Ultimate Ratios . . . deserves the 

 highest praise for accuracy of conception. It has 

 been justly commended by D'Alembert, who ex- 

 pounded it copiously, and adapted it as the basis of 

 the Higher Calculus. The same doctrine was like- 

 wise elucidated by our acute countryman Robins ; 

 . . . Landen, one of those men so frequent in 

 England whose talents surmount their narrow 

 education, produced in 1758, a new form of the 

 Fluxionary Calculus, under the title of Residuai 

 Analysis, which, though framed with little elegance, 



^ Dissertation Fourth, in the Encyclopcedia Britannica^ 7th ed., 

 voi. i, 1842, pp. 600, 601. 



18 



