I20 



LIMITS AND FLUXIONS 



whether the imagination can any better pursue the 

 subdivision of the line, or even of the hour itself, to 

 the end of the hour, vvhìch subdivisions he must 

 own to be brought to a period by the end of the hour. 

 But there is no need to strain our imagination^ to 

 labour in every case, or indeed in any case, after 

 some idea of motion however intricate ; no subtle 

 inquiry is at ali necessary, since we are obliged to 

 own the conclusion to be true and certain. ..." 



" However, since Mr. 

 Robins is pleased to talk so 

 much about straining our 

 imagination, . . . let us see, 

 if we cannot find some plain 

 and easy way of represent- 

 ing to the imagination, that 

 actual equality, at which the 

 inscribed and circumscribed 

 figures will arrive with each 

 other, and with the curvi- 

 linea! figure, at the expiration of the finite time " 



(p. III). 



Let the curvilineal figure ABE equal in area the 

 rectangle with sides EA and AF. When the moving 

 point describing the base EA in a finite time is at C, 

 let the rectangle with the base EA and height Cd 

 be equal to the sum of the parallelograms inscribed 

 in ABE (not drawn in the figure) which stand on 

 CA and upon as many other adjoining parts of EA 

 as can be taken equal to CA. Let lidd be the curve 

 traced by the moving point d. 



eE 



