54 LIMITS AND FLUXIONS 



Here Stone simply writes " fluxìon " where 

 De l'Hospital writes " difìerence," which is a 

 mischievous procedure, seeing that the two words 

 stand for things totally difìferent. De rHospital's 

 wordiiig is *'La portion infiniment petite dont une 

 quantité variable augmente ou diminuè continuelle- 

 ment, en est appellée la Difìférence. " Stone also 

 changes from the Leibnizian to the Newtonian 

 notation, by writing x instead of dx. Then foUow 

 two postulates : 



''Grant that two Quantities, whose Difìférence 

 is an infinitely small Ouantity, may be taken (or 

 used) indifferently for each other : or (which is the 

 same thing) that a Ouantity, which is increased or 

 decreas'd only by an infinitely small Quantity, may 

 be consider'd as remaining the same. 



" Grant that a Curve Line may be consider'd 

 as the Assemblale of an infinite Number of in- 

 finitely small right Lines : or (which is the same 

 thing) as a Polygon of an infinite Number of Sides, 

 each of an infinitely small Length, which determine 

 the Curvature of the Line by the Angles they make 

 with each other." 



De l'Hospital's " prendre la difìférence" is 

 rendered by Stone " to find the fluxions." The 

 fluxion oi xy is found by taking the product of x-\-x 

 and J+j, and neglecting xy, " because ij is a 

 Quantity infinitely small, in respect of the other 

 Terms yx and xj/." 



72. Further on in Stone's translation (p. 73) we 

 read : 



