NE WTON 27 



but a Superficies infinitely narrow. And vvhen he 

 consider'd the Ordinate as the Moment of the Area, 

 he understood by it the Rectangles under the geo- 

 metrica! Ordinate and a Moment of the Abscissa, 

 tho' that Moment be not always expressed." Again, 

 p. 179: "And this is the Foundation of the 

 Method of Fluxions and Moments, which Mr. 

 Newton in his Letter dated Octob. 24, 1676, 

 comprehended in this Sentence. Data cequatione 

 quotcunque fluentes quantitates involvente, invenire 

 Fluxiones ; et vice versa. In this Compendium 

 Mr, Newton represents the uniform Fluxion of 

 Time, or of any Exponent of Time by an Unit ; 

 the Moment of Time or its Exponent by the Letter 

 o ; the Fluxions of other Quantities by any other 

 Symbols ; the Moments of those Quantities by the 

 Rectangles under those Symbols and the Letter ; 

 and the Area of the Curve by the Ordinate inclosed 

 in a Square, the Area being put for a Fluent and 

 the Ordinate for its Fluxion. When he is demon- 

 strating a Proposition he uses the Letter for a 

 finite Moment of Time, or of its Exponent, or of 

 any Quantity flowing uniformly, and performs the 

 whole Calculation by the Geometry of the Ancients 

 in finite Figures or Schemes without any Approxi- 

 mation : and so soon as the Calculation is at an 

 End, and the Equation is reduced, he supposes that 

 the moment decreases in infiìiitum and vanishes. 

 But when he is not demonstrating but only investi- 

 gating a Proposition, for making Dispatch he 

 supposes the Moment to be infinitely little, and 



