82 On the PRINCIPLES, &c. 



EXAMPLE V. 



So to divide a flraight line AB, that the redlangle under the 

 two parts AC, CB fhall be the greatefl poflible. 



-B 



Let AB bereprefented by A, AC by X, and confequently CB 

 by A— X. Then the redangle AC, CB is equal to AX— X% 



a a 



the antecedental of which is AX — 2XX, which, when fup- 

 pofed equivalent to nothing, (according to ^nt. Cal. p. 7.) gives 

 A equal to 2X, or AC equal to CB. 



To multiply examples would be ufelefs. I will take an op- 

 portunity, as foon as I conveniently can, of applying this cal- 

 culus to feveral phyfical problems of importance, and particularly 

 fome refpe(51ing the refiftance of fluids ; and will fliew, that as it 

 furnifhes a much greater variety of ways for exprefling antece- 

 dentals than the fluxionary calculus does for fluxions, fo it will 

 open new and extenfive rules for finding antecedents, as yet 

 altogether unknown in the inverfe method of fluxions. 



Although the notation be in reality of no importance, I 



prefer X, Y, &c. to X, Y, &c. as more indicative of the ori- 

 gin of this mode of reafoning, which was derived from an exa- 

 mination of the antecedents of ratios in general geomeuical 

 comparifon. 



IV. Ob- 



