ANTECEDEKTAL CALCULUS. 6j 



ceeds the geometrical expreffion, 



- ^ Q- Q- %-^^ ^^ ^ , V the 



aforefaid geometrical expreffion. 



It is almoft unneceflTary to obferve, that the two expreflions, 

 which have refpedlively to B ratios, having to the ratios of 

 A+N to B, and A— N to B the ratio of R to Q^ give us 



A — + — . A--->: N + — . — — ^A -— -^ N" ± + &c. 



— -^= — -^= -^= ^';_Q -^= for the gco- 



. '^ 



metrical magnitude, which has to B a ratio, having to the ratio 

 of A— N to B the ratio of R to Q^ But as this expreffion mufl 

 vary indefinitely with the endlefs variations in the quantity of 

 the magnitude B, its geometrical flandard of comparifon, fo, 

 when we fuppofe it to become numerical, we get an indefinite 

 number of arithmetical formulse, referring to different ftandards 

 of comparifon. For B may be then reprefented by 



1, 2, 3,4,5, &c. 

 i,/2, ^3, ■/4,V5. &c. 

 J- J- J- 1- J- B,c 

 or &c. Sic.Jine limit e. 



And in that particular cafe, when it is reprefented by i or 

 unit, this geometrical formula gives the arithmetical one, (put- 

 ting r and q for R and Q»_) 



q q q q n 3 ~ i ^9 32 1 



which 



