[ 68 ] 



rj ii between 2 and 3, 2^ and 3^ are the limits, of which zb 

 is nearer to a-, and being lefs than a, make a—zb\c, and by 

 fubftltuting we have this equation : 



which by redudion becomes 



5 b^= 1 2 b'^c+G bc^-\-c^ Zjlj. ivV/? anfwer. 



In this equation alTo we are to determine the Hmits of b 

 the greater quantity with refpedt to c the lefs ; which may be 

 done by fubftituting fome multiple of c for b : and according as 

 the left fide of the refulting equation is lefs or greater than the 

 right fide, that multiple is lefs or greater than the truth. And 

 to avoid unneceffary trials, let the coefficient of the firft term 

 on the right fide of the equation, be divided by the coefficient of 

 the term that ftands on the left fide j and the quotient, (ne- 

 gleding the fradion,) multiplied into the lefs quantity, will be 

 one of the limits, or near it. And when all the terms on the right 

 fide have affirmative figns, the limit thus found will be lefs than the 

 truth ; but when fome of them have negative figns, it will probably 

 be greater than the truth. Thus, in the lafl; equation above, 

 divide i2 by 5, and the quotient being 2, make b—zc, and 

 upon trying it will be found, that 2c is lefs than the truth ; 

 therefore make b—T, c, and upon trial 3 c will be found 

 greater than the truth. Therefore zc and 3^ are the limits of 

 b, of which 3 c feems nearer to the truth ; therefore make 

 1=0^0 — d, and by fubftltuting, this equation refults, 



and by redudlion, 



S(^=-^'Jc^d — 33fi/^+5'^'+V. Second anfiver. 



Here 



