C 375 3 
Example. 
Let a= 2 j then the firfl fraction, /. c. that in the 
fmallefl numbers, that makes — — 2, is when b 
=3, and r=2 j fo that 
A J i 
£ <7r 2 f 
are And the terms following the firfl 
* ±1 9j? £_7_7 3^6? A?/. 
3‘ +f s dlc ii‘ 7o*2os* =3 78* v “'^* 
$ 
2. But if = i.e, if the firfl fraction - of 
the feries have the fquare of its numerator an unit lefs 
than acc , the multiple of the fquare of its denomina- 
tor by the number a ; the fecond term fliall have the 
fquare of its numerator an unit greater than the faid 
multiple of the fquare of its denominator ; and the 
third term fliall have the faid fquare an unit lefi'er, 
and fo on alternately. 
For, by Prop. 2. the fecond term ~ fliall be fuch, 
that dd -^- l =a : and therefore, by Prop. 4. the third 
term^ fhall be fuch, that^~a=^. And by Prop. 
y. it follows, that the next term ~ k fliall be fuch, that 
-T7 — = a ; and fo on alternately, by Prop. 4, and 
Example. 
Let a — 2 ; then the firfl fraction b - that makes*-^-i-i 
J C ft 
= 2, is when b — i, and c— 1. So that 
r 
d 
