[ 374 ] 
Prop. 6 . 
But if b z — acc- f-i, and (P—aee — i, all other things 
remaining as in Prop. 3. Then ihail bd-\-aci -J- 1 — 
% 
. bd+ace +i_ , . , , „ 
a Xcd+be . n c. ■ — — —a. which maybe lhewn, 
cd-\-be 
as the reft were. 
Now, let a be any number propofed, and let the 
fraction - be fuch, that either— — - — a, or 
c cc cc 
and take the fractions - and j. before deferibed : then 
aco ' 
the feries of ff actions converging to ^ a will be as 
follows : 
7>- i - = the firft term of the feries. 
u ac J c 
the fecond term >. Every term is formed from 
2 be e I the preceding ; and the 2 
the third term. I fractions - and f in the 
cd-\-bc g f ac b 7 
fame manner as the fe- 
cond from the firft, and 
thefe fractions. 
'■ f+a i g __ h term. 
cfJr g « • • t 
&c. in tnjin. 
And from the foregoing propofitions it follows, 
i . That if — y — = a y then every fraction of the 
icries fhall be fuch. 
That if from the fquare of its numerator be taken 
an unit, the remainder, divided by the fquare of its 
denominator, fhall be equal to a. 
For, by Prop . i. the fra&ion ^ fhall be fuch ; and 
by Prop. 3. the next fra&ion ^ fhall likewife be fuch ; 
and fo all the following terms. 
Example. 
