[ 3/2 ] 
Beaufe hb^-\—acc, then acc — lb— i j and fquafing 
Z>* — zab z c z -\-a z c^=- 1 . 
Whence, as in the foregoing, it will follow, that 
bb\--acc Z 1 
— a = a. 
ibc 
Prop. 3 . 
Let the fraction - be fuch, that - b — = a. i. e. b b 
— a cc -f- 1 ; alfo let j be another fraction, having the 
fame property with i. e. fuch, that dd—aee-\- 1. 
Then, if from the fraction—, and the two others men- 
b c 
tioned in Prop. 1. viz. — , and ^ a new fraction be 
formed, in the fame manner as the fraction 
was formed from and the fame two — and 7, which 
c ac b 7 
fraction will be ^77 ; this new fraction fhall have 
ca-\-be 
the fame property with the other two b and i.e. 
bd-\-ace — i _ 
cd-\-be 
a. 
Hypoth. 1 . bb—acc-\- 1 
2. dd—aee-\-i 
3. ac z d z —a z c z e z -\-ac z [ 2 .] 
4. b^d i —ab z e z -\-b z [2.] 
f. b z d z —ab 2 e z -\-ac*-\-i [4, 1 .] 
6 . b 2 d z -\-a z c z e z =ab z e z -\-a z c z e z ~{-ac z -\-l [ 5 .] 
7 . b z d z \-a z c z e z —ac z d z -\-ab z e z 4-1 [ 6 . 3 ] 
8. b?-d l -\-iabcde-\-a L c x e l ~ac l d'A r 2abcde\-ab*e’-\- 1 [7]- 
/. e . 
