[ 37i ] 
Prop. i. 
Let a be any number propofed, and ~ be fuch a 
fraction, that h e. bb — acc-\- i , then, if 
two other fractions be taken, one of which is — , the 
firft divided by the propofed number a , and the other 
is p the reciprocal of the firft fradion; then the 
fraction bb ~- * - , whofe numerator is the fum of the 
produds of the numerators, and of the denomina- 
tors of the fractions \ and p £ ; and its denominator 
the fum of the products of the numerators, and of 
the denominators of the fradions - and - b , fliall have 
the fame property with the fradion * i. 
Becaufe bb = acc -f- i 
bb — acc — i, and fquaring 
b* — a ab z c*-\-a*c+=i. And adding 4 ab % c % 
b++ zaPc'+a H%=4ab z c*+ 1 . 
Whence b — 1 = ^ • 
2 be 
Prop. 2. 
If - be fuch a fradion, that^— a, i. c. bb+i=acc> 
c Cl - 
all other things remaining as in Prop. 1. then fhall 
the fradion formed as there deferibed, be 
A a a 2 
Eecaufc 
