OF ALGEBRAIC QUANTITIES. 
347 
For let a! =■ x, and V = y , 
p i 
then / = x + y, 
S 
28. Let a and b be any quantities whatever, and f a quantity 
such that d — V = / ; then ^ — f. 
P q s 
For, since d — V — /, 
p q « 
d = V + /, 
p q s 
(by preceding Art.) a — b 
•’* T — J- 
29. Let a and b be any quantities whatever, and let a be inclined to unity 
at an angle = «, and b at an angle = (3, a and (3 being each positive and less 
than c the circumference of the circle, and let a b = /; 
then d + V = / , if a, + (3 be less than c, 
p q p + q 
= / , if u -f- |3 be not less than c. 
P +- q + 1 
For let g be a positive quantity, in length = a, 
h = b, 
e& 
then a = g ^l^T, 
b = h 
O' 
« + /3 
g a m c 
o) 
also a' = g' + « + p c . — 1, 
p 0 
b' = h' + (3 + qc. s /— l, 
.-. d + b' == g' + h' + a -f- j3 + p + q . c . — 1 ; 
p q 0 0 
2 v 2 
