OF ALGEBRAIC QUANTITIES. ? 347 



For let d = x, and V = y, 

 p ? 



then/ = x -jr y, 



s 



28. Let a and b be any quantities whatever, and/ a quantity 

 such that a' — b' =/' ; then -r- = /". 



For, since a! — b' = f, 



p q s 



a' = 6' +/, 

 1' ? » 

 .•. (by preceding Art.) a = bf, 



■• b —J- 



29. Let a and & be any quantities whatever, and let a be inclined to unity 

 at an angle = a, and b at an angle = /3, a and /3 being each positive and less 

 than c the circumference of the circle, and let ab ■=■/; 



then a' + 6' = /' , if a + |3 be less than c, 



= /' , if a + j3 be not less than c. 



For let g- be a positive quantity, in length = a, 

 h =6, 



« 



then a = g p^'c', 

 b = h n\T, 



also a' = g' -{■ a -\- p c . ^ — I, 



P 



7 



••• a' + 6' = ^ + A' + « + |3 + P + 9.C . y^=T; 



p ; 



2 y2 



« + /3 



