t 228 ] 



will give a fimple quadratic, placing at the fame lide thofe 

 pairs the equation will ftand, 



4 < __ 4 4 



*/a' + 3 \/ab^ = c— 3 Va'i) — '/D* and fquaring this equation 



as/a + 6a-/l) + ^6 </a = c + ga-/b + i'^l> — 6c ^a^6 — 2c v^' + 6l> V^ 



Let the terms be colleded uniting fuch furds as admit it, 

 and fubftituting letters for the cocfRcients ^a + i> —y 



— 3^ — ij =3 s 



4 * 



the equation will now be 6c V<i'^ + 2c ^3' = c' + j v^^ — s V^ 



1 1 * 4 ft 1 « 



whence by fquaring 36fa "^b + ^\cb '^a + ^b "^6= c -\-yb + za + zcy 

 vl> _ 2CZ ^a — 2yz ^ab. 



» • t 



Let ;^6ca + ^b — 2cy = v 



* .» 

 c* -\.yb + aj = X 



ft > 



2^b + 2CZ = / 



The equation will then by tranfpofition fland thus, 



V '/b -\- 1 '^a = X — lyz "^ba and fquaring 



v'^b-Vta-\- tvt ■^ab = x — J^yzx -^ba + <\.yzha let the rationals = r 

 and the coefficient 2v/ + 4j'zx = s and the equation will be s ^ab 

 = r and fquaring s^ab — r'' where all the terms arc rational. 



Nearly 



I 



