f 



[ 227 ] 



whence tranfpofing and fimplifying we have, 

 J 4. « .4 .» +tqay 



— %\apy 



which latter equation has but one furd, whence ioxp.q.p'^ 

 and y' fubftituting their values and conneding the terms we have 

 after dividing all by a' 



— y + Say — 184^)' + 486^)'— 365a = 74^j— 304^7)/+ 364^ + 4_y 

 ♦ •Wa'' ay which equation fquared and transformed into an original 

 equation gives an equation free from furds the fame as Dodor 

 Hales's final equation. 



* >< 3s 44 Si <* r X 



^ * + looSay— 1464^)'— 2762^)'+ 368o<7j' + 2916^^ — 972^/ + 729* 

 = o. 



By the fame management we may take away the afymmetry 

 of an equation having furds of a more intricate nature. 



Let there be propofed the equation confifting of a cubic furd 



* 4 J 

 and two biquadratics </ a-\- ^b= ^c. 



Involve both fides to the cube and the equation will then 

 fta nd, 



of thcfe furds we may obferve that the produd of two pairs 



F f 2 will 



