n6 A NEW SOLUTION,^. 



16976 1061 



160^3 ~~ 10/3 



b = 



— 1584 _ 99 



160 \/3 *""" IO /3 



r — — 39Q3* ___ ___ 4879 



— 43 20 °V / 3 "~ " " 54°<V3 



To find whether z can be expreffed by a furd as -—-: I write 



P — — 4879» ? = 54°°> and r == 3 3 a nd I have thefe two 

 equations, 



9/* 



„a_ 3"' — 5400 



^ - 3v 



I find, that 7, 17, and 41, are divifors of 4879. It is evident 

 that + 7 would give r negative : I therefore try — 7, and it 

 does not fucceed : Neither does +17; but trying — 1 7, I find 

 v 2 rr 64, and confequently » = + 8 : And — 8 is found to 

 fucceed in the other equation : therefore p =; — 17 v = — 8, 



and z = g^. 



We have then, z = g~ = *y 



J + *V3 2 5V3 



„ _ p + */3 _ 4i 

 •* — i — vVs — —9^3 



1061 , 17 



^ r^/3 "^ 8^3 8488 + 170 — 8658 __ 



Therefore, x - — t / = 792 + 1?0 - -557 - 9 



„ 4. _ 



10^3 3^3 



1061 7 



X 



io-v/3 

 99 



25V3 _ 



7 "~ 



53°5 — x 4 

 495 — '4 



_ 5291 



— 481 



10-/3 



" ^V^ 





1061 



41 







IO-/3 

 . 99 

 ic-/3 



9^3 _ 



4.1 



9^3 



9549 — 410 



691 — ■ 410 



_. 9*39, 



~~ 4S1 



= II 



ioy.3 9V3 ^49 — 4*u — y^vy — IfJ 



And fo the three roots are, 9, 11, and 19. 



END OF PART FIRS&. 



