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XVI. Essay on the Resolution of Algebraic Equations : attempting 
to distinguish particularly , the real Principle of every Method , 
and the true Causes of the Limitations to which it is subject. 
By Giffin Wilson, Esq. Communicated by Edward Whitaker 
Gray, M. D. Sec. R. S. 
Read June 6 , 1799. 
INTRODUCTION. 
1 • Th e practical management of algebraic equations, as far as 
respects the solution of problems depending upon them, is well 
understood ; but their general theory , being considered as an 
abstruse and purely speculative subject, is no where, that I have 
seen, so fully analysed, as with all the assistance to be derived 
from the application of the principles of combination, it appears 
to me it might be. 
2. The difficulties under which the higher branches of algebra 
still labour are generally known. No degree of equations beyond 
the second, is yet perfectly resolved : cubics present frequently 
an irreducible case : biquadratics have, by several methods, been 
reduced to cubics ; but no formula exhibiting to the eye the 
actual resolution of a biquadratic has yet appeared : and, for the 
fifth degree, and all upwards, not even a clue which promises 
a general resolution has been struck out, by the continued la- 
bour and ingenuity of mathematicians for several centuries. 
3. This failure in the chain, beginning at the third degree. 
