An essay on the resolution of equations

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Taylor and Francis, 1858
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Page 82 - ... or, in other words, to express a root of the general equation of the fifth degree by a finite combination of radicals and rational functions. The problem had long engaged the attention of mathematicians, and was attacked by the most celebrated analysts of the last century with great skill and vigour, but without success. In the early part of the present century, Abel, the young and gifted Norwegian mathematician, attempted...
Page 49 - And if #„ xt, x^, xv xb are the roots of the given equation of the fifth order, and it' , /3, y, 8, e represent in an undetermined or arbitrary order of succession the five indices 1, 2, 3, 4, 5, and if t denote an imaginary fifth root of unity (I conform myself to Mr. Jerrard's notation), then P\> Pv 1}3> and the other auxiliary quantities /, u, are obtained from the system of equations — * Communicated by the Author.
Page 83 - Let us for a moment consider the nature of the difficulty which had to be overcome.

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