This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1866 Excerpt: ... the reductions; and yi, y, and y3 are the known irrational functions of ai, a2, a3, and a4 previously determined. This process being supposed to be gone through for one transformed quartic and its form of, we may go through it again in precisely the same manner for the other transformed quartic and its corresponding ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1866 Excerpt: ... the reductions; and yi, y, and y3 are the known irrational functions of ai, a2, a3, and a4 previously determined. This process being supposed to be gone through for one transformed quartic and its form of, we may go through it again in precisely the same manner for the other transformed quartic and its corresponding form of; and we thus obtain another set of values of ifai, fa, px2, and ifa4, in which i represents the other value of z. That is, in the case under consideration, we first determine kxi' + Ixi, kx + Ixfi, kx3' + Ix3, kxS 21-21-21-22-11. Now, if we form any symmetric function of kxi + Ixi and kxi + l'xi; this will be a function of xi all whose coefficients are rational functions of ai, a, a3, and a4; then xi itself is absolutely determined by expelling all powers of xi higher than the first by means of the original quartic in an. For example, if we take the sum of fei2 + Ixi and kxi' + I'xi, we obtain and a4, which represent one set yi', yJ, 2/3, represent the other set also by simply changing throughout the sign of VJ6. 28. We thus acquire a new form of solution for the quartic, the essence of which consists in the introduction of a special irrational element pervading the whole process and the final result, and producing a material change in the character of the root, inasmuch as each term of it now contains only two constituents. Had we taken $ of the form ho? + lx, we should have obtained another new form of solution of the quartic, whose distinction would have depended on the introduction of a known irreducible radical VI, producing a similar effect on the root; and had we taken-fy of the form hx + kx', we should have obtained another new form of solution of the quartic involving another known irreducible radical V-/,0 with similar ...
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Add this copy of An Essay on the Resolution of Algebraic Equations to cart. $72.52, new condition, Sold by Just one more Chapter rated 3.0 out of 5 stars, ships from Miramar, FL, UNITED STATES, published 2012 by Hardpress Publishing.
