The book An Essay On the Resolution of Algebraic Equations was written by author Charles James Hargreave Here you can read free online of An Essay On the Resolution of Algebraic Equations book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is An Essay On the Resolution of Algebraic Equations a good or bad book?
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34- I3. 14)- (II . 23"- 12 . R3) (Tl. 24-T2. 14)}/2-A; -h{(ri. 22-1^. 12)(n. 4r-U. 14)~(Ii. 24-12. 14)2}/t2 = 0. THE QUINTIC. 79 This can be divided into two parts by means of the dispos- able constants ; the first two terms being made equal to zero ; and the last three terms (which contain only h and k) being also separately equated to zero. We thus have a quadratic in h and k with rational coefficients, (which I propose to call the first quadratic), whose solution gives a linear relation be- ...tween h and k. The coefficient of this relation is a quadratic- irrational of the 30th degree. Substituting for h in the equation formed by the sum of the first two terms above being made zero, we have another quadratic equation with quadratic-irrational coefficients, (which I call the second quadratic) ; and its solution gives a linear relation between m, I and k, whose coefficient is what we may call a quadratic-quadratic-irrational. We have thus linear values for k and h in terms of I and m. Sub- stituting these in the cubic equation of condition, which, in this notation, is .
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