This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1876 edition. Excerpt: ...for the solution of cubics, the solution of the proposed biquadratic is reduced to that of the two quadratics, and assume the first member to be the product of two quadratic factors (x2 ] kx + f) and (xa--kx + g), thus, + (f + g-W)x2 + (gk-fk)x+fg = 0. 2. Equating coefficients of equal powers of x in 1 ...
Read More
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1876 edition. Excerpt: ...for the solution of cubics, the solution of the proposed biquadratic is reduced to that of the two quadratics, and assume the first member to be the product of two quadratic factors (x2 ] kx + f) and (xa--kx + g), thus, + (f + g-W)x2 + (gk-fk)x+fg = 0. 2. Equating coefficients of equal powers of x in 1 and 2, we obtain the equations, f + g--w = q, gk--fk = r, fg = s. 3.. Having found / and g in terms of k from the first two of these equations, and substituting in the third, we have (k+l+q)(i-l + q)=t8, from which we obtain by reduction, k + 2qk + (q2--4s) k2--r2 = 0, or, putting z for k2, we have the reducing cubic, z3 + 2qz2 + (q2--4s) z--r2 = 0. When from this cubic a value of z has been determined, its square root is k, and k being known, / and g become known from the first two of the equations in 3, and we obtain the four roots of the biquadratic from the two quadratics, x2 + kx + f = 0, x2--kx + g = 0. Ex. x--2ix2 + 15x-2 = 0. The reducing cubic is, 2a _ 4822 + 5842 _ 225 = 0. Prom this we find one root, z = 25, ... k = 5, /= 2, g =--1; and we can determine the four roots of the proposed from the equations, x2 + 5x + 2 = 0, x2--5x--1 = 0. 129. We shall give one more solution, of some interest as proceeding by a method analogous to that pursued in Cardan's solution of the cubic; a method that has been applied to tin solution of equations of higher degree than the fourth, and fails only in so far as that the reducing equations obtained are of higher degree than the original equation. namely those combinations the product of whose terms is negative. If r is negative, the admissible values of x are, Vti+Vh+Vts, Vti--Vh--Vh, --Vii+Vti--Vts, --Vti--Vtt+Vts. 131. The occurrence of the eight values of x in the solution has an explanation...
Read Less
Add this copy of A Treatise on the Theory and Solution of Algebraical to cart. $37.84, new condition, Sold by Books2anywhere rated 5.0 out of 5 stars, ships from Fairford, GLOUCESTERSHIRE, UNITED KINGDOM, published 2024 by Bod Third Party Titles.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of A Treatise on the Theory and Solution of Algebraical to cart. $41.64, new condition, Sold by Paperbackshop International rated 5.0 out of 5 stars, ships from Fairford, GLOS, UNITED KINGDOM, published 2024 by Bod Third Party Titles.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of A Treatise on the Theory and Solution of Algebraical to cart. $61.08, new condition, Sold by Books2anywhere rated 5.0 out of 5 stars, ships from Fairford, GLOUCESTERSHIRE, UNITED KINGDOM, published 2024 by Bod Third Party Titles.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of A Treatise on the Theory and Solution of Algebraical to cart. $67.21, new condition, Sold by Paperbackshop International rated 5.0 out of 5 stars, ships from Fairford, GLOS, UNITED KINGDOM, published 2024 by Bod Third Party Titles.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of A Treatise on the Theory and Solution of Algebraical to cart. $49.17, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2024 by Outlook Verlag.
Add this copy of A Treatise on the Theory and Solution of Algebraical to cart. $65.28, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2024 by Outlook Verlag.
Add this copy of A Treatise on the Theory and Solution of Algebraical to cart. $48.63, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2016 by Wentworth Press.
