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. 1914 edition. Excerpt: ...of a cube whose volume shall be double that of a given cube. Take the edge of the given cube as the unit of length and denote by x the length of an edge of the required cube. Then x3--2 = 0. Since no one of the divisors of 2 is a root of this cubic equation, the theorem stated in 8 implies the ...
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. 1914 edition. Excerpt: ...of a cube whose volume shall be double that of a given cube. Take the edge of the given cube as the unit of length and denote by x the length of an edge of the required cube. Then x3--2 = 0. Since no one of the divisors of 2 is a root of this cubic equation, the theorem stated in 8 implies the impossibility of the duplication of a cube by ruler and compasses. 10. f Cubic Equations with a Constructive Root. It remains to prove the theorem in 8 from which we have drawn such important conclusions. Suppose that (20) x3 + oa? + ffx + 7 = 0 (o, 3, y rational) is a cubic equation having a root Xi such that a line of length Xi or--Xi can be constructed by ruler and compasses. We shall prove that one of the roots of (20) is rational. The construction is in effect the determination of various points as the intersections of auxiliary straight lines and circles. Choose rectangular axes of coordinates. The coordinates of the intersection of two straight lines are rational functions of the coefficients of the equations of the two lines. To obtain the coordinates of the intersection of the straight line y = mx + b with the circle (x-p)2 + y-q)2 = r2, we eliminate y and obtain a quadratic equation for x. Thus x, and hencealso y, involves no irrationality (besides irrationalities in m, b, p, q, r) other than a square root. Finally, the intersections of two circles are given by the intersections of one of them with their common chord, so that this case reduces to the preceding. Hence the coordinates of the various points located by the construction, and therefore also the length Xi of the segment joining two of them, are found by a finite number of rational operations and extractions of real square roots, performed upon rational...
Read Less
Add this copy of Elementary Theory of Equations to cart. $15.25, good condition, Sold by BookDepart rated 4.0 out of 5 stars, ships from Shepherdstown, WV, UNITED STATES, published 1914 by John Wiley & Sons.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. Hardcover; surplus library copy with the usual stampings; reference number taped to back cover; fading, soiling, and edge wear to exterior; cover clot h wearing at corners; binding reinforced; otherwise in good condition with clean text.
Add this copy of Elementary Theory of Equations to cart. $16.27, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Elementary Theory of Equations (1914) to cart. $18.00, very good condition, Sold by Second Story Books rated 4.0 out of 5 stars, ships from Rockville, MD, UNITED STATES, published 1914 by John Wiley & Sons, Inc.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Book. Reprint of 1914 Edition by Kessinger Publishing 's Legacy Reprint; Octavo; VG; Hardcover; Blue and white text with black text; Boards are sturdy; Text block is clean; 184p. 1319632. FP New Rockville Stock.
Add this copy of Elementary Theory of Equations to cart. $20.00, very good condition, Sold by J. Hood, Booksellers, Inc. rated 5.0 out of 5 stars, ships from Baldwin City, KS, UNITED STATES, published 1914 by John Wiley & Sons.
Add this copy of Elementary Theory of Equations to cart. $27.44, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Elementary Theory of Equations to cart. $29.32, good condition, Sold by ThriftBooks-Reno rated 5.0 out of 5 stars, ships from Reno, NV, UNITED STATES, published by John Wiley & Sons.
Add this copy of Elementary Theory of Equations to cart. $31.50, like new condition, Sold by Phatpocket Limited rated 4.0 out of 5 stars, ships from Waltham Abbey, ESSEX, UNITED KINGDOM, published 2009 by BiblioLife.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Like New. Used-Like New. Book is new and unread but may have minor shelf wear. Ships from UK in 48 hours or less (usually same day). Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. 100% money back guarantee. We are a world class secondhand bookstore based in Hertfordshire, United Kingdom and specialize in high quality textbooks across an enormous variety of subjects. We aim to provide a vast range of textbooks, rare and collectible books at a great price. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions. We provide a 100% money back guarantee and are dedicated to providing our customers with the highest standards of service in the bookselling industry.
Add this copy of Elementary Theory of Equations (Classic Reprint) to cart. $31.84, new condition, Sold by Revaluation Books rated 4.0 out of 5 stars, ships from Exeter, DEVON, UNITED KINGDOM, published 2012 by Forgotten Books.
