WHOSE LOVE FOR LEARNING AND DEVOTION TO THE TRUTH, ARE ONLY EQUALED BY THE MAGNIFICENT CONTRIBUTIONS WHICH THEY HAVE MADE TO THE CAUSE OF EDUCATION, THIS VOLUME IS RESPECTFULLY INSCRIBED AS A CHEERFUL CONTRIBUTION TO THE CAUSE WHICH WE ALL ADVOCATE IN COMMON, AND AS A SMALL TESTIMONIAL OF THE ESTEEM IN WHICH THEY ARE HELD BY THE AUTHOR. THE QUADRATURE OF THE CIRCLE, THE SQUARE ROOT OF TWO, AND THE RIGHT-ANGLED TRIANGLE, BY WILLIAM ALEXANDER MYERS, FIRST EDITION. "Where is the wise."-1st Cor., i, 20. "Now the serpent was more subtile than any of the beasts of the earth which the Lord God had male,”—Gen. iii, 1. CINCINNATI: WILSTACH, BALDWIN & CO., PRINTERS, Nos. 141 AND 143 RACE STREET. 1873. PUBLIC LIBRARI ASTOR, LENOX AND TILDEN FOUNDATIONS R 1924 L AUTHORS MADE USE OF IN THE PRESENT VOLUME. Should the student desire more general information upon the subjects treated of in the present volume, he is referred to the following works which have been freely used by the author wherever they have been found to be of service to his cause. They will be found to be among the best of their kind “Montuclas' History of Mathematics;" "Hutton's Recreations;" "DeMorgan on the Law of Probabilities;" "Elements of Euclid," by Todhunter; “Elements of Euclid," by Thompson; "Davies' Le Gendre;" "Robinson's Geometry;" Chauvenet's Geometry;" "Loomis' Geometry and Trigonometry;" "Bullfinch's Beauties of Mythology;" "Minifee's Draughting and Architecture;" "Home and School Journal;" "Chambers' Encyclopædia," and the "Douay Bible." *Zviered according to Act of Congress, in the Office of the Librarian at Washington, D. C., BY WILLIAM ALEXANDER MYERS, March 31st, 1873. All Rights Reserved. THE following pages are intended to explain certain mathematical truths, which were discovered by the author while engaged in a series of investigations made during the hours of rest from the labors of the college and the counting room. They consist chiefly of new methods employed in the solution of problems which have heretofore been regarded by mathematicians as impossible; and, although the author's mind has been employed with the subject for a number of years, the result of the investigations are now published for the first time. If the discoveries should not come up to that standard of brilliancy which commands attention, it is hoped that they may be found worthy of a fair and impartial consideration. The author scarcely dares to hope, with the many examples of failure before him, that at the outset the entire mathematical world will bow in submission to his decree, or submit unconditionally to the power of his reason or the force of his logic; nor does he desire that the glorious fabric, which the mathematical genius of the world combined has reared as a monument to the memory of departed greatness, should crumble into dust by a single touch. Ah, no! Rather let the ivy of remembrance forever remain green upon their mausoleums, and the vines of gladness encircle their remains. But if Genius, while pursuing her walks amid these temples of departed greatness, should suddenly be inspired by Wisdom, and conceive Truth, who would be so poor as to refuse a garland with which to crown her brow, wher truth sits enthroned? The discoveries are as follows: 1. The Quadrature of the Circle. |