Excerpt from On the Theory and Solution of Algebraical Equations: With the Recent Researches of Budan, Fourier, and Sturm, on the Seperation of the Real and Imaginary Roots of Equations There has long appeared to me to be great want of a compendious work on the theory and solution of Equations in the English language; and the successful researches of Homer, Budan, Fourier, and Sturm, have now so entirely changed the state of this department of analysis, as to render such a publication almost indispensable. The improvements of Mr. Horner, which have so greatly contributed to perfect the numerical solution of equations of all orders, were first published in the Philosophical Transactions of the Royal Society, in the year 1819; but strange as it may appear, have as yet excited but little attention from British mathematicians. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.