MOREOVER, THE NEW METHOD OF CUBIC AND HIGHER EQUATIONS, OF THE MORE RECENTLY DISCOVERED, THEOREM OF STURM. BY GEORGE R. PERKINS, A. M., PRINCIPAL, AND PROFESSOR OF MATHEMATICS IN THE UTICA ACADEMY, AND AUTHOR OF “HIGHER ARITHMETIC." UTICA: NEW YORK: 1842. Entered, according to Act of Congress, in the year 1841, by GEORGE R. PERKINS, in the Clerk's Office of the Northern District of New York GROSH & WALKER, Printers. Histos acis Tutta n-21-28 26926 PREFACE. In presenting this volume to the public, I would not claim to have unfolded many new principles of Algebra ; I only claim to have judiciously combined and arranged principles already known. By commencing this work with the most elementary parts and gradually ascending to the more complicated, I have designed to adapt it to the wants of students of every grade. While I acknowledge, that, in general, the principles have long been known, I think I am justifiable in claiming some of the methods of operation as original. This work will be found to contain, for the first time, I believe in any American school book, a demonstration and application of STURM's THEOREM ; by the aid of which, we may at once determine the number of real roots, of any algebraic equation, with much more ease than could be done by any previously discovered methods. The method of finding the numerical values of the roots of cubic and higher equations, as fully explained under the last chapter, will no doubt be new to many, and interesting to all lovers of this science. It is particularly interesting on account of the ease with which it resolves itself into the method of extracting any root of a number, as explained in my HIGHER ARITHMETIC. It would be extremely difficult to point out the exact sources from which I have drawn for this work, and even could I do so, these principles have been so long in use, we could not with safety say when, and with whom, they each originated. While I acknowledge the aid of many works on this science, I would give by far the greatest share of credit, to the eighth edition of BOURDON's most excellent treatise on Algebra. GEO. R. PERKINS. Utica, July, 1842. |