Excerpt from Researches Respecting the Imaginary Roots of Numerical Equations: Being a Continuation of Newton's Investigations on That Subject, and Forming an Appendix to the Theory and Solution of Equations of the Higher Orders
It is further shown in the note to this article that two imaginary roots may be indicated in an interval though the real part of the imaginary pair lie wholly without that interval.
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Excerpt from Researches Respecting the Imaginary Roots of Numerical Equations: Being a Continuation of Newton's Investigations on That Subject, and Forming an Appendix to the Theory and Solution of Equations of the Higher Orders
I have called the Researches to which these few pages are devoted a continuation of those of Newton on the subject of the Imaginary Roots of Equations; because, as I have shown in the second chapter, a principle first announced by that illustrious analyst in his Arithmetica Universalis, is competent to furnish all the more important of the conclusions to which I have arrived.
This principle was delivered by Newton without demonstration; and although several attempts have, at different times been made to establish its truth, I believe that no satisfactory proof of its accuracy has till now been offered.
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.
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Librería: Forgotten Books, London, Reino Unido
Paperback. Condición: New. Print on Demand. This book extends and develops the numerical process by which an equation is analyzed and solved. Specifically, it explores the analysis of imaginary and real roots of numerical equations. After introducing conditions for imaginary roots, the author demonstrates principles that enable a demonstration of Newton's rule for determining the presence of imaginary roots. Several criteria for determining imaginary roots from the three leading and three final coefficients of an equation are provided, along with general rules for applying those criteria to any intermediate interval. These criteria, among the most important of the book's conclusions, greatly enhance both the efficiency and effectiveness of the numerical equation-solving process. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781332033102_0
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Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de America
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332033102
Cantidad disponible: 15 disponibles
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332033102
Cantidad disponible: 15 disponibles
Librería: Buchpark, Trebbin, Alemania
Condición: Hervorragend. Zustand: Hervorragend | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar. Nº de ref. del artículo: 26039335/1
Cantidad disponible: 1 disponibles