A Historical Survey of Algebraic Methods of Approximating the Roots of Numerical Higher Equations Up to the Year 1819 (Classic Reprint) - Couverture souple

Nordgaard, Martin Andrew

Couverture souple

ISBN 10 : 133338887X ISBN 13 : 9781333388874

Editeur : Forgotten Books, 2018

Synopsis

The digital edition of all books may be viewed on our website before purchase. Excerpt from A Historical Survey of Algebraic Methods of Approximating the Roots of Numerical Higher Equations Up to the Year 1819



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A propos du livre

Présentation de l'éditeur

The feature of mathematics which we may call scientific approximation did not receive the recognition among the ancient Greek geometers that has been accorded it by mathematicians of modern times. Since their work in pure mathematics was based on geometry, the Greek scholars evaluated irrational roots as readily as rational roots by the construction of lines. But when it came to applied mathematics, numerical approximation was often not only desirable but absolutely necessary; and so we have some remarkably close approximations by Archimedes (c. 225 B. c.) in his work in mechanics, by Heron of Alexandria {c. 200 A. D.) in his work as surveyor, and by Theon of Alexandria (c. 375 a. d.) in his astronomical computations. Archimedes even used numerical approximations in the domain of pure geometry in his Measurement of the Circle. On the whole, however, the Greek mind did not take to this form of mathematical activity. The Hindus and the A rabs used approximation methods more extensively than the Greeks, and notable work was done by Brahmagupta (c. 510 a. d.), Bhaskara (c. 1150 a. d.), and an unknown Arab computer mentioned by Chelebi. However, it was during the Renaissance, when the newly discovered general formula for solving the cubic was found to be inoperative for the irreducible case, that approximation methods became a vital problem, and for two centuries the keenest mathematical minds worked to find smooth, effective methods for approximating cube and higher roots. The purpose of this research is to trace the history of the different methods of approximating roots of numerical higher equations that were used up to 1819, the date of the publication of Horner smethod; we purpose to trace their early beginnings in finding the roots of numbers and in solving incomplete equations, and to watch their growth into systematically developed general methods for sol
(Typographical errors above are due to OCR software and don't occur in the book.)

Présentation de l'éditeur

Historical Survey of Algebraic Methods of Approximating the Roots of Numerical Higher Equations up to theY ear 1819 By Martin Andrew Nordgaard Assistant Professor of Mathematics Grinnell College, Grinnell, Iowa Submitted in Partial Fulfillment of the Requirements for theD egree of Doctor of Philosophy in the Faculty of Philosophy.
(Typographical errors above are due to OCR software and don't occur in the book.)

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Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 133338887X
• ISBN 13: 9781333388874
• Reliure: Broché
• Nombre de pages: 79
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