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Synopsis
Excerpt from Newton's Interpolation Formulas
In Proposition V Newton points out the application of the above four formulas when it is required to find any intermediate term of a series, of which certain terms are given.
In Proposition VI he points out that approximate expressions for the area of a curve, of which certain ordinates are known, can be derived from the preceding for'mulas.
In the Scholium Newton gives well-known formulas for the bisection of an interval, and for finding the area, when four ordinates are known He then goes on to describe a process by which the problem of finding the approximate area when 2u+l ordinates are known can be reduced to the case of finding the area in terms of n+1 ordinates. It will be found on examination that Newton's process amounts to exactly the same thing as applying the formula for u+1 ordinates separately to the two halves of the curve of which 2n+1 ordinates are given.
The meaning of his next paragraph is not entirely clear, but Newton's idea may have been to simplify the process of finding the approximate area by taking the sums of the ordinates in two's or three's, &c., using these sums as new ordinates and passing through their extremities a new curve, the area of which, taken between suitable limits, would approximate to the area required.
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- PublisherForgotten Books
- Publication date2020
- ISBN 10 1332169031
- ISBN 13 9781332169030
- BindingPaperback
- LanguageEnglish
- Number of pages60
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Newton's Interpolation Formulas (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book presents the comprehensive work of 17th-century scientist and mathematician Isaac Newton on interpolation by methods of finite differences. These methods involve the use of the differences between values in a series to find intermediate terms, which has applications in constructing tables and solving problems related to areas and volumes. The book begins with an explanation of the fundamental formula of finite differences, which allows any value in a series to be expressed in terms of the initial value and its leading differences. The author provides detailed examples and applications of this formula and discusses its significance in the history of mathematics. Overall, this book offers a valuable resource for those interested in the development of finite difference methods and their applications in various fields. 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. Seller Inventory # 9781332169030_0
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Newton's Interpolation Formulas Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332169030
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Newton's Interpolation Formulas Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332169030
Quantity: 15 available