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A Source Book in Mathematics, 1200-1800 (Princeton Legacy Library) Paperback – September 21, 1986

by D. J. Struik (Editor)

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These selected mathematical writings cover the years when the foundations were laid for the theory of numbers, analytic geometry, and the calculus.

Originally published in 1986.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

A Source Book in Mathematics, 1200-1800 (Princeton Legacy Library)

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Product Details

Series: Princeton Legacy Library
Paperback: 448 pages
Publisher: Princeton University Press (September 21, 1986)
Language: English
ISBN-10: 0691023972
ISBN-13: 978-0691023977
Product Dimensions: 1.2 x 9.5 x 6.2 inches
Shipping Weight: 1.8 pounds
Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
Amazon Best Sellers Rank: #1,624,679 in Books (See Top 100 in Books)
- #1268 in Books > Science & Math > Mathematics > History

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14 of 17 people found the following review helpful

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By Viktor Blasjo on May 7, 2010

Format: Paperback

This is an excellent source book. One of the many benefits of reading original sources is that it frees us from the often dogmatic single-mindedness of modern textbooks. I would like to illustrate this by looking at some excerpts from this book on the topic of power series. The modern approach to power series representations of functions is of course to find the coefficients by repeated differentiation. However, history teaches us that this approach is backwards and obscures some important insights.

The first published derivation of the so-called general Maclaurin series (by Taylor in 1715, excerpted here on pp. 329-333) was based on entirely different ideas than that of repeated differentiation, namely Newton's forward-difference formula. It may be summarised as follows. An infinite polynomial A+Bx+Cx^2+Dx^3+... has infinite degrees of freedom. Therefore we expect to be able to construct an infinite polynomial passing through an infinite number of given points, just as a parabola of the form y=Ax^2+Bx+C can be constructed going through essentially any three points, but not any four, owing to its having three coefficients. Newton's forward-difference formula constructs such a polynomial, namely a polynomial which takes the same values as a given function at the x-values 0,b,2b,3b,.... Taylor's derivation of his series consists in letting b go to zero is this formula. The nowadays more popular method of finding the series by repeated differentiation was not published until decades later by Maclaurin in 1742 (pp. 338-340). Thus history alerts us to the fact that the blind-computation approach favoured today robs us of an opportunity to "see" the infinitely many degrees of freedom of a power series in an illuminating way that is based on open-minded reasoning.Read more ›

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