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James Stirling. ‘This about series and such things.’ A discussion of the later work of the Scottish mathematician James Stirling (1692-1770), based mainly on material from his notebooks, one of which is inscribed with the above title. (English) Zbl 0701.01003

Edinburgh: Scottish Academic Press. viii, 208 p. £25.00 (1988).
This interesting book, well furnished with instructive notes, a biographical sketch, a brief description and dating on the Stirling- notebooks often mentioned in the discussions on problems history of the 18th century, represents a valuable contribution with its extracts and some for the first time printed Latin texts from Stirling manuscripts. In connexion with the development of transformation of series concerning close-fitting and rapid (number of terms) numerical evaluation, the troublesome work of selecting and editing should be highly appreciated: with the notebook-texts (Appendix D, Chapter 1-4, esp. 1.3), the Methodus Differentialis Newtoniana of 1719 and the Methodus Differentialis of 1730, the known Stirling material in this field is now accessible. Stirling’s published paper on gravitation and the figure of the earth (1735/36) is now completed with far extended research material from the 1730s/1740s notebooks (Chapter 5). The communication of Stirling in this area (Royal Society 1733) is given in Appendix B. Extracts and explications on Stirling’s trigonometric and geometric work - not so far reaching as the above mentioned contributions - are given in chapter 3. An approximate Stirling construction for the ellipse by means of circular arcs is remarkable and the author elaborated a Basic program for ellipse- approximation (Appendix C). An English translation (Chapter 6) of Euler letters (1736 and 1738) and of a letter from Robert Simpson (1740) completes this book as a source for scientists interested in the development of mathematical methods in the 18th century.
Reviewer: H.Krieger

MSC:

01A50 History of mathematics in the 18th century
01A70 Biographies, obituaries, personalia, bibliographies
26-03 History of real functions

Biographic References:

Stirling, James
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