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Calculus and analytical mechanics in the age of enlightenment. (English) Zbl 0953.01009

Variorum Collected Studies Series. 582. Brookfield, VT: Variorum. x, 308 p. (1997).
This book consists of a collection of the author’s essays on the history of calculus and analytical mechanics. Many of the essays have been reviewed in Zentralblatt MATH. Contents: I. “The calculus as algebraic analysis: some observations on mathematical analysis in the 18th century” [Arch. Hist. Exact Sci. 39, No. 4, 317-335 (1989; Zbl 0761.01004)]; II. “Joseph Louis Lagrange’s algebraic vision of the calculus” [Hist. Math. 14, 38-53 (1987; Zbl 0617.01012)]; III. “Lagrange’s analytical mathematics, its Cartesian origins and reception in Comte’s positive philosophy” [Stud. Hist. Philos. Sci. 21, 243-256 (1990)]; IV. “The origins of Euler’s variational calculus” [Arch. Hist. Exact Sci. 47, No. 2, 103-141 (1994; Zbl 0809.01007)]; V. “J. L. Lagrange’s changing approach to the foundations of the calculus of variations” [ibid. 32, 151-191 (1985; Zbl 0567.01011)]; VI. “Isoperimetric problems in the variational calculus of Euler and Lagrange” [Hist. Math. 19, No. 1, 4-23 (1992; Zbl 0743.01015)]; VIII. “D’Alembert’s principle: the original formulation and application in Jean d’Alembert’s TraitĂ© de dynamique” [Centaurus 28, No. 1, 31-61 (1985; Zbl 0569.01004); ibid., No. 2, 145-159 (1985; Zbl 0571.01019)]. IX. “J. L. Lagrange’s early contributions to the principles and methods of mechanics” [Arch. Hist. Exact Sci. 28, 197-241 (1983; Zbl 0526.01017)]; XII. “The concept of elastic stress in eighteenth-century mechanics: some examples from Euler” [in Hamiltonian dynamical systems (Cincinnati, OH, 1992). New York, NY: Springer-Verlag. IMA Vol. Math. Appl. 63, 1-14 (1995; Zbl 0833.73003)]. Items VII and X are short book reviews and item XI is a substantial article. Remarks on these follow. VII Review of John T. Cannon and S. Dostrovsky’s [The evolution of dynamics: vibration theory from 1687 to 1742. New York-Heidelberg-Berlin: Springer-Verlag (1981; Zbl 0473.73001)]. X. Review of H. Pulte’s [Das Prinzip der kleinsten Wirkung und die Kraftkonzeptionen der rationalen Mechanik. Stuttgart: Franz Steiner-Verlag (1989; Zbl 0684.01005)]. XI. “Mathematical technique and physical conception in Euler’s investigation of the elastica” [C. G. Fraser, Centaurus 34, No. 3, 211-246 (1991; Zbl 0752.01005)].

MSC:

01A50 History of mathematics in the 18th century
00B15 Collections of articles of miscellaneous specific interest
26-03 History of real functions
70-03 History of mechanics of particles and systems
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