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**Unrolling time. Christian Huygens and the mathematization of nature.**
*(English)*
Zbl 0687.01005

Cambridge: Cambridge University Press. xi, 238 p. £30.00; $ 42.50 (1989).

Huygen’s Horologium oscillatorium, containing accounts of his invention and development of isochronous pendulum clocks together with the associated mathematical theories of evolutes, curvature and rectification, is one of the masterpieces of seventeenth century scientific literature. The author offers a detailed reconstruction of the progression of ideas that led to the composition of the work. Use has been made with beneficial results of the original manuscripts, which have been generally neglected by scholars since the achievement of Chr. Huyghen’ Oeuvres complĂ¨tes in 1950 [Zbl 0041.33902]. In the main text, Huygens’ ideas and demonstrations are described with a minimum of technical details, so that they should be accessible to the general reader. For the specialist there is an extensive collection of notes in which the flavour of Huygens’ geometrical mode of thinking has been preserved. Although Huygens did not use the differential notation of Leibniz, he was nevertheless a master of infinitesimal analysis, a fact that is generally overlooked but which the author admirably emphasizes. For example, Huygens employed indefinitely small particles of space and time, including the technique of summing infinitely many ‘line’ segments to achieve an area. Also he casually employed the infinitesimal triangle that Leibniz later adopted from Pascal as one of the fundamental ideas of his differential calculus. Several of Huygens’ manuscripts are illustrated. An extensive bibliography and a good analytical index conclude this excellent dissertation.

Reviewer: E.J.Aiton

### MSC:

01A45 | History of mathematics in the 17th century |

01-02 | Research exposition (monographs, survey articles) pertaining to history and biography |