Abstract
Descartes lived from 1628 to 1649 in The Netherlands and his stay had quite an impact there. The Dutchman Frans van Schooten junior translated Descartes’ Geometry into Latin. Van Schooten also wrote a book on mechanisms to draw conic sections. His pupil and friend, the Dutch statesman Johan de Witt, wrote a book on conic sections on the basis of Descartes’ ideas. Through Van Schooten’s translation Newton got to know Descartes work. Thinking about curves in terms of their kinematical generation led Newton to his calculus. Motion also played a role in Leibniz work on the calculus. We also briefly discuss the work of Huygens and Newton on circular motion and Huygens calculations on gear trains.
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Notes
- 1.
Bos (2001), pp. 340–341.
- 2.
Witt (1997), pp. 40–41.
- 3.
- 4.
Westfall (1980), p. 107.
- 5.
Whiteside (1967), p. 299.
- 6.
Huygens (1929), pp. 255–301. Mahoney published a translation. See: https://www.princeton.edu/~hos/mike/texts/huygens/centriforce/huyforce.htm.
- 7.
The parabola y = x2/2 is for small x an excellent approximation of the semicircle y = 1 − √(1 − x2).
- 8.
The translation is Mahoney’s.
- 9.
Huygens (1703), pp. 431–460. Also in Huygens (1944). Huygens text is not easy to read. For an accessible presentation of Huygens calculations see Rockett and Szüsz (1992), pp. 59–60.
- 10.
Fowler (1994), p. 736.
- 11.
Quoted by Blåsjö (2016), pp. 17–18.
- 12.
Blåsjö (2016), pp. 64–65.
- 13.
Bos (1988), p. 9.
- 14.
The logarithmica corresponds to y = ax. It would take some time before this notation was accepted. The inverse function is x = lny/lna = ∫(1/y)dy/lna.
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Koetsier, T. (2024). De Witt, van Schooten, Newton and Huygens. In: A History of Kinematics from Zeno to Einstein. History of Mechanism and Machine Science, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-031-39872-8_8
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DOI: https://doi.org/10.1007/978-3-031-39872-8_8
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