Abstract
In the following extract of [17], Jakob Bernoulli , the brother of Johann, about whom we wrote in Chap. 4, analyzed various methods of construction of “mechanical” or “transcendental” curves, that is, curves which are not “algebraic” (defined by a polynomial equation). Those methods created a common framework for Descartes’ algebraic curves and for the curves furnished by the differential and integral calculus:
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Notes
- 1.
I found this extract in the paper [171, Sect. 2] of Smadja, which is my main source of information for the content of this chapter.
References
J. Bernoulli, Constructio Curvae Accesus and Recessus aequabilis, ope rectificationis Curvae cujusdam Algebraicae, addenda nuperae Solutioni mensis Junii. Acta Eruditorum, Sept. 1694. Republished in Die Streitschriften von Jacob und Johann Bernoulli, ed. by H.H. Goldstine (Birkhäuser, Boston, 1991). Jac. Op. LX, pp. 188–192
J. Bernoulli, Constructio facilis Curvae Recessus aequabilis a puncto dato, per rectificationem Curvae Algebraicae. Acta Eruditorum, Oct. 1694. Republished in Opera Omnia Johann Bernoulli, vol. I, ed. by J.E. Hofmann, G. Olms (Hildesheim, 1968). XIX, pp. 119–122
A.I. Smadja, La lemniscate de Fagnano et la multiplication complexe (2004). halshs-00456361
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Popescu-Pampu, P. (2016). Jakob Bernoulli and the Construction of Curves. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_5
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