Abstract
During his youth, Newton had carefully studied the geometric calculus of Descartes, which served him as a source of inspiration for the development of the “calculus of fluxions”, his version of the differential calculus. This partially explains why he undertook to classify the curves of degree three according to various species, in analogy with the classification of those of degree two, the conic sections, into ellipses, parabolas, hyperbolas or pairs of lines. The following is the first paragraph of the chapter containing this classification from his work [140], published in 1711:
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E. Brieskorn, H. Knörrer, Plane Algebraic Curves (Birkhäuser Verlag, Boston, 1986). Translation by J. Stillwell of the first German edition of 1981
I. Newton, Analysis per quantitatum series, fluxiones, ac differentias; cum enumeratione linearum tertii ordinis, ed. by W. Jones, London (1711). English translation: Enumeration of lines of the third order, generation of curves by shadows, organic description of curves, and construction of equations by curves. transl. ed. by C.R.M. Talbot, H.G. Bohn, London, 1860
J. Stillwell, Mathematics and its History, 2nd edn. (Springer, New York, 2002)
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Popescu-Pampu, P. (2016). Newton and the Classification 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_3
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DOI: https://doi.org/10.1007/978-3-319-42312-8_3
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