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On Kepler’s system of conics in Astronomiae pars optica. (English) Zbl 1355.01011

In 1604, Kepler published his “non-cone based” system of conics within his Astronomiae pars optica (Optical part of astronomy). It can be seen as the first attempt to unify the theory of conic sections. Kepler introduced the expression “focus” applying the principle of analogy. The main aim of the paper under review is to explain for the first time how Kepler may have conceived his plane system of conics. Two constructions are presented based on an orthogonal projection and on the theory of shadows, respectively. The author adds mathematical foundations to these constructions and provides a detailed analysis of the behavior of conics in Kepler’s system. Finally, he draws some conclusions showing how Kepler made analogy a tool for discovering new results. Unfortunately, especially the Latin titles of works are often misprinted and not at all reliable. Read: commentaries (twice), quatuor, Richtscheyt, Krafft, paralipomena, physics coelestis…de motibus stellae Martis, doliorum, Crepusculis etc.

MSC:

01A45 History of mathematics in the 17th century
78-03 History of optics and electromagnetic theory

Biographic References:

Kepler, Johannes
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References:

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