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Conics in Greek Geometry: Apollonius, Harmonic Division, and Later Greek Geometry

In: Collineations and Conic Sections

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  • Christopher Baltus

    (State University of New York at Oswego, Department of Mathematics)

Abstract

Why would Greek geometers study the conic sections? We have no direct answer to that question in any ancient text that has survived. It was not, generally, for the scientific applications of conic sections. The earliest practical applications we know of are in sundials, with medieval Arabic scientists. Only in the early modern period, with Galileo (1564–1642), was the parabolic path of bodies in motion recognized. And only with Kepler (1571–1630) were the orbits of planets seen to be ellipses. An exception to this picture is a short work, On Burning Mirrors, whose author, Diocles, Diocles was active about 200 BC. It was, it seems, the first to give the focus of a parabola, with the property that a surface formed by revolving a parabola about its axis would reflect the sun’s rays to the focus of that parabola. But it did not spark work in applications; there is no surviving mention of On Burning Mirrors until the sixth century AD, by Eutocius of Askalon, and, again, in Islamic work of the eleventh century.

Suggested Citation

  • Christopher Baltus, 2020. "Conics in Greek Geometry: Apollonius, Harmonic Division, and Later Greek Geometry," Springer Books, in: Collineations and Conic Sections, chapter 0, pages 45-57, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46287-1_4
    DOI: 10.1007/978-3-030-46287-1_4
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