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Conic Sections in Early Modern Europe. Second Part: Philippe de la Hire on Conics

In: Collineations and Conic Sections

Author

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  • Christopher Baltus

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

Abstract

After the preliminary work on circles, La Hire moved to the conic sections. He defined them as had Apollonius: the section of a conic surface by a plane is a conic section. But he immediately moved beyond Apollonius, as had Desargues, by claiming that properties established for the base circle apply to the conic section. La Hire wrote in Philippe de La Hire (Nouvelle Méthode en Géométrie pour les Sections des Superficies coniques et Cylindriques, Paris, 1673, p 15), following the first seventeen lemmas, “All that follows is a simple application of these lemmas …in all the conic and cylindrical sections.” The harmonic relation is preserved in a projection, and the projection he has in mind is of a base circle of a cone, in a base plane, and lines in that base plane associated with that circle, onto the plane that cuts the cone in the conic section. La Hire describes the projection of a line eg in the base plane: “cut at points e, f, p, g in three harmonic parts. …the lines drawn joining these points of division to the vertex A [of the cone] will meet line EG on the slicing plane in points E, F, P, G and by Lemma 5 or 6 it will be cut in these points E, F, P, G harmonically in 3 parts. …”

Suggested Citation

  • Christopher Baltus, 2020. "Conic Sections in Early Modern Europe. Second Part: Philippe de la Hire on Conics," Springer Books, in: Collineations and Conic Sections, chapter 0, pages 71-86, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46287-1_6
    DOI: 10.1007/978-3-030-46287-1_6
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