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The Mathematical Content of the Rough Draft on Conics

In: The Geometrical Work of Girard Desargues

Author

Listed:
  • J. V. Field

    (Science Museum)

  • J. J. Gray

    (The Open University)

Abstract

Desargues began with the remark that lines will be supposed to contain a point at infinity, which may be reached by travelling in either direction along the line. This enabled him to treat pencils of parallel and intersecting lines on a par; a pencil of parallel lines being regarded as a pencil of lines intersecting at a point at infinity. The use of points at infinity also simplified his treatment of points in involution, as we shall see. He then unleased a plethora of botanical names for simple configurations of points and lines which, taken together, only serve to obscure the text. Of those terms, we need only say that those which connote line segments, such as trunk, branch, shoot and limb, may be taken to mean ‘line’ or ‘line segment’, whereas those which suggest points, such as knot, butt, post and stump, mean ‘point’. Then he reached his first useful term, the tree.

Suggested Citation

  • J. V. Field & J. J. Gray, 1987. "The Mathematical Content of the Rough Draft on Conics," Springer Books, in: The Geometrical Work of Girard Desargues, chapter 0, pages 47-59, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8692-6_4
    DOI: 10.1007/978-1-4613-8692-6_4
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