This returns to Poncelet’s Traité and looks in more detail at his theory of lines and conics ‘meeting’. It draws on Apollonius’s theory of conjugate diameters of a conic and of a conic auxiliary to a given one (with respect to a pair of conjugate diameters). An early version of Poncelet’s book met with a mixed reception: it was given a critical yet fair review by Cauchy, who objected precisely to Poncelet’s implausible ideas. Poncelet, however, rejected the algebraic remedy offered by Cauchy, and the final book retains those ideas. This shows the strength of Poncelet’s belief in the importance of simple general ideas in geometry which could match those of algebra.
KeywordsDescriptive Geometry Projective Transformation Conic Section Creative Mathematician Polar Line
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