Note on the Treatment of Conic Sections and Conicoids By Pure Geometry

Extract

The object of the following note is to derive Pascal’s theorem and the Anharmonic and Harmonic properties of Conic Sections directly from the focus and directrix definition by the early introduction of an extended form of Carnot’s theorem, viz. “the product of the ratios in which the sides of a closed polygon, taken in order, are cut by a conic = +1.” When the above have been demonstrated the simpler properties are known to be easily deducible. Subsequently the treatment of Conicoids by Pure Geometry is introduced by means of the same theorem.