A first course in projective geometry . Fio. 65. Let QVQ, qi-q (Fig 65) be any two ordinates of the diameterPV. Then, since PV meets the conic again at infinitj^, Newtonstheorem erives & QV2 my^ Ai V^Trrr-T-.— = — . Also = unity. ) P^ 1700 ^ . QV2 qv- . QV2 ^ ^ • • -^^^ = ^ • • -1^^ = P? PV This constant is of course a length, and it will be seenshortly how to determine it. CARNOTS THEOREM 129 § 4. The Cartesian Equations of the different speciesof Conic referred to their Principal Axes. Take the particular cases of Theorems I. and II. of § 3, whenthe diameters are the a
A first course in projective geometry . Fio. 65. Let QVQ, qi-q (Fig 65) be any two ordinates of the diameterPV. Then, since PV meets the conic again at infinitj^, Newtonstheorem erives & QV2 my^ Ai V^Trrr-T-.— = — . Also = unity. ) P^ 1700 ^ . QV2 qv- . QV2 ^ ^ • • -^^^ = ^ • • -1^^ = P? PV This constant is of course a length, and it will be seenshortly how to determine it. CARNOTS THEOREM 129 § 4. The Cartesian Equations of the different speciesof Conic referred to their Principal Axes. Take the particular cases of Theorems I. and II. of § 3, whenthe diameters are the axes of the curves. Let PNP (Fig. 66) be the double ordinate of ACA, thetransverse or major axis of a central conic. Then PNP isperpendicular to ACA. A and A are the vertices of the
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