A first course in projective geometry . Fig. 64a. Fig, 646. The truth of the latter statement is manifest on examiningFig. 56a. For any pair of conjugate lines through C withrespect to the circle will project into conjugate diameters ofthe hyperbola. Drawing any line through C, the conjugateline is the line joining C to its pole; and this pole is insidethe circle if the line is outside, and vice versa. It followsthat one of the pair of conjugate lines through C cuts thecircle, while the other does not. Accordingly, if a diameterof the hyperbola be drawn cutting the curve, the conjugatediameter
A first course in projective geometry . Fig. 64a. Fig, 646. The truth of the latter statement is manifest on examiningFig. 56a. For any pair of conjugate lines through C withrespect to the circle will project into conjugate diameters ofthe hyperbola. Drawing any line through C, the conjugateline is the line joining C to its pole; and this pole is insidethe circle if the line is outside, and vice versa. It followsthat one of the pair of conjugate lines through C cuts thecircle, while the other does not. Accordingly, if a diameterof the hyperbola be drawn cutting the curve, the conjugatediameter will not cut the curve, and therefore cannot be saidto have any definite length. It is convenient, nevertheless, to measure off a real lengthCD along this diameter, such that ^^? ^-^^ (Fig. 646). PV. VP CP2 128 PROJECTIVE GEOMETRY CD thus defined will then, in the case of the hsrperbola, in future be called the length of the semi-diameter conjugate to can now add a further corollary to >^ 2, viz. that if twotangents be draw
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