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Elementary Co-Ordinate Geometry for Collegiate Use and Private Study

Elementary Co-Ordinate Geometry for Collegiate Use and Private Study


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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1886 edition. Excerpt: ...poles and perpoles of all RLs. through the centre lie on the RL. at 00. 114. The foci of the involutions on the axes are called foci of the curve; hence a centric conic has four foci: two real, two imaginary. They enjoy important properties. The central distance, ae, of a real focus is called the linear eccentricity of the conic; e itself is the eccentricity proper. It is the ratio of the central distance of a focus to the half-axis 0n which the focus lies. Now in case of the imaginary focus the central distance of the focus is imaginary in both and H; but the half-axis is real in and imaginary in H; hence their quotient is imaginary in but real in H; i.e., one eccentricity is real, one imarjinary in . both are real in //. The polar of a focus is called a Directrix. Suppose the real foci (ae, O), (--ae, O) on the X-axis; the directrices are By Art. 113 a focus is a double point in which have fallen together pole and perpole of a certain RL., the directrix. Asa pole glides along this directrix, both its polar and its perpolar turn about the focus always _ L to each other. Call the tract from a focus to a point a focal radius of that point, and any RL. through a focus a focal chord. From any point P of the directrix draw a chord cutting the conic at 7 and I'; to the pole Q of this chord, and from the focus F, draw FQ cutting the chord at P. By Art. 71, since the polar of P is FQ, P, 1', P, I form an harmonic range; hence FPFPI is an harmonic pencil. But FP is clearly the perpolar of P, as this perpolar must go through P and through F. Hence FP and FP are-L; hence they halve the s of FI and FV (Art, 41). Hence, the focal radius of the pole of a chord halves the 2 at the focus subtended by the chord....


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Product Details
  • ISBN-13: 9781130735147
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 62
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1130735141
  • Publisher Date: 13 Sep 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 127 gr


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