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Analytic Geometry for Colleges, Universities, and Technical Schools

Analytic Geometry for Colleges, Universities, and Technical Schools


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 Excerpt: ...(', if), Fig. 43, be the extremities Substituting this value in (1) and multiplying through by 4, we have area OP"TR' X 4 = 4 ab; i.e., area CTC'T' = area BB'H'H. 99. To show that the ordinate of any point on the ellipse is to the ordinate of the corresponding point on the circumscribing circle as the semi-conjugate axis of the ellipse is to the semitransverse axis. Let DP', DP" be the ordinates of the corresponding points P (', y') and P" x," y"). Since P' (x!, y') is on the ellipse, we have =-x'2). Since P" (x," y") is on the circle whose radius is a, we have y"2 = a-x" Dividing these equations, member by member, we have Similarly we may prove that xx: xt:: a: b, where xi is the abscissa of any point on the ellipse, and x2 is the corresponding abscissa of a point on the inscribed circle. 100. The principles of the preceding article give us a method of describing the ellipse by points when the axes are given. From O, Fig. 45, as a centre with radii equal to the semiaxes OA, OB describe the circles A'RA, BCB'. Draw any radius OR of the larger circle, cutting the smaller circle in M; draw MN to OA', cutting the ordinate let fall from R in N; N is a point of the ellipse. Since MN is parallel to the base of the triangle RD'O, we have D'N: D'R:: OM: OR; i. e., if: y" b: a; hence, the construction. 103. To show that the area of the ellipse is to the area of the circumscribing circle as the semi-minor axis of the ellipse is to its semi-major axis. Inscribe in the ellipse any polygon ARR1R3K8E4A', and from its vertices draw the ordinates RD, RlD1) etc., producing them upward to meet the circle in P, Px, Pa etc. Joining these points we form the inscribed polygon APP1P2P8P4A' in the circle. Let (x, y0), (x', yx), ...


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Product Details
  • ISBN-13: 9781153275460
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 46
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1153275465
  • Publisher Date: 11 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 100 gr


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