A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections

A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections

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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. 1885 edition. Excerpt: ...side of a fixed line NN', and through S any line be drawn meeting the circle in P, and MN in R; then if RO be joined, meeting a parallel to OP, drawn through S in, the locus of j is an ellipse.--(boscovich.) 7. Prove that the radius of the Boscovich Circle, divided by its distance from the fixed lkie, is equal to the eccentricity. 8. CB is a fixed diameter of a given circle, A a fixed point in CB produced. Through A draw any line meeting the circle in D and E. Join CD and produce to F, making CF= AE the locus of F is the ellipse 120. To express lhe co-ordinales Q" a poinl P on an ellzpse ABA'B' zn lerfns ofa single oarlahle. Let AA', RB' be the transverse and the conjugate axes of the ellipse upon AA' as diame-. ter; describe the circle AP'A. Let P be any point of the ellipse, MP its ordinate; produce MP to meet the circle AP'A' in P. join 0P', and denote the angle N M MOP' by di; then, since OM: oe, OP' = a, we have x = a cos gb. This value, substituted in the equation (361) of the ellipse, gives _y = 6 sin 15: therefore the co-ordinates of P are a cos f, 6 sin gb. DEE.-The czrcle descrzhed on AA' as dzamefer zs called the AUXILIARY czrcle of 1'he ellzpse, and 1'he angle 15 ihe ECCENTRIC angle. The term eccentric has been 'taken from Astronomy; the angle rp in that science being called the eccentric anomaly. Hence we have the following theorem: -The locus of a point P which divides an ordinate of a semicircle in a given ratio is an ellipse; or again, D' from all lhe polnfs en ihe czrcunzjhrence of a circle in one plane perpendzculars 6e lei fall on anolher plane, inclined lo lhe _/brmer al any angle, lhe locus q" lhezh' feel zs an ellzpse (called THE...show more

Product details

  • Paperback | 76 pages
  • 189 x 246 x 4mm | 154g
  • General Books
  • Rarebooksclub.com
  • United Kingdom
  • English
  • black & white illustrations
  • 1236987454
  • 9781236987457