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Home > Medicine & Health Science textbooks > Medicine: general issues > History of medicine > Elements of Conic Sections; In Three Books in Which Are Demonstrated the Principal Properties of the Parabola, Ellipse, & Hyperbola
Elements of Conic Sections; In Three Books in Which Are Demonstrated the Principal Properties of the Parabola, Ellipse, & Hyperbola

Elements of Conic Sections; In Three Books in Which Are Demonstrated the Principal Properties of the Parabola, Ellipse, & Hyperbola


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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. 1742. Excerpt: ... XIV. If upon two right lines, AB and CD, mutually bisecting each other; and cutting one another at right angles, two opposite hyperbolas, as AF, BG, be described, and upon the fame right lines two other opposite hyperbolas be described, in such a manner, that CD, the second axis os the first two, is the transverse axis of the last twoi and the transverse axis of the first two is the second axis of the last two: These four hyperbolas are called conjugate hyperbolas. PROPOSITION L Theorem I. If from any point in the periphery of an hyperbola two right lines be drawn to the foci, the excess by which the greater exceeds the smaller, is equal to the transverse axis, LE T FDE! be any hyperbola, whose foci are A and C, and its transverse axis KE, and from any point in it, as D, let the right lines, DA, DC, be drawn to the foci; I lay, the excess by which DA the greater exceeds DC the sinaller, is equal to KE the transverse axis. For let ADB be the generating rule, and BDC the generating threed, and let the small pin, with which the hyperbola was described, be at the point D; from both take DB, which is common, then will the excess by which the remainder AD exceeds the remainder DC, be equal to the excess by which the generating rule AB exceeds the generating threed BDC. The lame may be proved of any other point in the periphery of the hyperbola. And because the vertexes of the transverse axis are in the periphery of the hyperbolas, therefore the excess by which KC exceeds K A, as also by which EA exceeds EC, is equal to the excess by which the rule exceeds the generating threed, that is, the excess by which AD exceeds DC; and therefore these excesses are all equal to one another; and by adding EC to both AE and EC/then will the excess by which AC exceeds twice ...


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Product Details
  • ISBN-13: 9781150859663
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 56
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1150859660
  • Publisher Date: 01 Feb 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 118 gr


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Elements of Conic Sections; In Three Books in Which Are Demonstrated the Principal Properties of the Parabola, Ellipse, & Hyperbola
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