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Home > History and Archaeology > History > A Geometrical Treatise of Conic Sections. to Which Is Added, a Treatise on the Primary Properties of Conchoids, the Cissoid [&C.].
A Geometrical Treatise of Conic Sections. to Which Is Added, a Treatise on the Primary Properties of Conchoids, the Cissoid [&C.].

A Geometrical Treatise of Conic Sections. to Which Is Added, a Treatise on the Primary Properties of Conchoids, the Cissoid [&C.].


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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. 1802. Excerpt: ... bOOK lar to any rectilineal sigure inscribed in the other f and IV. two conic sections are also called Similar, if a segment 'can be taken of one of them similar to a segment of the other.. III. If a straight line touch two conic sections in the fame point, the two sections are faid to touch one another in the fame point. IV. If a circle so touch a conic section in any point, that no other circle, touching it in the fame point, can pass between it and the section, on either side of the point of contact, it is faid to have the fame Curvature with the Seclion in the point of contacl; or it is faid to be the Osculating Circle for that point. PROP. I. Any two parabolas are similar to one another; and the similar reclilineal figures inscribed in them are to one another as the squares of the parameters of the axes. fig. 117. Let A B c, a b c be two parabolas, of which B E, b e x 18. are the axes, and p, p their parameters; and let Abc a be any rectilineal sigure inscribed in the one parabola; a rectilineal sigure similar to Abcd may be inscribed in the other, and the similar rectilineal sigures inscribed in them are to one another as p2 to p. For draw from b, the vertex, the straight line ha to the curve, so that the angle eb a may be equal to the angle E B A. Draw bc to the curve, so that the angle e be may be equal to the angle E B C. Draw B D, and draw b d to the curve, so that the angle e b d may be equal to the angle Ebd; and draw a d. Let A p be an ordinate to the axis B E, and let a e be an ordinate to the axis b e. Then, as the angles at E and e are right angles, the triangles A E E, a b e are equiangular, BoOK and (4. vi.)-& n: -& A:: b e: e a. But, by the sixth 1V Desinition Book III. Be: ea:: ea: p; and b e: e a:: e a: p. We have therefore the two fo


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Product Details
  • ISBN-13: 9781235728761
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 68
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1235728765
  • Publisher Date: 01 Feb 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 141 gr

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A Geometrical Treatise of Conic Sections. to Which Is Added, a Treatise on the Primary Properties of Conchoids, the Cissoid [&C.].
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