 | Mathematics - 1871 - 124 pages
...by CW MBRRIFIELD, FES) — Prove that the radius of curvature at any point of a parabola is double the portion of the normal intercepted between the curve and the directrix. Solution by 3. MBRKIFIELD, PH.D., FRAS ; the Rev. JL Киснш, MA ; and others. Let P be any point... | |
 | W. J. C. Miller - Mathematics - 1871 - 136 pages
...by CW MEHRIFIEI/D, FRS) — Prove that the radius of curvature at any point of a parabola is double the portion of the normal intercepted between the curve and the directrix. Solution by tfie PROPOSER. Assuming that the focal distance is equal to the (^ perpendicular on the... | |
 | Charles Taylor - Mathematics - 1881 - 488 pages
...diameter and iis conjugate. J For proofs of Exx. 603-4 see the section on curvature in Main 'a NEWTO.V, Appendix (sec above p. 219, note). 607. The radius...point P of a parabola, if PY be the projection of SP upon the tangent, the chord of curvature through the vertex is a third proportional to AP and 2PY.... | |
 | Charles Taylor - Mathematics - 1881 - 512 pages
...curvature at any point of a parabola is double of the portion of the normal intercepted between thecurve and the directrix. 608. At any point of a parabola...latus rectum and the parameter of the diameter to tho point. 609. At any point P of a parabola, if PY be the projection of SP upon the tangent, the chord... | |
 | Charles Taylor - Conic sections - 1883 - 164 pages
...parabola, PR subtends a right angle at S. 358. The radius of curvature at any point of a parabola is double the portion of the normal intercepted between the curve and the directrix. 359. Shew that the centre of curvature may be regarded as the point of ultimate intersection of two... | |
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Appendix (sec above p. 219, note). 607. The radius of curvature at any point of a parabola is double of the portion of the normal intercepted between the curve and the directrix. 608. At any point of a parabola the intercept made by the circle of curvature... 