 | 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... | |
 | Samuel Earnshaw - Differential equations, Partial - 1881 - 602 pages
...diameter and its conjugate. t For proofs of Exx. 60S-4 see the section on curvature in Main's NBWTOK, Appendix (sec above p. 219, note). 607. The radius...point P of a parabola, if PY be the projection of 8P upon the tangent, the chord of curvature through the vertex is a third proportional to AP and 2PY.... | |
 | 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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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. 