A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 21
... circle be described touching the parabola at P and cutting it in Q ; then when the point is made to approach indefinitely near to P , the circle is called the Circle of Curvature at the point P. ( See fig . Prop . XIX . ) PROP . XIX ...
... circle be described touching the parabola at P and cutting it in Q ; then when the point is made to approach indefinitely near to P , the circle is called the Circle of Curvature at the point P. ( See fig . Prop . XIX . ) PROP . XIX ...
Page 24
... circle described about the triangle BAC is equal to 5 AS . ( See fig . Prop . III . ) 2. If from the point G , GK be drawn at right angles to SP , then PK = 2 AS . ( See fig . Prop . III . ) 3. If the triangle SPG is equilateral , then ...
... circle described about the triangle BAC is equal to 5 AS . ( See fig . Prop . III . ) 2. If from the point G , GK be drawn at right angles to SP , then PK = 2 AS . ( See fig . Prop . III . ) 3. If the triangle SPG is equilateral , then ...
Page 26
... circle described about the triangle OQQ . Prove that the circle described about the triangle QEQ ' will pass through the focus . ( See fig . Prop . XIII . ) 22. PSP is any focal chord of a parabola . Prove that AP , Ap will meet the ...
... circle described about the triangle OQQ . Prove that the circle described about the triangle QEQ ' will pass through the focus . ( See fig . Prop . XIII . ) 22. PSP is any focal chord of a parabola . Prove that AP , Ap will meet the ...
Page 27
... circle is described cutting the parabola again in two points . If these points be joined the portion of the axis between the two chords is equal to the latus rectum . 32. If OQ , OQ ' be a pair of tangents to a parabola , and the chord ...
... circle is described cutting the parabola again in two points . If these points be joined the portion of the axis between the two chords is equal to the latus rectum . 32. If OQ , OQ ' be a pair of tangents to a parabola , and the chord ...
Page 28
... circle of curvature at P. 41. If a circle described upon the chord of a parabola as diameter meet the directrix it also touches it , and all chords for which this is possible intersect in a point . 42. If a parabola roll upon another ...
... circle of curvature at P. 41. If a circle described upon the chord of a parabola as diameter meet the directrix it also touches it , and all chords for which this is possible intersect in a point . 42. If a parabola roll upon another ...
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Common terms and phrases
AC² angle ZSP auxiliary circle BC² BERNARD DRAKE bisects the angle CA² Cambridge CD be conjugate CD² centre circle be described circle described circle of curvature cloth CO.'S PUBLICATIONS cone Conic Sections conjugate diameters conjugate hyperbola CP² Crown 8vo curve cutting plane drawn at right drawn parallel ellipse Euclid Fcap Fellow of St Fellow of Trinity focal chord focus intersect John's College join SP late Fellow latus rectum let the tangent M.A. Fellow MACMILLAN & CO.'S major axis mean proportional meet CD meet the axis meet the directrix meet the ellipse meeting the asymptotes pair of tangents parabola parallelogram perpendicular PN² produced to meet Prop prove QV² radius right angles Second Edition triangle Trinity College University of Cambridge vertex
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