A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 21
... 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 . The chord of the ...
... 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 . The chord of the ...
Page 22
... X and the tangent at Pin R. Also draw QV parallel to PR , and PW parallel to the axis ; then since RP touches the circle at P , .. RQ.RX = PR . ( Euclid , III . 36. ) Τ R ૨ Y P G X W U But PR - QV2 = 4 SP : PV , 22 CONIC SECTIONS .
... X and the tangent at Pin R. Also draw QV parallel to PR , and PW parallel to the axis ; then since RP touches the circle at P , .. RQ.RX = PR . ( Euclid , III . 36. ) Τ R ૨ Y P G X W U But PR - QV2 = 4 SP : PV , 22 CONIC SECTIONS .
Page 25
... touching the parabola , the angle between this line and the line to the focus from the same point is constant . 12. A circle and parabola have the same vertex and axis . BA'C is the double ordinate of the parabola which touches the ...
... touching the parabola , the angle between this line and the line to the focus from the same point is constant . 12. A circle and parabola have the same vertex and axis . BA'C is the double ordinate of the parabola which touches the ...
Page 28
... touches it , and all chords for which this is possible intersect in a point . 42. If a parabola roll upon another equal parabola , the vertices originally coinciding , the focus traces out the directrix . 43. The circle of curvature at ...
... touches it , and all chords for which this is possible intersect in a point . 42. If a parabola roll upon another equal parabola , the vertices originally coinciding , the focus traces out the directrix . 43. The circle of curvature at ...
Page 58
... touching the ellipse 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. PROP . XXVI . If PH be the chord of the circle of ...
... touching the ellipse 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. PROP . XXVI . If PH be the chord of the circle of ...
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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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