A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 6
... . PROP . IV . If the tangent to the parabola at any point P intersect the directrix in the point Z ; then SZ will be at right angles to SP . Let P ' be a point on the parabola near to P. K M P M ' Ꮓ 2 Χ Α P 6 CONIC SECTIONS .
... . PROP . IV . If the tangent to the parabola at any point P intersect the directrix in the point Z ; then SZ will be at right angles to SP . Let P ' be a point on the parabola near to P. K M P M ' Ꮓ 2 Χ Α P 6 CONIC SECTIONS .
Page 9
... intersect in the directrix . Again draw PM , QM ' at right angles to the directrix ; then since MP , PZ = SP , PZ , each to each , and the angle MPZ = the angle SPZ , .. the angle MZP = the angle SZP , .. the angle SZP is half of the ...
... intersect in the directrix . Again draw PM , QM ' at right angles to the directrix ; then since MP , PZ = SP , PZ , each to each , and the angle MPZ = the angle SPZ , .. the angle MZP = the angle SZP , .. the angle SZP is half of the ...
Page 11
... intersect the tangent at the vertex in Y , then SY will bisect PT at right angles , and will be a mean proportional between SA and SP . Draw PN at right angles to the axis ; then since A Y is parallel to PN , .. TY : YP :: TA : AN . But ...
... intersect the tangent at the vertex in Y , then SY will bisect PT at right angles , and will be a mean proportional between SA and SP . Draw PN at right angles to the axis ; then since A Y is parallel to PN , .. TY : YP :: TA : AN . But ...
Page 16
... intersect in the diameter corresponding to that chord . DEF . A line QV , drawn parallel to the tangent at P from a point in the curve , is called the Ordinate to the diameter PV . = PROP . XV . 17. If QV be an ordinate to the diameter ...
... intersect in the diameter corresponding to that chord . DEF . A line QV , drawn parallel to the tangent at P from a point in the curve , is called the Ordinate to the diameter PV . = PROP . XV . 17. If QV be an ordinate to the diameter ...
Page 19
... intersect one another , the rectangles contained by their segments are in the ratio of the parameters of the diameters which bisect the chords . P P W S R Q V q ' Let the chords Qq , Q'q ' intersect one another in the point O. Bisect Qq ...
... intersect one another , the rectangles contained by their segments are in the ratio of the parameters of the diameters which bisect the chords . P P W S R Q V q ' Let the chords Qq , Q'q ' intersect one another in the point O. Bisect Qq ...
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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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