A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 7
William Henry Drew. K M P M ' Ꮓ 2 Χ Α P R Draw the chord PP ' , and produce it to meet the directrix in Z ; join SZ . Draw PM , P'M ' at right angles to the directrix ; join SP , SP ; and produce PS to meet the parabola in Q. Then ...
William Henry Drew. K M P M ' Ꮓ 2 Χ Α P R Draw the chord PP ' , and produce it to meet the directrix in Z ; join SZ . Draw PM , P'M ' at right angles to the directrix ; join SP , SP ; and produce PS to meet the parabola in Q. Then ...
Page 9
... chord inter- sect at right angles in the directrix . Let PSQ be a focal chord , and let the tangent at P meet the directrix in Z. Join SZ ; then by the last Proposition the angle ZSP is a right angle , and .. also the angle ZSQ is a ...
... chord inter- sect at right angles in the directrix . Let PSQ be a focal chord , and let the tangent at P meet the directrix in Z. Join SZ ; then by the last Proposition the angle ZSP is a right angle , and .. also the angle ZSQ is a ...
Page 16
... chords parallel to the tangent at the vertex , and the tangents at the extremities of any chord will 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 ...
... chords parallel to the tangent at the vertex , and the tangents at the extremities of any chord will 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 ...
Page 18
... and let the tangent at P meet the axis produced in 7 ; then 2 QV2 = 4. SP . PV , But PVST SP , = .. QV 4 SP2 ; = or QV 2 SP , = .. QQ ' = 4 SP . ( Prop . XV . ) ( Prop . VII . ) PROP . XVII . 19. If two chords of a 18 CONIC SECTIONS .
... and let the tangent at P meet the axis produced in 7 ; then 2 QV2 = 4. SP . PV , But PVST SP , = .. QV 4 SP2 ; = or QV 2 SP , = .. QQ ' = 4 SP . ( Prop . XV . ) ( Prop . VII . ) PROP . XVII . 19. If two chords of a 18 CONIC SECTIONS .
Page 19
William Henry Drew. PROP . XVII . 19. If two chords of a parabola 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 ...
William Henry Drew. PROP . XVII . 19. If two chords of a parabola 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 ...
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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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