A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 4
... Hence the curve recedes at the same time both from the axis and directrix ; and since the angle SMP can never exceed a right angle , and the lines SP and MP will therefore always meet , it is evident that the curve will branch off to an ...
... Hence the curve recedes at the same time both from the axis and directrix ; and since the angle SMP can never exceed a right angle , and the lines SP and MP will therefore always meet , it is evident that the curve will branch off to an ...
Page 7
... Hence , when PZ is the tangent , the angle ZSP is a right angle , or SZ is perpendicular to SP . COR . Conversely , if SZ be drawn at right angles to SP , meeting the directrix in Z , and PZ be joined , PZ will be a tangent at P. PROP ...
... Hence , when PZ is the tangent , the angle ZSP is a right angle , or SZ is perpendicular to SP . COR . Conversely , if SZ be drawn at right angles to SP , meeting the directrix in Z , and PZ be joined , PZ will be a tangent at P. PROP ...
Page 19
... ( Euclid , II . 5 , ) - = QV2 - RW2 , = 4 SP . PV - 4 SP . PW , ( Prop . XV . ) = 4 SP . RO . So Q'O . Oq ' = 4 SP ' . RO . Hence Q0.0q : Q'O . Oq ' :: 4 SP : 4 SP ' . By Euclid , II . 6 , the same may C 2 CONIC SECTIONS . 19 PROP. XVII. ...
... ( Euclid , II . 5 , ) - = QV2 - RW2 , = 4 SP . PV - 4 SP . PW , ( Prop . XV . ) = 4 SP . RO . So Q'O . Oq ' = 4 SP ' . RO . Hence Q0.0q : Q'O . Oq ' :: 4 SP : 4 SP ' . By Euclid , II . 6 , the same may C 2 CONIC SECTIONS . 19 PROP. XVII. ...
Page 21
... Hence the sum of all the exterior triangles will be equal to half the sum of all the interior triangles . Now when the number of the triangles is increased in- definitely , the sum of the exterior triangles will represent the exterior ...
... Hence the sum of all the exterior triangles will be equal to half the sum of all the interior triangles . Now when the number of the triangles is increased in- definitely , the sum of the exterior triangles will represent the exterior ...
Page 23
... Hence the chord of the circle of curvature parallel to the axis = 4 SP . COR . 1. If PU be the diameter of the circle of curvature , and PF the chord through the focus ; then since the angle FPU = the angle WPU , ( Prop . VIII . ) .. PF ...
... Hence the chord of the circle of curvature parallel to the axis = 4 SP . COR . 1. If PU be the diameter of the circle of curvature , and PF the chord through the focus ; then since the angle FPU = the angle WPU , ( Prop . VIII . ) .. PF ...
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Common terms and phrases
AC² angle ZSP auxiliary circle BC² BERNARD DRAKE bisects the angle CA² Cambridge 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 diameter PV 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 produced to meet Prop prove radius right angles Second Edition tangent triangle Trinity College University of Cambridge vertex
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