A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 1
... equal to the distance from the fixed line , that is , when SP is equal to PM , the Conic Section is K ' called a Parabola . S P ( 2. ) When the distance from the fixed point is less than the distance from the fixed line , that is , when ...
... equal to the distance from the fixed line , that is , when SP is equal to PM , the Conic Section is K ' called a Parabola . S P ( 2. ) When the distance from the fixed point is less than the distance from the fixed line , that is , when ...
Page 4
... equal to the angle SMP ; then SP = PM , .. Pis a point on the curve . So by taking any number of points , M ' , M " , on the directrix , we may obtain as many points , P ' , P " , on the curve as we please , and the line which passes ...
... equal to the angle SMP ; then SP = PM , .. Pis a point on the curve . So by taking any number of points , M ' , M " , on the directrix , we may obtain as many points , P ' , P " , on the curve as we please , and the line which passes ...
Page 13
... equal to the angle SOQ ' , ..the angle SQO = the angle SOQ ' . So the angle SOQ = the angle SQ ' O , .. the remaining angle OSQ = the remaining angle OSQ ' . S And therefore the triangle OSQ is similar to the triangle CONIC SECTIONS . 13.
... equal to the angle SOQ ' , ..the angle SQO = the angle SOQ ' . So the angle SOQ = the angle SQ ' O , .. the remaining angle OSQ = the remaining angle OSQ ' . S And therefore the triangle OSQ is similar to the triangle CONIC SECTIONS . 13.
Page 21
... 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 figure 0QPQ ' , and the sum of the interior triangles ...
... 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 figure 0QPQ ' , and the sum of the interior triangles ...
Page 23
... equal . 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 ...
... equal . 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 ...
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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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