A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 11
... common part SN , the remainder NG SX = 2 AS . = . PROP . IX . 11. If PN be an ordinate to the parabola at the point P ; then PN2 = 4 AS . AN . Since TPG is a right angle , and PN perpendicular to TG , .. PN is a mean proportional ...
... common part SN , the remainder NG SX = 2 AS . = . PROP . IX . 11. If PN be an ordinate to the parabola at the point P ; then PN2 = 4 AS . AN . Since TPG is a right angle , and PN perpendicular to TG , .. PN is a mean proportional ...
Page 14
... directrix . Join OM , OM ' ; and let OV meet MM ' in Z. Then , since OM OM ' , ( Prop . XI . ) = .. the angle OMZ = the angle OM'Z , and the angle OZM = the angle , OZM ' , and the side OZ is common to the triangles OZM 14 CONIC SECTIONS .
... directrix . Join OM , OM ' ; and let OV meet MM ' in Z. Then , since OM OM ' , ( Prop . XI . ) = .. the angle OMZ = the angle OM'Z , and the angle OZM = the angle , OZM ' , and the side OZ is common to the triangles OZM 14 CONIC SECTIONS .
Page 15
William Henry Drew. and the side OZ is common to the triangles OZM , OZM ' , .. MZ M'Z . = And because the lines QM , ZV , Q'M ' are parallel , .. QV : Q ' V :: MZ : M'Z . But MZ = M'Z , .. QV = Q ' V , .. QQ is bisected in V. PROP . XIV ...
William Henry Drew. and the side OZ is common to the triangles OZM , OZM ' , .. MZ M'Z . = And because the lines QM , ZV , Q'M ' are parallel , .. QV : Q ' V :: MZ : M'Z . But MZ = M'Z , .. QV = Q ' V , .. QQ is bisected in V. PROP . XIV ...
Page 24
... common tangent to a parabola and the circle described on the latus rectum as diameter ; prove that SP and SQ make equal angles with the latus rectum . 5. Prove that PY . PZ = SP2 , and that PY . YZ = AS . SP . ( See fig . Prop . VII ...
... common tangent to a parabola and the circle described on the latus rectum as diameter ; prove that SP and SQ make equal angles with the latus rectum . 5. Prove that PY . PZ = SP2 , and that PY . YZ = AS . SP . ( See fig . Prop . VII ...
Page 25
... common tangent at P , and intersect in Q and R ; and QV , UR be drawn parallel to the axis of the parabola meeting the circle in V and U re- spectively , then VU is parallel to the tangent at P. 18. AB and AC are two lines at right ...
... common tangent at P , and intersect in Q and R ; and QV , UR be drawn parallel to the axis of the parabola meeting the circle in V and U re- spectively , then VU is parallel to the tangent at P. 18. AB and AC are two lines at right ...
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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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