A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 4
... sides of the axis . COR . 2. The parabola may be described practically in the following manner . K M Α S x Let S be the focus and KX be the directrix ; and let a rigid bar QM , having a string of the same length as itself fastened at ...
... sides of the axis . COR . 2. The parabola may be described practically in the following manner . K M Α S x Let S be the focus and KX be the directrix ; and let a rigid bar QM , having a string of the same length as itself fastened at ...
Page 13
... side of the directrix O is situated , since O is nearer to the directrix than to the focus . ( Prop . II . ) Draw MQ and M'Q ' parallel to the axis meeting the parabola in Q and Q ' . Join OQ , OQ ; these will be the tangents required ...
... side of the directrix O is situated , since O is nearer to the directrix than to the focus . ( Prop . II . ) Draw MQ and M'Q ' parallel to the axis meeting the parabola in Q and Q ' . Join OQ , OQ ; these will be the tangents required ...
Page 14
... 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 .
... 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 ...
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 ...
Page 27
... sides produced meet the tangents at the opposite angles are in the same straight line . 37. If the tangents OQ , OQ ' be cut by a third tangent in R , R ' prove that OR RQ R'Q ' OR ' . 38. If from the vertex of a parabola chords be ...
... sides produced meet the tangents at the opposite angles are in the same straight line . 37. If the tangents OQ , OQ ' be cut by a third tangent in R , R ' prove that OR RQ R'Q ' OR ' . 38. If from the vertex of a parabola chords be ...
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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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