A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 4
William Henry Drew. On the directrix take any point M ; join SM ; and draw MP at right angles to the directrix . At the focus S make the angle MSP equal to the angle SMP ; then SP = PM , .. Pis a point on the curve . So by taking any ...
William Henry Drew. On the directrix take any point M ; join SM ; and draw MP at right angles to the directrix . At the focus S make the angle MSP equal to the angle SMP ; then SP = PM , .. Pis a point on the curve . So by taking any ...
Page 5
... join SP ; then since SP- PM , .. SP and PQ = QM . But SP and PQ > SQ , .. QM > SQ . ( 2. ) Let be a point outside the parabola . Draw MQ at right angles to the directrix , and produce it to meet the parabola in P ; join SP ; then since SQ ...
... join SP ; then since SP- PM , .. SP and PQ = QM . But SP and PQ > SQ , .. QM > SQ . ( 2. ) Let be a point outside the parabola . Draw MQ at right angles to the directrix , and produce it to meet the parabola in P ; join SP ; then since SQ ...
Page 7
... join SP , SP ; and produce PS to meet the parabola in Q. Then , since the triangles ZMP , ZM'P ' are similar , .. ZP : ZP ' :: MP : M'P ' , .. SZ bisects the angle P'SQ . :: SP : SP ' , ( Euclid , VI . Prop . A. ) Now when P ' is ...
... join SP , SP ; and produce PS to meet the parabola in Q. Then , since the triangles ZMP , ZM'P ' are similar , .. ZP : ZP ' :: MP : M'P ' , .. SZ bisects the angle P'SQ . :: SP : SP ' , ( Euclid , VI . Prop . A. ) Now when P ' is ...
Page 8
... SP , and the perpendicular PM on the directrix . K M 2 X M ' A S 2 P R K Let the tangent at P meet the directrix in the point Z ; join SZ ; then since the angle ZSP is a right angle , ( Prop . IV . ) : . ZS2 + SP2 = PZ2 . Also ZM2 + MP2 ...
... SP , and the perpendicular PM on the directrix . K M 2 X M ' A S 2 P R K Let the tangent at P meet the directrix in the point Z ; join SZ ; then since the angle ZSP is a right angle , ( Prop . IV . ) : . ZS2 + SP2 = PZ2 . Also ZM2 + MP2 ...
Page 9
... Join SZ ; then by the last Proposition the angle ZSP is a right angle , and .. also the angle ZSQ is a right angle ... SP , PZ , each to each , and the angle MPZ = the angle SPZ , .. the angle MZP = the angle SZP , .. the angle SZP is ...
... Join SZ ; then by the last Proposition the angle ZSP is a right angle , and .. also the angle ZSQ is a right angle ... SP , PZ , each to each , and the angle MPZ = the angle SPZ , .. the angle MZP = the angle SZP , .. the angle SZP is ...
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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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