A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 29
... Ellipse is the curve traced out by a point which moves in such a manner that its distance from a given fixed point ... meeting A Y and A ' Y ' , drawn at right angles to AA ' , in the points Y and Y ' . On YY ' as diameter describe a circle ...
... Ellipse is the curve traced out by a point which moves in such a manner that its distance from a given fixed point ... meeting A Y and A ' Y ' , drawn at right angles to AA ' , in the points Y and Y ' . On YY ' as diameter describe a circle ...
Page 31
... ellipse is therefore symmetrical , not only with respect to the line A A ' , but also with respect to the line OC ... meet SS ' in G. Produce MP to meet X'M ' in M ' , and draw OM ' passing through the focus S ' ; then since SP PM :: SA ...
... ellipse is therefore symmetrical , not only with respect to the line A A ' , but also with respect to the line OC ... meet SS ' in G. Produce MP to meet X'M ' in M ' , and draw OM ' passing through the focus S ' ; then since SP PM :: SA ...
Page 33
... ellipse . 25. DEF . If BCB ' be drawn at right angles to ACA ' , meeting the ellipse in B and B ' , it is evident that AA ' and BB ' are respectively the longest and shortest lines that can be drawn in the ellipse . ( See fig . Prop ...
... ellipse . 25. DEF . If BCB ' be drawn at right angles to ACA ' , meeting the ellipse in B and B ' , it is evident that AA ' and BB ' are respectively the longest and shortest lines that can be drawn in the ellipse . ( See fig . Prop ...
Page 35
... ellipse will be less or greater than AA ' according as the point is inside or outside the ellipse . A S P S ' A ' ( 1. ) Let Q be a point inside the ellipse . Join SQ , S'Q ; and produce SQ to meet the ellipse in P ; join S'P ; then ...
... ellipse will be less or greater than AA ' according as the point is inside or outside the ellipse . A S P S ' A ' ( 1. ) Let Q be a point inside the ellipse . Join SQ , S'Q ; and produce SQ to meet the ellipse in P ; join S'P ; then ...
Page 36
... ellipse near to P , ( see fig . Prop . VI . ) and PP ' be joined , the line PP ' produced , in the limiting position ... meet the directrix in Z ; join SZ . Draw PM , P'M ' at right angles to the directrix , and join SP , SP ' . Produce PS to ...
... ellipse near to P , ( see fig . Prop . VI . ) and PP ' be joined , the line PP ' produced , in the limiting position ... meet the directrix in Z ; join SZ . Draw PM , P'M ' at right angles to the directrix , and join SP , SP ' . Produce PS to ...
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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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