A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 3
... AS AX , = .. A is a point on the curve , The point A is called the Vertex , and the line Ax , with respect to which the curve is evidently symmetrical , is called the Axis . On the directrix take any point M ; join SM B 2 CHAPTER I. ...
... AS AX , = .. A is a point on the curve , The point A is called the Vertex , and the line Ax , with respect to which the curve is evidently symmetrical , is called the Axis . On the directrix take any point M ; join SM B 2 CHAPTER I. ...
Page 9
... vertex A is perpendicular to the axis . PROP . VI . 8. The tangents at the extremities of a focal chord inter- sect at right angles in the directrix . Let PSQ be a focal chord , and let the tangent at P meet the directrix in Z. Join SZ ...
... vertex A is perpendicular to the axis . PROP . VI . 8. The tangents at the extremities of a focal chord inter- sect at right angles in the directrix . Let PSQ be a focal chord , and let the tangent at P meet the directrix in Z. Join SZ ...
Page 11
... vertex in Y , then SY will bisect PT at right angles , and will be a mean proportional between SA and SP . Draw PN at right angles to the axis ; then since A Y is parallel to PN , .. TY : YP :: TA : AN . But AT = AN , ( Prop . VII ...
... vertex in Y , then SY will bisect PT at right angles , and will be a mean proportional between SA and SP . Draw PN at right angles to the axis ; then since A Y is parallel to PN , .. TY : YP :: TA : AN . But AT = AN , ( Prop . VII ...
Page 16
... Vertex . The diameter consequently bisects all chords parallel to the tangent at the vertex , and the tangents at the extremities of any chord will intersect in the diameter corresponding to that chord . DEF . A line QV , drawn parallel ...
... Vertex . The diameter consequently bisects all chords parallel to the tangent at the vertex , and the tangents at the extremities of any chord will intersect in the diameter corresponding to that chord . DEF . A line QV , drawn parallel ...
Page 25
... vertex and axis . BA'C is the double ordinate of the parabola which touches the circle at A ' , the extremity of the diameter through the vertex A. PP ' is any other ordinate of the parabola parallel to this , meeting the axis in N ...
... vertex and axis . BA'C is the double ordinate of the parabola which touches the circle at A ' , the extremity of the diameter through the vertex A. PP ' is any other ordinate of the parabola parallel to this , meeting the axis in N ...
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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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