Mathematical Questions and Solutions, from the "Educational Times.", Volume 21F. Hodgson, 1874 |
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A₁ a²b² ABCD axes axis B₁ bisectors bisects brachystochronous centre of gravity Ceulen chords circle conic cos² curve Denoting diagonal distance drawn at random ellipse equal excentricity fixed point focus G. S. CARR given h₁ h₂ Hence hyperbola hypocycloid inclination inscribed intersection inverse J. J. SYLVESTER J. J. WALKER J. W. L. GLAISHER locus M.A. Let negative pedal normal ovals parabola parallel passing perpendicular plane polar equation polar reciprocal Professor TOWNSEND Professor WOLSTENHOLME Proposed by Professor prove quadric quadrilateral question radius random lines respectively rhombus right angles sec² semi-axis sides Similarly sin² Solution by J. J. Solution by Professor straight line tangent tangential equation theorem vertex whence αξ аф
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Page 68 - IV. Solution by JL McKENZIE. 1. This theorem is the reciprocal of the following : — " If a line T touch a circle of radius r, and through the point of contact another line L be drawn making with T a constant angle a, the envelope of L is a concentric circle of radius r cosa.
Page 30 - ... agreeing as they should do with the known relation xy = ac + bd : the quadrilateral is thus determined by means of either of its diagonals. It is however interesting to treat the question in a different manner. Considering a, b, c, d, x, y as the sides and diagonals of a quadrilateral, we have between these quantities a given relation, say J!