Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two ...

Cover Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two ...
Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two ...
William Allen Whitworth
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^ /(1. -i>o) ? " b* c" 16—2 S44 THE OBNBBAL EQUATION Obs. If the equation he written in the form tt/+ r/3*+ ti7*+ 2ttyS7 + 2vyji + 2wafi=^0, the conditions that it should represent a circle become «? + w&*— 2tt'6c = tt7fl? + lie"- 2r'ca = i«i" + t«i*- 2wab in iriUnear coordinates, and in triangular coordinates they be- come v-^-w — ^u tr + u — 2t;^ K + 1? — 2k?' ? " V ? • Or the conditions in trilinear coordinates will be given by any two of the equations P ? be a^ ca €? P ab 7 P ?
c? be ca ab
... P ca ah be if ah be'' ca be cos A ea cosB " ctbcos G ' and in triangular coordinates by any two of the equations t? + m; — 2m' _ ti? -f tt - 2v' _ u + v-^ 2w' ? P c* u + u "v' — w v + v —V) — u' _ to-^w'^u' --v' be cos A ca cos B db cos G The student will not be surprised if by other methods he- obtains these conditions under. other forma. In a case where only one condition is arrived at the equation expressing that condition must be identically the same however it be obtained, but a system of two simultaneous equations can always be re« placed by any two of the equations formed by combining them.

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