Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two ...
Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two ...
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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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You can find similar books in the "Read Also" column, or choose other free books by William Allen Whitworth to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
^ /(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.
What to read after Trilinear Coordinates And Other Methods of Modern Analytical Geometry of Two ...?
You can find similar books in the "Read Also" column, or choose other free books by William Allen Whitworth to read onlineMoreLess
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