The Principles of Analytical Geometry, Part 1 |
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Page 15
... point ( x'y ' ) and making an angle a with the axis of x , and either side of this equation denotes the length ( 1 ) along the line from the fixed point ( x'y ' ) to any other point ( xy ) . 20. To find the equation to a line DT such ...
... point ( x'y ' ) and making an angle a with the axis of x , and either side of this equation denotes the length ( 1 ) along the line from the fixed point ( x'y ' ) to any other point ( xy ) . 20. To find the equation to a line DT such ...
Page 19
... points x'y ' and x " y " , y - y ' = y " — y ' ( x - x ' ) , ac " - this ... fixed , we have or y " - y — y ' = Y ' " ' — Y ' ′ ( x — x ' ) , - 0 y — y ... points " y " and x'y ' approach inde- finitely near each other , or if y ' = y ...
... points x'y ' and x " y " , y - y ' = y " — y ' ( x - x ' ) , ac " - this ... fixed , we have or y " - y — y ' = Y ' " ' — Y ' ′ ( x — x ' ) , - 0 y — y ... points " y " and x'y ' approach inde- finitely near each other , or if y ' = y ...
Page 22
passes through x'y ' , we must have Ax + By + C + k ( A's ' + B'y ' + C ' ) = 0 , from which we can find the value of k in terms of fixed quantities , and substituting this value in the above equation we shall obtain the required ...
passes through x'y ' , we must have Ax + By + C + k ( A's ' + B'y ' + C ' ) = 0 , from which we can find the value of k in terms of fixed quantities , and substituting this value in the above equation we shall obtain the required ...
Page 28
( where denotes the distance along this line from the fixed point x'y ' to any point xy . ) Hence y = sl + y ' , and x = cl + x ' . Substituting these values for x and y in the equation we have Ax + By + C = 0 ........ A ( cl + x ' ) + ...
( where denotes the distance along this line from the fixed point x'y ' to any point xy . ) Hence y = sl + y ' , and x = cl + x ' . Substituting these values for x and y in the equation we have Ax + By + C = 0 ........ A ( cl + x ' ) + ...
Page 38
is transferred to a point x'y ' , the direction of the axes being unaltered , we substitute for x , ( x + x ... fixed . Let Ox and Oy be the original axes , OX and OY the new axes when turned through an angle 0 . 이 10 x P S M M T Let OM = x ...
is transferred to a point x'y ' , the direction of the axes being unaltered , we substitute for x , ( x + x ... fixed . Let Ox and Oy be the original axes , OX and OY the new axes when turned through an angle 0 . 이 10 x P S M M T Let OM = x ...
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The Principles of Analytical Geometry: Designed for the Use of Students Henry Parr Hamilton No preview available - 2016 |
Common terms and phrases
ANALYTICAL GEOMETRY angle POX axes being inclined axes being rectangular axis of x bisecting the angle centre Chapter chord of contact circle x² Conic Sections cosa+y cosw Crown 8vo cuts the circle denotes the distance diameter Differential Calculus equal equation becomes equation x² evidently ex recensione Find the coordinates Find the equation Find the length Find the locus fixed point x'y given circle given line Greek HYPERIDES initial line line cutting line joining line OX line represented line ST line whose equation lines are parallel middle points origin of coordinates P₁ perpendicular point of intersection points whose coordinates polar coordinates polar equation PQ² radical axis radius referred required equation Second Edition Shew siny Ox straight line passing substituting tangent Third Edition touching the circle triangle Trinity College University of Cambridge values x²²