The Principles of Analytical Geometry, Part 1 |
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Page 7
... satisfy ( 1 ) , or we will have Ax ' + By ' + C = 0 ..... ( 2 ) . Similarly , Ax " + By " + C = 0 .... ( 3 ) . Take ( 2 ) from ( 3 ) , therefore therefore A = В B * A ( x " — x ' ) + B ( y " —y ' ) = 0 ; y " -y ' x " - x ' QT - PN QM or ...
... satisfy ( 1 ) , or we will have Ax ' + By ' + C = 0 ..... ( 2 ) . Similarly , Ax " + By " + C = 0 .... ( 3 ) . Take ( 2 ) from ( 3 ) , therefore therefore A = В B * A ( x " — x ' ) + B ( y " —y ' ) = 0 ; y " -y ' x " - x ' QT - PN QM or ...
Page 20
... satisfy that equation , or we must have similarly AX + BY + C = 0 , AX + B'Y + C ' = 0 . Solving for X and Y , we have X = = BC ' - B'C AB'A'B - and Y = AC ' A'C A'B - AB ' If in either of these expressions for X or Y , we have AB'A'B ...
... satisfy that equation , or we must have similarly AX + BY + C = 0 , AX + B'Y + C ' = 0 . Solving for X and Y , we have X = = BC ' - B'C AB'A'B - and Y = AC ' A'C A'B - AB ' If in either of these expressions for X or Y , we have AB'A'B ...
Page 21
... satisfy ( 3 ) ; therefore that point must lie on the line represented by ( 3 ) . We know that an infinite number of straight lines can be drawn through the intersection of ( 1 ) and ( 2 ) , and this fact , equa- tion ( 3 ) asserts ...
... satisfy ( 3 ) ; therefore that point must lie on the line represented by ( 3 ) . We know that an infinite number of straight lines can be drawn through the intersection of ( 1 ) and ( 2 ) , and this fact , equa- tion ( 3 ) asserts ...
Page 32
... satisfy either of the first two equations , will evidently satisfy the third . Again , if we multiply the equations to three straight lines together , we have a cubic equation which will represent the three lines . Taking , as an ...
... satisfy either of the first two equations , will evidently satisfy the third . Again , if we multiply the equations to three straight lines together , we have a cubic equation which will represent the three lines . Taking , as an ...
Page 41
... satisfy the equation . COR . ( 3 ) . If , besides passing through the origin , the circle has its centre in either of the coordinate axes , as for instance , in the axis of x , then a = r and b = 0 , and the equation becomes x2 + y2 ...
... satisfy the equation . COR . ( 3 ) . If , besides passing through the origin , the circle has its centre in either of the coordinate axes , as for instance , in the axis of x , then a = r and b = 0 , and the equation becomes x2 + y2 ...
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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