The Principles of Analytical Geometry, Part 1 |
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Page 1
... points N and M draw the lines NP , MP parallel respectively to OX and OY ; their intersection determines the point P. 2. Instead of two lines of reference being given suppose there is only one OX , then if S ' it is known that the point ...
... points N and M draw the lines NP , MP parallel respectively to OX and OY ; their intersection determines the point P. 2. Instead of two lines of reference being given suppose there is only one OX , then if S ' it is known that the point ...
Page 2
... intersection is termed the origin ; the lengths PM and PN are called the coordinates of the point P. PN or OM being the abscissa and PM or ON the ordinate of P. If the angle between the fixed lines be a right angle , the axes are said ...
... intersection is termed the origin ; the lengths PM and PN are called the coordinates of the point P. PN or OM being the abscissa and PM or ON the ordinate of P. If the angle between the fixed lines be a right angle , the axes are said ...
Page 20
... point of intersection . Let the equations to the two lines be Ax + By + C = 0 A'x + B'y + C ' = 0 ..... ........ ( 1 ) , • ( 2 ) . Let X , Y denote the coordinates of the point of inter- section . Then since X , Y lies on ( 1 ) its ...
... point of intersection . Let the equations to the two lines be Ax + By + C = 0 A'x + B'y + C ' = 0 ..... ........ ( 1 ) , • ( 2 ) . Let X , Y denote the coordinates of the point of inter- section . Then since X , Y lies on ( 1 ) its ...
Page 21
... intersection of ( 1 ) and ( 2 ) ; for it is an equation of the first degree and therefore repre- sents some straight line ; and the coordinates of the point in which ( 1 ) and ( 2 ) intersect evidently satisfy ( 3 ) ; therefore that point ...
... intersection of ( 1 ) and ( 2 ) ; for it is an equation of the first degree and therefore repre- sents some straight line ; and the coordinates of the point in which ( 1 ) and ( 2 ) intersect evidently satisfy ( 3 ) ; therefore that point ...
Page 24
9. Find the equation to the line passing through the intersection of the two lines Ax + By + C = 0 , A'x + B'y + C ' = 0 , and through the point ( a , 0 ) , ( 1 ) by finding the coordinates of intersection ; ( 2 ) by using the equation ...
9. Find the equation to the line passing through the intersection of the two lines Ax + By + C = 0 , A'x + B'y + C ' = 0 , and through the point ( a , 0 ) , ( 1 ) by finding the coordinates of intersection ; ( 2 ) by using the equation ...
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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