The Principles of Analytical Geometry, Part 1 |
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Page 4
... line is a locus whose equation is of the first degree . As another example the equation y = 0 refers not to one point but to all points whose y = 0 , it will therefore represent the axis of x . the equation x = 0 will represent the axis ...
... line is a locus whose equation is of the first degree . As another example the equation y = 0 refers not to one point but to all points whose y = 0 , it will therefore represent the axis of x . the equation x = 0 will represent the axis ...
Page 7
... represented by ( 1 ) . Then since this equation expresses a relation be- tween the x and the y of any point N T M on the line , x ' and y ' substituted for x and y will satisfy ( 1 ) , or we will have Ax ' + By ' + C = 0 ..... ( 2 ) ...
... represented by ( 1 ) . Then since this equation expresses a relation be- tween the x and the y of any point N T M on the line , x ' and y ' substituted for x and y will satisfy ( 1 ) , or we will have Ax ' + By ' + C = 0 ..... ( 2 ) ...
Page 8
... line : for if not , let L be in the straight line joining P and T. Then therefore LV TR PV PR ; = R T P R V M N LV = QV , which is impossible ; so that the general equation Ax + By + C = 0 will always represent a straight line . S 14 ...
... line : for if not , let L be in the straight line joining P and T. Then therefore LV TR PV PR ; = R T P R V M N LV = QV , which is impossible ; so that the general equation Ax + By + C = 0 will always represent a straight line . S 14 ...
Page 9
... line is represented by an equation of the first degree : but in discussing any par- ticular straight line in reference to fixed axes , it is necessary that we should know the two conditions which this line fulfils ; as , for instance ...
... line is represented by an equation of the first degree : but in discussing any par- ticular straight line in reference to fixed axes , it is necessary that we should know the two conditions which this line fulfils ; as , for instance ...
Page 17
... line cuts the axis of x it is only necessary to put y = 0 in the equa- A B tion + y + 1 = 0 , and we have x = - that is , OS = - C A C OS = a ; therefore = α . A C A 9 but D Again , to find where the line cuts the axis THE STRAIGHT LINE .
... line cuts the axis of x it is only necessary to put y = 0 in the equa- A B tion + y + 1 = 0 , and we have x = - that is , OS = - C A C OS = a ; therefore = α . A C A 9 but D Again , to find where the line cuts the axis THE STRAIGHT LINE .
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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