A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, Reader, and Dyer, 1869 - 377 страници |
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Страница x
... substituting the Co - ordinates of any Point in the Equation of a Conic Diameter of Circle circumscribing Triangle formed by two Tangents and their Chord . 230 231 · • • Property of Chords of Intersection of two Conics , each having ...
... substituting the Co - ordinates of any Point in the Equation of a Conic Diameter of Circle circumscribing Triangle formed by two Tangents and their Chord . 230 231 · • • Property of Chords of Intersection of two Conics , each having ...
Страница 11
... Substituting these successively in the second equation , we obtain the corresponding values of y , y = +2 , y = 2 , y = + 1 , y = - - 1 . The two given equations , therefore , represent the four points ( + 1 , + 2 ) , ( − 1 , − 2 ) ...
... Substituting these successively in the second equation , we obtain the corresponding values of y , y = +2 , y = 2 , y = + 1 , y = - - 1 . The two given equations , therefore , represent the four points ( + 1 , + 2 ) , ( − 1 , − 2 ) ...
Страница 18
... Substituting which values in the general form , it becomes a x У + = 1 . b This equation holds whether the axes be oblique or rect- angular . It is plain that the position of the line will vary with the signs of the quantities a and b ...
... Substituting which values in the general form , it becomes a x У + = 1 . b This equation holds whether the axes be oblique or rect- angular . It is plain that the position of the line will vary with the signs of the quantities a and b ...
Страница 23
... also pass through the point " y " , this equation must be satisfied when the co - ordinates x " , y " , are substituted for x and y ; hence y " — y ' " -x = m . Substituting this value of m , the equation of the THE RIGHT LINE . 23.
... also pass through the point " y " , this equation must be satisfied when the co - ordinates x " , y " , are substituted for x and y ; hence y " — y ' " -x = m . Substituting this value of m , the equation of the THE RIGHT LINE . 23.
Страница 24
... Substituting this value of m , the equation of the line becomes - y — y ' _ y " — y ' X - = 0 % - ― x In this form the equation can be easily remembered , but , clearing it of fractions , we obtain it in a form which is some- times more ...
... Substituting this value of m , the equation of the line becomes - y — y ' _ y " — y ' X - = 0 % - ― x In this form the equation can be easily remembered , but , clearing it of fractions , we obtain it in a form which is some- times more ...
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anharmonic ratio asymptotes ax² axes bisected bisectors chord of contact circumscribing coefficients common tangents condition conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the co-ordinates find the equation find the locus fixed lines fixed point foci focus four points given circles given line given point Hence hyperbola imaginary points infinite distance inscribed intercept joining the points last Article length line at infinity line joining line meets meet the curve middle points origin parabola parallel Pascal's theorem perpendicular point of contact point x'y points at infinity points of intersection polar polar equation pole proved quadratic quadrilateral radical axis radius vector rectangle right angles right line second degree sides sin² square substituting tangential equation theorem values vanish vertex vertices