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 páginas |
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Página 1
... called the co - ordinates of the point P. PM is often called the ordinate of the point P ; while PN , which is equal to OM the intercept cut off by the ordinate , is called the abscissa . B The fixed lines XX ' and YY ' are termed THE ...
... called the co - ordinates of the point P. PM is often called the ordinate of the point P ; while PN , which is equal to OM the intercept cut off by the ordinate , is called the abscissa . B The fixed lines XX ' and YY ' are termed THE ...
Página 2
... called the origin . The axes are said to be rectangular or oblique , ac- cording as the angle at which they intersect is a right angle or oblique . It will readily be seen that the co - ordinates of the point M on the preceding figure ...
... called the origin . The axes are said to be rectangular or oblique , ac- cording as the angle at which they intersect is a right angle or oblique . It will readily be seen that the co - ordinates of the point M on the preceding figure ...
Página 6
... called the transformation of co - ordinates . We shall consider three cases separately : first , we shall suppose the origin changed , but the new axes parallel to the old ; secondly , we shall suppose the directions of the axes changed ...
... called the transformation of co - ordinates . We shall consider three cases separately : first , we shall suppose the origin changed , but the new axes parallel to the old ; secondly , we shall suppose the directions of the axes changed ...
Página 9
... called the pole ; and this method is called the method of polar co- ordinates . θ B It is very easy , being given the x and y co - ordinates of a point , to find its polar ones , or vice versâ . C First , let the fixed line Y coincide ...
... called the pole ; and this method is called the method of polar co- ordinates . θ B It is very easy , being given the x and y co - ordinates of a point , to find its polar ones , or vice versâ . C First , let the fixed line Y coincide ...
Página 50
... called the centre of mean position of the given points . 51. If the equation of any line involve the co - ordinates of a certain point x'y ' in the first degree , thus , ( Ax ' + By + C ) x + ( A'x ' + B'y ' + C ' ) y + ( A ′′ x ' + B'y ...
... called the centre of mean position of the given points . 51. If the equation of any line involve the co - ordinates of a certain point x'y ' in the first degree , thus , ( Ax ' + By + C ) x + ( A'x ' + B'y ' + C ' ) y + ( A ′′ x ' + B'y ...
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Términos y frases comunes
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