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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Резултати 1 - 5 от 45.
Страница 2
... considered as positive , lines measured in the oppo- site direction must be con- M Y Р , N Р P3 ' N ' Y ' · X M sidered as negative . It is , of course , arbitrary in which direction we measure positive lines , but it is customary to ...
... considered as positive , lines measured in the oppo- site direction must be con- M Y Р , N Р P3 ' N ' Y ' · X M sidered as negative . It is , of course , arbitrary in which direction we measure positive lines , but it is customary to ...
Страница 4
... considered negative . If indeed we are only concerned with the single distance between two points , it would be un- meaning to affix any sign to it , since by prefixing a sign we in fact direct that this distance shall be added to , or ...
... considered negative . If indeed we are only concerned with the single distance between two points , it would be un- meaning to affix any sign to it , since by prefixing a sign we in fact direct that this distance shall be added to , or ...
Страница 12
... considered the geometrical signification of the given equation . Thus , for example , we saw ( Ex . 3 , p . 4 ) , that the equation ( x − 2 ) 2 + ( y − 3 ) 2 = 16 - expresses that the distance of the point xy from the point ( 2 , 3 ) ...
... considered the geometrical signification of the given equation . Thus , for example , we saw ( Ex . 3 , p . 4 ) , that the equation ( x − 2 ) 2 + ( y − 3 ) 2 = 16 - expresses that the distance of the point xy from the point ( 2 , 3 ) ...
Страница 18
... considered A B Ax + By + C = 0 , or C x + y + 1 = 0 . This equation must be satisfied by the co - ordinates of every point on MN , and there- fore by those of M , which ( see Art . 2 ) are x = α , y = 0 . Hence we have A · 0a + 1 = 0 ...
... considered A B Ax + By + C = 0 , or C x + y + 1 = 0 . This equation must be satisfied by the co - ordinates of every point on MN , and there- fore by those of M , which ( see Art . 2 ) are x = α , y = 0 . Hence we have A · 0a + 1 = 0 ...
Страница 64
... considered as intersecting it at an infinite distance , but ( Art . 40 ) an equation of the form a + C = 0 represents a line through the intersection of the lines a = 0 , C = 0 , or ( Art . 67 ) through the intersection of the line a ...
... considered as intersecting it at an infinite distance , but ( Art . 40 ) an equation of the form a + C = 0 represents a line through the intersection of the lines a = 0 , C = 0 , or ( Art . 67 ) through the intersection of the line a ...
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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