A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, and Company, 1879 - Broj stranica: 399 |
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Stranica 9
... y coordinates of a point , to find its polar ones , or vice versa . C First , let the fixed line . coincide with the POLAR COORDINATES . 9 Problems where it is proved that a Moveable Line always passes through Fixed Point.
... y coordinates of a point , to find its polar ones , or vice versa . C First , let the fixed line . coincide with the POLAR COORDINATES . 9 Problems where it is proved that a Moveable Line always passes through Fixed Point.
Stranica 10
... coincide with the axis of x , then we have OP : PM :: sin PMO : sin POM ; denoting OP by p , POM by 0 , and YOX by w , then Y P PM or y ρ sin 0 = sin w ; 0 M X p sin ( w - 0 ) and similarly , OM = x = sin w For the more ordinary case of ...
... coincide with the axis of x , then we have OP : PM :: sin PMO : sin POM ; denoting OP by p , POM by 0 , and YOX by w , then Y P PM or y ρ sin 0 = sin w ; 0 M X p sin ( w - 0 ) and similarly , OM = x = sin w For the more ordinary case of ...
Stranica 55
... coincides with the third . It is cos ( aẞ ' ) cos ( By ' ) cos ( ya ' ) = cos ( a'ẞ ) cos ( ẞ'y ) cos ( y'a ) . But the symmetry of this equation shews that this is also the condition that the perpendiculars from the vertices of the ...
... coincides with the third . It is cos ( aẞ ' ) cos ( By ' ) cos ( ya ' ) = cos ( a'ẞ ) cos ( ẞ'y ) cos ( y'a ) . But the symmetry of this equation shews that this is also the condition that the perpendiculars from the vertices of the ...
Stranica 69
... coincide ; and when a and b are imaginary , that the lines are imaginary . It may seem to the student a matter of indifference which mode of speaking we adopt ; we shall find , how- ever , as we proceed , that we should lose sight of ...
... coincide ; and when a and b are imaginary , that the lines are imaginary . It may seem to the student a matter of indifference which mode of speaking we adopt ; we shall find , how- ever , as we proceed , that we should lose sight of ...
Stranica 78
... coincide . We shall , therefore , not say that the tangent meets the circle in only one point , but rather that it meets it in two coincident points ; just as we do not say that the corre- sponding quadratic has only one root , but ...
... coincide . We shall , therefore , not say that the tangent meets the circle in only one point , but rather that it meets it in two coincident points ; just as we do not say that the corre- sponding quadratic has only one root , but ...
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Ostala izdanja - Prikaži sve
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Pregled nije dostupan - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Pregled nije dostupan - 2016 |
Uobičajeni izrazi i fraze
anharmonic ratio asymptotes ax² axes bisected by² centre chord of contact circumscribing coefficients coincide common tangents condition conic having double conic section conic touching conjugate diameters coordinates corresponding denote determine directrix double contact drawn ellipse equal find the equation find the locus fixed line fixed point foci focus four points given conic given line given point harmonic Hence hyperbola imaginary points infinite distance inscribed intercept last Article line at infinity line joining line meets meet the curve middle points mẞ origin parabola parallel Pascal's theorem perpendicular point of contact point x'y points at infinity points of intersection polar pole proved quadratic quadrilateral radical axis radius vector reciprocal rectangle represents right angles right line second degree sides square substituting tangential equation theorem trilinear coordinates values vanish vertex vertices
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