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 23
... quantities A , B , C. For if we multiply or divide the equation by any constant it will still represent the same line : we may divide therefore by C , when the equation will only A B contain the two constants . Choosing , then , any of ...
... quantities A , B , C. For if we multiply or divide the equation by any constant it will still represent the same line : we may divide therefore by C , when the equation will only A B contain the two constants . Choosing , then , any of ...
Stranica 25
... quantities x and y , from the two given equations . We said ( Art . 14 ) that the position of a point was deter- mined , being given two equations between its coordinates . The reader will now perceive that each equation represents a ...
... quantities x and y , from the two given equations . We said ( Art . 14 ) that the position of a point was deter- mined , being given two equations between its coordinates . The reader will now perceive that each equation represents a ...
Stranica 32
... quantity multiplied respectively by A and A ' , we get for the double area the expression - - - { A ( B'C " — B " C ' ) + A ' ( B " C – BC " ) + A " ( BC ' – B'C ' ) } " ̧ ( AB ' — BA ' ) ( A'B " — B′A " ) ( A ′′ B — B " A ) - - If the ...
... quantity multiplied respectively by A and A ' , we get for the double area the expression - - - { A ( B'C " — B " C ' ) + A ' ( B " C – BC " ) + A " ( BC ' – B'C ' ) } " ̧ ( AB ' — BA ' ) ( A'B " — B′A " ) ( A ′′ B — B " A ) - - If the ...
Stranica 34
... quantity , and added together , the sum is identically = 0 ; that is to say , if the following relation be true , no matter what x and y are : 1 ( Ax + By + C ) + m ( A'x + B'y + C ' ) + n ( A ′′ x + B " y + C " ) = 0 . For then those ...
... quantity , and added together , the sum is identically = 0 ; that is to say , if the following relation be true , no matter what x and y are : 1 ( Ax + By + C ) + m ( A'x + B'y + C ' ) + n ( A ′′ x + B " y + C " ) = 0 . For then those ...
Stranica 35
... quantity from the condition , that the coordinates just written shall satisfy the equation of the locus . Thus , in the present example , we have Α mx " + nx ' m + n + Bmy " + ny ' + C = 0 ; m + n m hence Ax ' + By + C n Ax " + By " + C ...
... quantity from the condition , that the coordinates just written shall satisfy the equation of the locus . Thus , in the present example , we have Α mx " + nx ' m + n + Bmy " + ny ' + C = 0 ; m + n m hence Ax ' + By + C n Ax " + By " + C ...
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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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