A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, and Company, 1879 - 399 páginas |
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Página 4
... root , is necessarily susceptible of a double sign . If the distance PQ , measured from P to Q , be considered positive , then the distance QP , measured from Q to P , is considered negative . If indeed we are only concerned with the ...
... root , is necessarily susceptible of a double sign . If the distance PQ , measured from P to Q , be considered positive , then the distance QP , measured from Q to P , is considered negative . If indeed we are only concerned with the ...
Página 11
... roots be a ,, a , α , & c . Now , if we substitute any of these values ( a , ) for x in the original equations , we get two equations in y , which must have a common root ( since the result of elimination be- tween the equations is ...
... roots be a ,, a , α , & c . Now , if we substitute any of these values ( a , ) for x in the original equations , we get two equations in y , which must have a common root ( since the result of elimination be- tween the equations is ...
Página 21
... root in the denominators is , of course , susceptible of a double sign , since the equation may be reduced to either of the forms xcos a + y cosẞ - p = 0 , x cos ( a + 180 ° ) + y cos ( B + 180 ° ) + p = 0 . 25. To find the angle ...
... root in the denominators is , of course , susceptible of a double sign , since the equation may be reduced to either of the forms xcos a + y cosẞ - p = 0 , x cos ( a + 180 ° ) + y cos ( B + 180 ° ) + p = 0 . 25. To find the angle ...
Página 31
... root used in finding them . If we are concerned with a single area we look only to its absolute magnitude without regard to sign . But if , for example , we are comparing two triangles whose vertices x , xy , are on opposite sides of ...
... root used in finding them . If we are concerned with a single area we look only to its absolute magnitude without regard to sign . But if , for example , we are comparing two triangles whose vertices x , xy , are on opposite sides of ...
Página 67
... roots of this equation , then it is resolvable into the factors ( − a ) ( ~ — b ) ( = − c ) & c . = 0 , and the original equation is therefore resolvable into the factors ( x — ay ) ( x — by ) ( x − cy ) & c . = 0 . - - It ...
... roots of this equation , then it is resolvable into the factors ( − a ) ( ~ — b ) ( = − c ) & c . = 0 , and the original equation is therefore resolvable into the factors ( x — ay ) ( x — by ) ( x − cy ) & c . = 0 . - - It ...
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Outras edições - Ver tudo
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Visualização integral - 1879 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Pré-visualização indisponível - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Pré-visualização indisponível - 2016 |
Palavras e frases frequentes
anharmonic ratio asymptotes ax² axes bisected bisectors by² centre chord of contact circumscribing coefficients common tangents condition conic having double conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the equation find the locus fixed line fixed point foci focus four points geometrically given conic given line given point Hence hyperbola imaginary points infinite distance inscribed intercept last Article 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 reciprocal rectangle right angles right line second degree sides sin² square substituting tangential equation theorem values vanish vertex vertices
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