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 vi
... radical Axis of two Circles • : Locus of Points whence Tangents to two Circles have a given Ratio Radical Centre of three Circles Properties of system of Circles having common radical Axis The limiting Points of the system · Properties ...
... radical Axis of two Circles • : Locus of Points whence Tangents to two Circles have a given Ratio Radical Centre of three Circles Properties of system of Circles having common radical Axis The limiting Points of the system · Properties ...
Página xii
... radical Axis Circles having for Diameters Diagonals of complete Quadrilateral have common radical Axis 277 277 • Locus of Point where Tangent meeting two fixed Tangents is cut in a given ratio 277 Degree of Polar Reciprocal in general ...
... radical Axis Circles having for Diameters Diagonals of complete Quadrilateral have common radical Axis 277 277 • Locus of Point where Tangent meeting two fixed Tangents is cut in a given ratio 277 Degree of Polar Reciprocal in general ...
Página 72
... radical . But the condition that the radical should be a perfect square is ( h2 −ab ) ( g2 — ac ) = ( hg — af ) 2 . - Expanding , and dividing by a , we obtain the required condition , abc + 2fgh — af2 — bg * — ch2 = 0. * viz . - - 1 ...
... radical . But the condition that the radical should be a perfect square is ( h2 −ab ) ( g2 — ac ) = ( hg — af ) 2 . - Expanding , and dividing by a , we obtain the required condition , abc + 2fgh — af2 — bg * — ch2 = 0. * viz . - - 1 ...
Página 73
... radicals ; or we may proceed more simply as follows : Since nothing shews whether the root a of the first quadratic is to be combined with the root B or B ' of the second , it is plain that 2h с may have This is also evident axes in the ...
... radicals ; or we may proceed more simply as follows : Since nothing shews whether the root a of the first quadratic is to be combined with the root B or B ' of the second , it is plain that 2h с may have This is also evident axes in the ...
Página 85
... radicals . The preceding article enables us , however , to obtain this equation in a still more simple form . For the equation which determines 7 : m will have equal roots if the line joining x'y ' , x " y " touch the given circle ; if ...
... radicals . The preceding article enables us , however , to obtain this equation in a still more simple form . For the equation which determines 7 : m will have equal roots if the line joining x'y ' , x " y " touch the given circle ; if ...
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Otras ediciones - Ver todas
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2016 |
Términos y frases comunes
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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