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 xv
... Square Three Conics derived from a single Cubic , method of forming its Equation . CHAPTER XIX . 362 362 363 • 365 365 366 368 THE METHOD OF INFINITESIMALS . Direction of Tangents of Conics Determination of Areas of Conics 371 • 372 ...
... Square Three Conics derived from a single Cubic , method of forming its Equation . CHAPTER XIX . 362 362 363 • 365 365 366 368 THE METHOD OF INFINITESIMALS . Direction of Tangents of Conics Determination of Areas of Conics 371 • 372 ...
Página 3
... ( x ′ — x " ) 2 + 2 ( y ' — y ' ) ( x ' — x ' ) cos w . - Similarly , the square of the distance of a point , x'y ' , from the origin = " + y " + 2x'y ' cos w . In applying these formula , attention must be paid to THE POINT . 3.
... ( x ′ — x " ) 2 + 2 ( y ' — y ' ) ( x ' — x ' ) cos w . - Similarly , the square of the distance of a point , x'y ' , from the origin = " + y " + 2x'y ' cos w . In applying these formula , attention must be paid to THE POINT . 3.
Página 4
... square 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 ...
... square 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 ...
Página 9
... square of the distance of = a point from the origin . X and Y in Art . 9 . Verify this by squaring and adding the expressions for Ex . 6. Verify in like manner in general that x2 + y2 + 2xy cosxOy = X2 + Y2 + 2XY cos XOY . If we write X ...
... square of the distance of = a point from the origin . X and Y in Art . 9 . Verify this by squaring and adding the expressions for Ex . 6. Verify in like manner in general that x2 + y2 + 2xy cosxOy = X2 + Y2 + 2XY cos XOY . If we write X ...
Página 21
... square root in the denominators is , of course , susceptible of a double sign , since the equation may be reduced to either of the forms x cos a + y cosẞ - p = 0 , x cos ( a + 180 ° ) + y cos ( B + 180 ° ) + p = 0 . 25. To find the ...
... square root in the denominators is , of course , susceptible of a double sign , since the equation may be reduced to either of the forms x cos a + y cosẞ - p = 0 , x cos ( a + 180 ° ) + y cos ( B + 180 ° ) + p = 0 . 25. To find the ...
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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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