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 9
... write X sina + Ý sin ß = Ĺ , X cos a + Y cos ẞ = M , the expressions in Art . 9 may be written y sin ∞ = L , x sin ∞ = M sin ∞ - L cos ; whence But sin2 ( x2 + y2 + 2xy cos w ) = ( L2 + M2 ) sin2w . L2 + M2 = x2 + Y2 + 2XY cos ( a ...
... write X sina + Ý sin ß = Ĺ , X cos a + Y cos ẞ = M , the expressions in Art . 9 may be written y sin ∞ = L , x sin ∞ = M sin ∞ - L cos ; whence But sin2 ( x2 + y2 + 2xy cos w ) = ( L2 + M2 ) sin2w . L2 + M2 = x2 + Y2 + 2XY cos ( a ...
Página 15
... write the equation in the form y х = m , and the question is : " To find the locus of a point P , such that , if we draw PM , PN parallel to two fixed lines , the ratio PM : PN may be constant . " Now this locus evidently is a right ...
... write the equation in the form y х = m , and the question is : " To find the locus of a point P , such that , if we draw PM , PN parallel to two fixed lines , the ratio PM : PN may be constant . " Now this locus evidently is a right ...
Página 16
... write down the equation that is PM = RM + PR , or PM = m.OM + PR , = mx + b . y = The equation , therefore , y = mx + b , being satisfied by every point of the line PQ , is said to be the equation of that line . It appears from the last ...
... write down the equation that is PM = RM + PR , or PM = m.OM + PR , = mx + b . y = The equation , therefore , y = mx + b , being satisfied by every point of the line PQ , is said to be the equation of that line . It appears from the last ...
Página 19
... write the formula x cosa + y sina - p , and consider a to denote the angle , ranging between 0 and 180 ° , made with the positive direction of the axis of x , by the perpendicular pro- duced . In using , then , the formula x cosa + y ...
... write the formula x cosa + y sina - p , and consider a to denote the angle , ranging between 0 and 180 ° , made with the positive direction of the axis of x , by the perpendicular pro- duced . In using , then , the formula x cosa + y ...
Página 37
... writing for x , p cos 0 , and for y , p sin ( see Art . 12 ) ; hence the equation becomes p ( cose cosa + sin @ sina ) = p ; or , as we got before , An equation of the form p cos ( 0 - a ) = p . p ( A cose + B sin 0 ) = C · can be ( as ...
... writing for x , p cos 0 , and for y , p sin ( see Art . 12 ) ; hence the equation becomes p ( cose cosa + sin @ sina ) = p ; or , as we got before , An equation of the form p cos ( 0 - a ) = p . p ( A cose + B sin 0 ) = C · can be ( as ...
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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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