A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, Reader, and Dyer, 1869 - 377 páginas |
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Página 9
... write X sin a + Y sinẞ = L , X cos a + Y cosẞ = M , the expressions in Art . 9 may be written y sin w = L , x sin∞ = M sin w - L cosa ; whence But - sin2 w ( x2 + y2 + 2xy cos w ) = ( L2 + M2 ) sin2 w . L2 + M2 = X2 + y2 + 2XY cos ( a ...
... write X sin a + Y sinẞ = L , X cos a + Y cosẞ = M , the expressions in Art . 9 may be written y sin w = L , x sin∞ = M sin w - L cosa ; whence But - sin2 w ( x2 + y2 + 2xy cos w ) = ( L2 + M2 ) sin2 w . L2 + M2 = X2 + y2 + 2XY cos ( a ...
Página 15
... write the equation in the form = m , and the question is , " to X 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 line ...
... write the equation in the form = m , and the question is , " to X 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 line ...
Página 16
... write down the equation that is , PM = RM + PR , or PM = m.OM + PR , y = mx + b . 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 , y = mx + b . 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 anglé , 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 sin a ...
... write the formula x cosa + y sina : -p , and consider a to denote the anglé , 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 sin a ...
Página 33
... Writing down by this article the general equation of a line through the intersection of the given lines , we determine k from the consideration that it must be satisfied by the co - ordinates x'y ' , and find for the required equation ...
... Writing down by this article the general equation of a line through the intersection of the given lines , we determine k from the consideration that it must be satisfied by the co - ordinates x'y ' , and find for the required equation ...
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Términos y frases comunes
anharmonic ratio asymptotes ax² axes bisected bisectors chord of contact circumscribing coefficients common tangents condition conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the co-ordinates find the equation find the locus fixed lines fixed point foci focus four points given circles given line given point Hence hyperbola imaginary points infinite distance inscribed intercept joining the points last Article length 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 rectangle right angles right line second degree sides sin² square substituting tangential equation theorem values vanish vertex vertices