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 16
... Draw OR through the origin parallel to PQ , and let the ordinate PM meet OR in R. Now it is plain ( as in Art . 18 ) ... draw the line QT parallel to OM , TM will beb , and PT therefore y - b , the question becomes : " To find the locus of ...
... Draw OR through the origin parallel to PQ , and let the ordinate PM meet OR in R. Now it is plain ( as in Art . 18 ) ... draw the line QT parallel to OM , TM will beb , and PT therefore y - b , the question becomes : " To find the locus of ...
Página 39
... drawn to intersect them parallel to a third fixed line OC , to find the locus of the point P where AB is cut in a given ratio ; viz . PA = nAB , Let us take the lines OA , OC for axes , and let the equation of OB be y = mx . Then since ...
... drawn to intersect them parallel to a third fixed line OC , to find the locus of the point P where AB is cut in a given ratio ; viz . PA = nAB , Let us take the lines OA , OC for axes , and let the equation of OB be y = mx . Then since ...
Página 44
... drawn parallel to the base of a triangle , and the points where it meets the sides joined to any two fixed points on the base ; to find the locus of the point of intersection of the joining lines . We shall preserve the same axes , & c ...
... drawn parallel to the base of a triangle , and the points where it meets the sides joined to any two fixed points on the base ; to find the locus of the point of intersection of the joining lines . We shall preserve the same axes , & c ...
Página 47
... drawn parallel to OC , as in Ex . 4 , p . 39 , meeting two fixed lines in points B , B ' ; and PA2 is taken = PB.PB ' , find the locus of P. Ans . mx ( m'x + n ' ) = y ( mx + m'x + n ' ) . Ans . 2mx ( m'x + n ' ) = y ( mx + m'x + n ...
... drawn parallel to OC , as in Ex . 4 , p . 39 , meeting two fixed lines in points B , B ' ; and PA2 is taken = PB.PB ' , find the locus of P. Ans . mx ( m'x + n ' ) = y ( mx + m'x + n ' ) . Ans . 2mx ( m'x + n ' ) = y ( mx + m'x + n ...
Página 50
... drawn through a fixed point according to any given law . Ex . 1. A and B are two fixed points ; draw through B any line , and let fall on it a perpendicular from A , AP ; produce AP so that the rectangle AP.AQ may be constant ; to find ...
... drawn through a fixed point according to any given law . Ex . 1. A and B are two fixed points ; draw through B any line , and let fall on it a perpendicular from A , AP ; produce AP so that the rectangle AP.AQ may be constant ; to find ...
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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