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 3
... express the distance between two points x'y ' , x " y " , the axes of co - ordinates being supposed rectangular . and By Euclid 1. 47 , hence PQ2 = PS2 + SQ2 , but PS = PM- QM ' = y ' — y ' , QS - OM - OM'x ' -x " ; 82 = PQ2 = ( x ' — x ...
... express the distance between two points x'y ' , x " y " , the axes of co - ordinates being supposed rectangular . and By Euclid 1. 47 , hence PQ2 = PS2 + SQ2 , but PS = PM- QM ' = y ' — y ' , QS - OM - OM'x ' -x " ; 82 = PQ2 = ( x ' — x ...
Página 4
... Express that the distance of the point xy from the point ( 2 , 3 ) is equal Ans . ( x - 2 ) 2 + ( y − 3 ) 2 = 16 . to 4 . --- Ex . 4. Express that the point xy is equidistant from the points ( 2 , 3 ) , ( 4 , 5 ) . Ans . ( x - 2 ) 2 + ...
... Express that the distance of the point xy from the point ( 2 , 3 ) is equal Ans . ( x - 2 ) 2 + ( y − 3 ) 2 = 16 . to 4 . --- Ex . 4. Express that the point xy is equidistant from the points ( 2 , 3 ) , ( 4 , 5 ) . Ans . ( x - 2 ) 2 + ...
Página 9
... express the square of the distance of a point from the origin . Verify this by squaring and adding the expressions for X and Y in Art . 9 . Ex . 6. Verify in like manner in general that x2 + y2 + 2xy cosxOy = X2 + Y2 + 2XY cos XOY . If ...
... express the square of the distance of a point from the origin . Verify this by squaring and adding the expressions for X and Y in Art . 9 . Ex . 6. Verify in like manner in general that x2 + y2 + 2xy cosxOy = X2 + Y2 + 2XY cos XOY . If ...
Página 10
... express the distance between two points , in terms of their polar co - ordinates . Let P and Q be the two points , then ΟΙ OP = p ' , POB = 0 ' ; OQ = p " , QOB = 0 " ; PQ2 = OP " + 0Q - 20P . OQ.cos POQ , 12 712 S2 = p22 + p112 — 2p'p ...
... express the distance between two points , in terms of their polar co - ordinates . Let P and Q be the two points , then ΟΙ OP = p ' , POB = 0 ' ; OQ = p " , QOB = 0 " ; PQ2 = OP " + 0Q - 20P . OQ.cos POQ , 12 712 S2 = p22 + p112 — 2p'p ...
Página 17
... 0 and y = mx + b , there are two other forms in which the equation of a right line is frequently used ; these we next proceed to lay before the reader . D 22. To express the equation of a line MN in THE RIGHT LINE . 17.
... 0 and y = mx + b , there are two other forms in which the equation of a right line is frequently used ; these we next proceed to lay before the reader . D 22. To express the equation of a line MN in THE RIGHT LINE . 17.
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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