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 1
... Suppose , for example , that we are given PN = a , PM = b , Now , if Y P N X ' X M Y we need only measure OM = a and ON = b , and draw the parallels PM , PN which will intersect in the point required . It is usual to denote PM parallel ...
... Suppose , for example , that we are given PN = a , PM = b , Now , if Y P N X ' X M Y we need only measure OM = a and ON = b , and draw the parallels PM , PN which will intersect in the point required . It is usual to denote PM parallel ...
Página 3
... Suppose , in the last figure , the angle YOX oblique and = w , then and or , PSQ = 180 ° - w , PQ * = PS " + QS2-2PS.QS.cos PSQ , - PQ2 = ( y ' —y " ) " + ( x ' — x ' ) 2 + 2 ( y ' - y " ) ( x - x " ) cosw . - Similarly , the square of ...
... Suppose , in the last figure , the angle YOX oblique and = w , then and or , PSQ = 180 ° - w , PQ * = PS " + QS2-2PS.QS.cos PSQ , - PQ2 = ( y ' —y " ) " + ( x ' — x ' ) 2 + 2 ( y ' - y " ) ( x - x " ) cosw . - Similarly , the square of ...
Página 4
... suppose we are given three points P , Q , R in a right line , and know the distances PQ , QR , we may infer , PR = PQ + QR . And with the explana- tion now given , this equation remains true , even though the point R lie between P and Q ...
... suppose we are given three points P , Q , R in a right line , and know the distances PQ , QR , we may infer , PR = PQ + QR . And with the explana- tion now given , this equation remains true , even though the point R lie between P and Q ...
Página 6
... suppose the origin changed , but the new axes parallel to the old ; secondly , we shall suppose the directions of the axes changed , but the origin to remain unaltered ; and thirdly , we shall suppose both origin and directions of axes ...
... suppose the origin changed , but the new axes parallel to the old ; secondly , we shall suppose the directions of the axes changed , but the origin to remain unaltered ; and thirdly , we shall suppose both origin and directions of axes ...
Página 14
... suppose b to be equal to nothing , we see that the equation y = 0 denotes the axis OX ; and in like manner that x = 0 denotes the axis OY . Let us now proceed to the case next in order of simplicity , and let us examine what relation ...
... suppose b to be equal to nothing , we see that the equation y = 0 denotes the axis OX ; and in like manner that x = 0 denotes the axis OY . Let us now proceed to the case next in order of simplicity , and let us examine what relation ...
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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