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 6
... evidently , equally true , whether the axes be oblique or rectangular . 9. Secondly , let the directions of the axes be changed , while the origin is unaltered . * The beginner may postpone the rest of this chapter till he has read to ...
... evidently , equally true , whether the axes be oblique or rectangular . 9. Secondly , let the directions of the axes be changed , while the origin is unaltered . * The beginner may postpone the rest of this chapter till he has read to ...
Página 9
... evidently cannot contain powers of x or y above the mth degree . Neither can transformation diminish the degree of an equation , since by transforming the transformed equation back again to the old axes , we must fall back on the ...
... evidently cannot contain powers of x or y above the mth degree . Neither can transformation diminish the degree of an equation , since by transforming the transformed equation back again to the old axes , we must fall back on the ...
Página 12
... evidently does not afford us conditions enough to determine the two unknown quantities x , y ; and an inde- finite number of systems of values of x and y can be found which will satisfy the given equation . And yet the co - ordinates of ...
... evidently does not afford us conditions enough to determine the two unknown quantities x , y ; and an inde- finite number of systems of values of x and y can be found which will satisfy the given equation . And yet the co - ordinates of ...
Página 15
... evidently is a right line OP , passing through O , the point of intersection of the two fixed lines , and dividing the angle between them in such a manner that sin POM = m sin PON . If the axes be rectangular , sin PON = cos POM ...
... evidently is a right line OP , passing through O , the point of intersection of the two fixed lines , and dividing the angle between them in such a manner that sin POM = m sin PON . If the axes be rectangular , sin PON = cos POM ...
Página 16
... therefore y - b , the question becomes : " To find the locus of a point , such that , if we draw PT parallel to OY to meet the fixed line QT , PT may be to QT in a constant ratio ; " and this locus evidently is the 16 THE RIGHT LINE .
... therefore y - b , the question becomes : " To find the locus of a point , such that , if we draw PT parallel to OY to meet the fixed line QT , PT may be to QT in a constant ratio ; " and this locus evidently is the 16 THE RIGHT LINE .
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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