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 страници |
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Страница xiii
... become a Circle , while a given Line passes to Infinity 318 Orthogonal Projection Determination of Focus of Section of a right Cone Locus of Vertices of right Cones from which a given Conie may be cut Method of deducing properties of ...
... become a Circle , while a given Line passes to Infinity 318 Orthogonal Projection Determination of Focus of Section of a right Cone Locus of Vertices of right Cones from which a given Conie may be cut Method of deducing properties of ...
Страница 7
... . Here we have a = 0 , B = 90 + 0 , a ' = 90-0 , B'— 0 ; and the general formulæ become y = X sin0 + Y cose , x = X cos 0 - Y sin 0 : y P X S N Ꮎ MR x the truth of which may also be seen directly , TRANSFORMATION OF CO - ORDINATES . 7.
... . Here we have a = 0 , B = 90 + 0 , a ' = 90-0 , B'— 0 ; and the general formulæ become y = X sin0 + Y cose , x = X cos 0 - Y sin 0 : y P X S N Ꮎ MR x the truth of which may also be seen directly , TRANSFORMATION OF CO - ORDINATES . 7.
Страница 8
... become if the origin be transformed to the point ( 2 , 3 ) ? - - Ans . X2 + Y2 = 31 . Ex . 2. The co - ordinates of a point to one set of rectangular axes satisfy the relation y2 — x2 6 : what will this become if transformed to axes ...
... become if the origin be transformed to the point ( 2 , 3 ) ? - - Ans . X2 + Y2 = 31 . Ex . 2. The co - ordinates of a point to one set of rectangular axes satisfy the relation y2 — x2 6 : what will this become if transformed to axes ...
Страница 13
... becomes imaginary . * The learner is recommended to use paper ruled into little squares , which is sold under the name of logarithm paper . 17. The whole science of Analytic Geometry is founded on THE RIGHT LINE . 13.
... becomes imaginary . * The learner is recommended to use paper ruled into little squares , which is sold under the name of logarithm paper . 17. The whole science of Analytic Geometry is founded on THE RIGHT LINE . 13.
Страница 16
... - 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 .
... - 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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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