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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Резултати 1 - 5 от 36.
Страница 31
... vanish , as they evidently ought to do , since the value of the total area must be independent of the manner in which we divide it into triangles ; and we have for double the area - - This may be otherwise written , - -- - ... - x ̧ ...
... vanish , as they evidently ought to do , since the value of the total area must be independent of the manner in which we divide it into triangles ; and we have for double the area - - This may be otherwise written , - -- - ... - x ̧ ...
Страница 34
... vanish identically , the lines represented by them meet in a point . Its co - ordinates are found by solving between any two , to be } ( x ' + x " + x ' ' ' ) , } ( y ' + y ' ' + y ' " ) . Ex . 2. Prove the same thing , taking for axes ...
... vanish identically , the lines represented by them meet in a point . Its co - ordinates are found by solving between any two , to be } ( x ' + x " + x ' ' ' ) , } ( y ' + y ' ' + y ' " ) . Ex . 2. Prove the same thing , taking for axes ...
Страница 45
... vanish together , and we get for our locus bx - ay = 0 , the equation of the diagonal of the parallelogram . Ex . 7. Given a point and two fixed lines : draw any two lines through the fixed point , and join transversely the points where ...
... vanish together , and we get for our locus bx - ay = 0 , the equation of the diagonal of the parallelogram . Ex . 7. Given a point and two fixed lines : draw any two lines through the fixed point , and join transversely the points where ...
Страница 54
... vanish identically . Ex . 2. Any two of the external bisectors of the angles of a triangle meet on the third internal bisector . Attending to the convention about signs , it is easy to see that the equations of two external bisectors ...
... vanish identically . Ex . 2. Any two of the external bisectors of the angles of a triangle meet on the third internal bisector . Attending to the convention about signs , it is easy to see that the equations of two external bisectors ...
Страница 60
... vanish when multiplied by sin2C , sin2A , sin2B , and added together . Ex . 4. Find , by Art . 25 , expressions for the sine , cosine , and tangent of the angle between la + mẞ + ny , l'a + m'ß + n'y . Ex . 5. Prove that a cos A + ẞ cos ...
... vanish when multiplied by sin2C , sin2A , sin2B , and added together . Ex . 4. Find , by Art . 25 , expressions for the sine , cosine , and tangent of the angle between la + mẞ + ny , l'a + m'ß + n'y . Ex . 5. Prove that a cos A + ẞ cos ...
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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