A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, and Company, 1879 - 399 páginas |
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Otras ediciones - Ver todas
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2016 |
Términos y frases comunes
anharmonic ratio asymptotes ax² axes bisected bisector chord of contact circumscribing coefficients coincide common tangents condition conic section conjugate diameters constant corresponding denote determine directrix double contact drawn ellipse equal find the equation find the locus fixed line fixed point foci focus four points geometrically given circles given line given point harmonic Hence hyperbola imaginary points infinite distance inscribed intercept last article line at infinity line joining line meets meet the curve middle points origin parabola parallel perpendicular point of contact point x'y points at infinity points of intersection polar polar equation pole proved quadratic quadrilateral radical axis radius vector reciprocal rectangle right angles right line roots second degree sides square substituting tangential equation theorem transform trilinear coordinates values vanish vertex vertices
Pasajes populares
Página 240 - Find the locus of a point, the square of whose distance from a given point is proportional to its distance from a given line.
Página 241 - A conic is the locus of a point whose distance from a fixed point called the focus is in a constant ratio to its distance from a fixed line called a directrix.
Página 179 - conic' is the locus of a point P which moves so that its distance from a fixed point S, called the 'focus,' is in a constant ratio to its distance from a fixed line called the 'directrix.
Página 242 - If two conies have each double contact with a third, their chords of contact with that conic, and two of the lines through their common points, will meet in a point and form a harmonic pencil. Let...
Página i - SALMON.— A TREATISE ON CONIC SECTIONS, containing an Account of some of the most Important Modern Algebraic and Geometric Methods.
Página 126 - The angles of the triangle formed by joining the points of contact of the inscribed circle of a triangle with the sides are equal to the halves of the supplements of the corresponding angles of the original triangle. 4. If ABC, A'B'C...
Página 97 - If through any point 0 on the circumference of a" circle any three chords be drawn, and on each as a diameter a circle be described; these three circles (which of course all pass through 0) will intersect in three other points which lie on one right Une.
Página 230 - R is equal to the cube of the normal divided by the square of the semiparameter, R= _ ___ ?, since N = 2/w sec w.
Página 229 - There are three points on a conic, whose osculating circles pass through a given point on the curve...
Página 5 - To find the coordinates of the middle points of the sides of the triangle, the coordinates of whose vertices are (2, 3), (4, — 5), (— 3, — 6).