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abscissa Algebra Analytical Geometry assumed asymptotes axes are rectangular bisect centre CHAP chords co-ordinate planes coefficients conjugate diameters construction cos2 denote directrix distance draw drawn parallel ellipse and hyperbola ellipse or hyperbola equal equation becomes equation required equation sought find the equation geometrical given line given point Hence hyperbolic paraboloid hyperboloid imaginary inclination indeterminate equation infinite latus rectum locus major axis manner meet the curve ordinate origin parabola parallel to AY parallelepiped perpendicular dropped plane of xy point of intersection points of contact polar equation principal diameters principal vertex Prob Prop quadratic equation rectangular axes right angles roots secant second order shewn sides sin2 square straight line supposed surface surface of revolution system of conjugate theory of equations triangle unknown quantity vertex whence
Pàgina 3 - to divide a given straight line into two such parts, that the rectangle contained by the whole line and one of the parts, shall be equal to the square of the other part;
Pàgina 112 - the hyperbola, the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the principal diameters
Pàgina 15 - To bisect a given triangle by a straight line drawn from a given point in one of its sides. Let
Pàgina 130 - The rectangle contained by the focal distances of any point, is equal to the square of the semi-diameter conjugate to that which passes through the
Pàgina 10 - the first is to the third as the difference between the first and second is to
Pàgina 196 - parallelepiped, the square of the diagonal is equal to the sum of the squares of the three edges.
Pàgina 247 - that every section of a sphere, made by a plane, is a circle.
Pàgina 64 - To find the area of a triangle, in terms of the co-ordinates of its angular points;