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abscissa Analytical Geometry assumed asymptotes axes are rectangular bisect BOLA centre chords co-ordinate planes coefficients conjugate diameters construction cosp denote DETERMINATE PROBLEMS directrix distance draw drawn parallel ELLIPSE AND HYPER 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 negative ordinate origin parabola parallelepiped perpendicular dropped 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 square straight line supposed surface surface of revolution system of conjugate triangle unknown quantity whence
Pàgina 11 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Pàgina 3 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Pàgina 248 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Pàgina 120 - Fig. 83,84. conjugate diameters is equal to the sum of the squares of the...
Pàgina 70 - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
Pàgina 119 - ... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Pàgina 18 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Pàgina 72 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Pàgina 83 - If two chords intersect in a circle, the difference of their squares is equal to the difference of the squares of the difference of the segments.