The principles of analytical geometry |
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The Principles of Analytical Geometry: Designed for the Use of Students Henry Parr Hamilton No preview available - 2016 |
Common terms and phrases
a²+b² a²b² abscissa Algebra ANALYTICAL GEOMETRY assumed asymptotes axes are rectangular bisect centre chords circle co-ordinate planes coefficients conical surface conjugate diameters constructed cubic equation denote diametral planes directrix distance drawn parallel ellipse and hyperbola equal equation becomes equation required equation sought equilateral hyperbola find the equation Geometry given line given point Hence hyperboloid imaginary inclination infinite latus rectum Let the equations Let y=0 locus major axis manner meet the curve negative ordinate origin parabola parallelepiped plane of xy point of intersection polar equation positive principal diameters PROB PROP quadratic equation rectangular axes right angles roots secant second order shewn sin² squares straight line supposed surface surface of revolution system of conjugate triangle vertex whence x²²
Popular passages
Page 62 - the hyperbola, the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the principal diameters
Page vii - To bisect a given triangle by a straight line drawn from a given point in one of its sides. Let
Page 80 - 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
Page ii - the first is to the third as the difference between the first and second is to
Page 144 - parallelepiped, the square of the diagonal is equal to the sum of the squares of the three edges.
Page 181 - that every section of a sphere, made by a plane, is a circle.
Page 19 - To find the area of a triangle, in terms of the co-ordinates of its angular points;
Page 2 - sides, and the line drawn from the vertex to the middle of the base, to find the