## 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 |

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according angle assumed asymptotes axes axis base becomes called centre CHAP chords circle co-ordinates coincides conjugate diameters constructed contained cosē curve denote described determined difference direction distance dividing draw drawn dropped ellipse equal equation equation becomes expressed find the equation follows former formulas Geometry given line given point Hence hyperbola imaginary inclination infinite intersection join known latter locus manner means meet negative obtained origin parabola parallel passes perpendicular plane plane of xy positive PROB problem produced projections PROP proportional proved quantity radius rectangular referred represent respectively right angles roots second order sides situated sought sphere squares straight line substitution supposed surface system of conjugate tangent trace triangle values whence

### Popular passages

Page 68 - 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 1 - To bisect a given triangle by a straight line drawn from a given point in one of its sides. Let

Page 86 - 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 iv - the first is to the third as the difference between the first and second is to

Page 152 - parallelepiped, the square of the diagonal is equal to the sum of the squares of the three edges.

Page 201 - that every section of a sphere, made by a plane, is a circle.

Page 20 - To find the area of a triangle, in terms of the co-ordinates of its angular points;

Page 4 - sides, and the line drawn from the vertex to the middle of the base, to find the