A Treatise on the Analytic Geometry of Three Dimensions

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Hodges, Figgis, & Company, 1882 - Geometry, Analytic - 612 pages
 

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Page 21 - and dividing by the square root of the sum of the squares of the coefficients of x, y, z.
Page 213 - a cone of any order may comprise two forms of sheet, viz. (1) a twin-pair sheet which meets a concentric sphere in a pair of closed curves, such that each point of the one curve is opposite to a point of the other curve
Page 383 - that the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles,
Page 369 - p is the perpendicular from the centre on the tangent plane at the point, and D is the diameter of the
Page 213 - sheet which meets a concentric sphere in a closed curve, such that each point of the curve is opposite to another point of the curve; (the plane affords an example of such a cone)
Page 28 - The angle between the line and the plane is the complement of the angle between the line and the perpendicular on the plane,
Page 3 - any plane is equal to the line multiplied by the cosine of the angle* which it makes with the
Page 17 - The angle between the planes is the same as the angle between the perpendiculars on them from the origin.
Page 120 - The edges of a tetrahedron intersect a quadric in twelve points, through which can be drawn four planes, each containing three points lying on edges passing through the same angle of the tetrahedron; then the lines of intersection of each such plane with the opposite face of the tetrahedron are generators of the same system of a certain hyperboloid.
Page 137 - we give the positive sign to X.*, the confocal conic will be an ellipse; it will also be an ellipse when

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