A Treatise on the Analytic Geometry of Three Dimensions |
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Common terms and phrases
ax² axes axis by² centre circle circular section coefficients condition cone confocal conjugate consecutive points constant coordinates corresponding cosẞ cosy cubic cuspidal cz² denote determine diameters differential direction-cosines directrix double point drawn ellipsoid envelope evidently expressed focal conic foci geodesic given line given point given surface Hence hyperbola hyperboloid infinity inflexional tangents last article line joining line of curvature locus meets the surface nodal normal osculating plane parallel perpendicular plane at infinity Plane Curves plane of xy plane passing point of contact polar plane quadric quartic radii radius of curvature radius vector reciprocal right angles right line ruled surface second degree sphere square substituting surface of revolution tangent plane tangential equation tetrahedron theorem touch the surface triangle U₁ umbilic values vanish vertex
Popular passages
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