A Treatise on the Analytic Geometry of Three DimensionsHodges, Smith, & Company, 1862 - 465 pàgines |
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Frases i termes més freqüents
ax² axes axis centre circle circular section co-ordinates coefficients condition confocal conjugate consecutive points constant corresponding cos² cosẞ cosy cubic curve of intersection denotes determine developable diameters differential direction-cosines directrix double point drawn edges ellipse ellipsoid envelope equal equation evidently fixed plane fixed point focal conic foci focus geodesic given line given point Hence hyperbola hyperboloid infinity last article line joining line of curvature meets the surface osculating plane paraboloid parallel perpendicular plane at infinity plane curve plane meets plane of xy point of contact point x'y'z polar plane principal planes proved Art quadric radii radius of curvature radius vector reciprocal represents right angles right line ruled surface second degree sphere sphero-conic substituting surface of revolution tangent plane tetrahedron theorem triangle umbilic values vanish λ²
Passatges populars
Pàgina 174 - To find the locus of the foot of the perpendicular from the focus of a sphero-conic on the tangent.
Pàgina 295 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Pàgina 137 - If a quadrilateral be inscribed in a conic, its opposite sides and diagonals will intersect in three points such that each is the pole of the line joining the other two.
Pàgina 154 - Hence we may immediately infer from the last article that the projection of the intersection of two confocal quadrics on a plane of circular section of one of them is a conic whose foci are the similar projections of the umbilics ; and, again, that given any curve...
Pàgina 199 - From the expressions in this article we deduce at once, as in the theory of central conies, that the sum of the reciprocals of the radii of curvature of two normal sections at right angles to each other is constant ; and again, if normal sections be made through a pair of conjugate tangents (see Art.
Pàgina 276 - ... is impossible. Cor. 3. The centre of a sphere, and the centre of any small circle of that sphere, are in a straight line perpendicular to the plane of the circle. Cor. 4. The square of the radius of any small circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XI., C. 1): hence, circles which are equally distant from the centre, are equal ; and of two circles which are unequally...