An Elementary Treatise on Solid Geometry |
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Common terms and phrases
2fyz 2gzx 2hxy a² b2 angular points ax² axes axis by² centre chords circular sections co-ordinate planes conic conicoid constant curve of intersection cut the surface cylinder cz² developable surface dF dF dF diametral planes direction-cosines drawn edges ellipse ellipsoid enveloping cone equal Find the equation fixed point given plane given points Hence the equation hyperbola hyperbolic paraboloid hyperboloid imaginary Let the equation line of intersection lines of curvature meet the surface middle point normal origin osculating plane parabola parallelopiped plane section plane whose equation planes parallel point of intersection polar plane principal plane projection radius of curvature reciprocal rectangular respectively right angles ruled surface second degree Shew sphere squares surface of revolution surface whose equation tangent plane tetrahedron three conjugate diameters three lines three perpendicular x² y² Y₁ zero
Popular passages
Page 69 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 152 - A conic lection it the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Page 18 - AB; therefore AB is less than PQ, or the distance which is perpendicular to both straight lines is less than any other distance. 60. To find the shortest distance between two straight lines whose equations are given. Let the equations of the two straight lines be x — a._y — /3_z—Y , x — a y — /?' _ z — y I mn
Page 12 - Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third.
Page 230 - ... where p is the radius of curvature of the edge of regression, at the point where the generator touches it.
Page 240 - In this work the author has endeavoured to explain the principles of Algebra in as simple a manner as possible for the benefit of beginners, bestowing great care upon the explanations and proofs of the fundamental operations and rules. A TREATISE ON ALGEBRA.
Page 3 - The cosines of the angles which a straight line makes with the positive directions of the co-ordinate axes are called its direction-cosines, and we shall in future denote these cosines by the letters I, m, n.
Page 224 - ... geodesic tangents of a line of curvature, which intersect at right angles, intersect on a sphero-conic, may similarly be obtained without transforming the equation. Let Q be the point where the two geodesic tangents intersect at right angles...
Page 153 - Find the equation of the locus of a point the square of whose distance from a given line is proportional to its distance from a given plane.
Page 165 - BC of the tetrahedron, then HB, HC are in equilibrium, and the resultant of the system is the resultant of HA, HD, that is, 2HF, where F is the middle point of the opposite edge AD. But the resultant is 4HG, therefore G bisects the line HF. Hence the lines joining the middle points of opposite edges of a tetrahedron are concurrent and bisect each other. Seventh Meeting, May 14th, 1886.