An Elementary Treatise on Solid Geometry |
Common terms and phrases
2fyz 2gzx 2hxy a² b2 angular points ax² axes axis b2 c² by² centre chords circular sections co-ordinate planes confocal conic consecutive constant curve of intersection cut the surface cylinder cz² developable surface dF dF dF diametral planes direction-cosines drawn dx dy edges ellipse ellipsoid enveloping cone equal find the condition Find the equation Find the locus fixed point given conicoid given plane given points hyperbolic paraboloid hyperboloid Let the equation line of intersection lines of curvature locus lx+my+nz meet the surface middle point normal osculating plane parabola parallelopiped plane section plane whose equation point of intersection polar plane principal planes quadric reciprocal respect right angles ruled surface second degree sheet Shew sphere squares surface of revolution surface whose equation tangent plane tetrahedron three conjugate diameters three perpendicular x² y² Y₁ zero
Popular passages
Page 44 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 171 - 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 95 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Page 14 - 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 20 - CLD be the given straight lines, and let KL be a line which is perpendicular to both. Then KL is the shortest distance between the given lines, for it is the projection of the line joining any other two points on the given linesl.
Page 5 - 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 46 - ... 2wk + d=0 ............ (i). Now the equation (i) represents a cylinder whose generating lines are parallel to the axis of z, and which is cut by the plane z = 0 in the curve represented by (i). Since parallel sections of a cylinder are similar and similarly situated curves, the section of the surface F (x, y, z) = 0 by z= k is similar to the conic represented by (i) and z — 0; and all such conies, for different values of k, are clearly similar and similarly situated : this proves the proposition....
Page 91 - Prove that the sum of the products of the perpendiculars from the two extremities of each of two conjugate diameters on any tangent to an ellipse is equal to the square of the perpendicular from the centre on that tangent, 34. Q is a point on the normal at any point P of an ellipse whose...
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.