Solid geometry and conic sectionsMACMILLAN AND Company, 1873 |
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Common terms and phrases
AC² altitude asymptotes axis BC² bisect called CD² central conic centre chord circle circumference cone conic section conjugate curve cylinder diameter dihedral directrix distance draw drawn edges ellipse equal and parallel equally distant Euclid XI faces Find the locus focus four right angles frustum given plane given point given straight line gonal height Hence join lateral surface latus rectum Let ABCD Let the plane line of intersection locus of points meet oblique ordinate parabola parallel planes parallel to CD parallelepiped parallelogram pass perpendicular plane ABC plane MN plane parallel polygon polyhedra polyhedron prism Proof prove pyramid radius ratio right angles right circular segments sides similar triangles Similarly sphere spherical triangle tangent tetrahedron THEOREM transversal triangle ABC trihedral angle vertex volume
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Page iii - SOLID GEOMETRY AND CONIC SECTIONS. With Appendices on Transversals and Harmonic Division. For the Use of Schools. By JM WILSON, MA New Edition.
Page v - Eleventh Book are usually all the Solid Geometry that a boy reads till he meets with the subject again in the course of his analytical studies. And this is a matter of regret, because this part of Geometry is specially valuable and attractive. In it the attention of the student is strongly called to the subject matter of the reasoning ; the geometrical imagination is exercised ; the methods employed in it are more ingenious than those in Plane Geometry, and have greater difficulties to meet ; and...
Page 5 - If a straight line be perpendicular to each of two straight lines at their point of intersection, it will be perpendicular to the plane in which these lines are.
Page 93 - ABCD. 2. A cone is the solid generated by the revolution of a rightangled triangle SAB, conceived to turn about the immoveable side SA. In this movement, the side AB describes a circle BDCE, named the base of the cone ; the hypothenuse SB describes the convex surface of the cone. The...
Page 14 - ... For a like reason, the sides BC, EF are equal and parallel ; so also are AC, DF; hence, the two triangles BAC, EDF, having their sides equal, are themselves equal (Prop.
Page 1 - The word tetrahedron is now often used to denote a solid bounded by any four triangular faces, that is, a pyramid on a triangular base ; and when the tetrahedron is to be such as Euclid defines, it is called a regular tetrahedron. Two other definitions may conveniently be added. A straight line is said to be parallel to a plane when they do not meet if produced. The angle made by two straight lines which do not meet is the angle contained by two straight lines parallel to them, drawn through any...
Page 15 - The angle which a straight line makes with its projection on a plane, is smaller than the angle it makes with any other line in the plane. Let AC be the given line, and BC its projection on the plane MN. Then the angle ACB is less than the angle made by AC with any other line in the plane, as CD. With C as a center and BC as a radius, describe a circumference in the plane...
Page 43 - As for example, The right cone is generated by the revolution of a right-angled triangle round one of the sides which contain the right angle.
Page 26 - Base ; and these two planes are to each other as the Squares of their Distances from the Vertex. LET ABCD be a...
Page 64 - If the first of two spherical triangles is the polar triangle of the second, then the second is the polar triangle of the first. If ABO (Fig. 14) is the polar triangle of ABC, then ABC is the polar triangle of A'B'C'.