Solid geometry and conic sections
MACMILLAN AND Company, 1873
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AC² altitude axis base BC² bisect called centre chord circle circular circumference common cone conic conjugate constant contain corresponding curve cylinder described diameter directrix distance divided Draw drawn edges ellipse equal Euclid extremities faces feet figure fixed focus follows formed four frustum given point harmonic height Hence hyperbola indefinitely intersect join lateral surface less limit line of intersection locus measured meet oblique opposite parabola parallel planes parallelepiped parallelogram pass pencil perpendicular plane MN polar poles polygon polyhedron prism produced projection Proof proportional prove pyramid radius ratio regular respectively right angles round segments sides similar Similarly solid sphere spherical triangle squares straight line surface tangent THEOREM touch transversal triangle ABC trihedral angle vertex vertices volume
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'.