Solid Geometry and Conic Sections: With Appendices on Transversals, and Harmonic Division |
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AC² altitude asymptotes axis BC² bisect called central conic centre chord circumference cone conic section conical surface conjugate curve cylinder diameter dihedral directrix distances draw drawn edges ellipse equal and parallel equally distant Euclid XI faces Find the locus focus four right angles frustum given plane given point height Hence hyperbola 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 polar polygon polyhedra polyhedron prism Proof prove pyramid radius right angles right circular segments sides similar triangles Similarly sphere spherical triangle tangent tetrahedron THEOREM transversal triangle ABC trihedral angle vertex volume
Popular passages
Page 80 - Prove that the lines joining the vertices of a triangle to the points of contact of the inscribed circle are concurrent.
Page iii - 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 99 - The locus of the foot of the perpendicular from the focus on a moving tangent is the circle on the major axis as diameter. 3. The locus of the point of intersection of perpendicular tangents is a circle with radius Va>
Page 2 - The projection of a point on a plane is the foot of the perpendicular let fall from the point to the plane. Def.
Page 51 - What is the locus of points at a given distance from a given finite straight line ? 9. To bisect the lateral surface of a right cone by a plane parallel to the base. 10. To divide in any required ratio the lateral surface of a cone by a plane parallel to the base.
Page 10 - Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Page 15 - The angle which a straight line makes with its projection on a plane is less than that which it makes with any other straight line that meets it in that plane.
Page 43 - A), and the volume of the cylinder THE CONE. • Def. 26. A conical surface in general is produced by a straight line constrained to pass through one fixed point, and to intersect a curve in space. Def. 27. A right circular cone is the solid produced by the revolution of a right-angled triangle round one of the sides containing the right angle. Thus let ABC be a triangle right-angled at B, and let it revolve round AB.
Page 26 - IV. another, that is, AG, EC, FD, BH have a common point of bisection. COR. Hence a parallelepiped is a prism on a parallelogram as base. THE PYRAMID. THEOREM 23. The areas of the sections of a pyramid made by planes parallel to the base are proportional to the squares of their distances from the vertex. Let ABCD be a pyramid on a triangular base BCD, and let EFG be a section parallel to the base.