## Solid Geometry, Volumes 6-9 |

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### Common terms and phrases

ABCDE altitude angles are equal auxiliary circle bisects called centre chord circumference circumscribed coincide convex cube curve diameter dihedral angles directrix distance draw drawn ellipse equidistant equivalent face angles feet Find the volume focal radii foci frustum given plane given point Hence homologous hyperbola inches inscribed intersection lateral area lateral edges lateral faces latus rectum limit locus lune parabola parallel planes parallelogram pass a plane perimeter perpendicular plane MN plane parallel plane passing polyhedral angle polyhedron prismatoid Proof PROPOSITION prove radius rectangular parallelopiped regular polygon regular pyramid respectively right circular cone right circular cylinder right prism right section S-ABC segment similar slant height sphere spherical angle spherical polygon spherical triangle square straight line symmetrical tangent tetrahedron THEOREM total surface triangular prism trihedral upper base vertex vertices

### Popular passages

Page 274 - If two planes are perpendicular to each other, a straight line drawn in one of them perpendicular to their intersection is perpendicular to the other plane.

Page 258 - ... of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.

Page 360 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 249 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.

Page 244 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.

Page 260 - COR. 1. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane.

Page 376 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 243 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 366 - A plane perpendicular to a radius at its extremity is tangent to the sphere. Let...

Page 395 - The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles.