## Solid Geometry, Volumes 6-9 |

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### Common terms and phrases

ABCDE altitude approaches axis base bisects called centre chord circle circular cone circumference circumscribed coincide common cone construct convex corresponding cube curve denote described diameter difference dihedral angles directrix distance divided draw drawn edges element ellipse equal equivalent face angles faces feet Find Find the volume foci focus formed frustum given plane given point greater Hence hyperbola inches included inscribed intersection lateral area lateral edges less limit measure meet opposite parabola parallel parallelopiped perpendicular plane plane MN plane passing pole polygon polyhedron prism Proof PROPOSITION prove pyramid radii radius ratio regular pyramid respectively right circular segment sides similar slant height solid sphere spherical triangle square straight line surface symmetrical tangent tetrahedron THEOREM third triangular trihedral vertex vertices volume zone

### 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.