## Solid Geometry |

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### Common terms and phrases

AABC ABCDE altitude angles are equal axis base edge bisecting plane circle circumference circumscribed cone cube cylinder D-ABC denote dihedral angles dimensions distance drawn equal bases equal parts occur equal spheres equally distant equi-dimension face angles Find the volume formula frustum geometry given plane Hence homologous inches inscribed isosceles lateral and total lateral area lateral edges lateral faces locus lune mutually equiangular mutually equilateral number of sides parallel planes perimeter perpendicular plane angles plane geometry plane MN polar triangle pole polyhedral angle prismatoid Proof prove pyramid whose base radii radius ratio rectangular parallelopiped regular polygons regular polyhedrons regular pyramid respectively right angle slant height sphere whose diameter spherical angle spherical excess spherical polygon spherical triangle straight line surface symmetrical tangent tetrahedron THEOREM total area triangular prism trihedral V-ABC vertex vertices ZABC

### Popular passages

Page 253 - Conversely, when two sides of a triangle are equal respectively to two sides of another, but the third side of the first is greater than the third side of the second...

Page 254 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.

Page 301 - Any oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Let ABCDE-A' be the oblique prism. At any point F in the edge AA', pass a plane perpendicular to AA' and forming the right section FGHIK Produce AA...

Page 253 - 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 389 - COR. 2. The volume of any truncated triangular prism is equal to the product of its right section by one third the sum of its lateral edges.

Page 373 - 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 347 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 396 - If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal, respectively, to two sides and the included angle of the other, I.

Page 254 - In any proportion the terms are in proportion by division; that is, the difference of the first two terms is to the second term as the difference of the last two terms is to the fourth.

Page 254 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.