## The Elements of Geometry |

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AB'C ABC and DEF ABCD approaches the limit axis base and altitude base multiplied bisect centre circle circular cone circumference circumscribed cone of revolution COROLLARY cube denote the volume diagonals diameter diedral angles dimensions distance equal and parallel equal bases equally distant equivalent face angles Find the volume frustum generatrix Hence inscribed intersection lateral area lateral edges lateral faces lateral surface lower base lune mutually equiangular O-ABC parallel planes parallelogram perimeter perpendicular to MN plane MN polar triangle prism is equal PROPOSITION radii radius rectangles rectangular parallelopiped regular polygon regular pyramid right angles right section SCHOLIUM similar polyedrons slant height sphere spherical angle spherical excess spherical polygon spherical pyramid spherical triangle squares tetraedron THEOREM tri-rectangular triangle triangles ABC triangular prism triangular pyramid triedral truncated upper base vertex vertices Whence

### Popular passages

Page 323 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.

Page 315 - A Sphere is a solid bounded by a curved surface all points of which are equally distant from a point within called the centre.

Page 324 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...

Page 349 - The lateral or total areas of two similar cones of revolution are to each other as the squares of their slant heights...

Page 252 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane.

Page 330 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...

Page 326 - If from the vertices of a spherical triangle as poles arcs of great circles are described, another spherical triangle is formed which is called the polar triangle of the first.

Page 334 - ADC ; the last two are therefore right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular to the base, and bisects the vertical angle.

Page 244 - 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.

Page 279 - DEF. The slant height of a regular pyramid is the altitude of any one of the lateral faces.