Solid Geometry

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Atkinson, Mentzer, 1913
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Page 394 - If two polygons are similar, they can be divided into the same number of triangles, similar each to each, and similarly placed. 294. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar.
Page 440 - 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 449 - Show that the locus of a point such that the sum of the squares of its distances from two fixed points is constant, is a circle.
Page 289 - The pupil will be much helped in the study of solid geometry by noticing that most of the theorems are but extensions or generalizations of theorems previously studied in the plane geometry. 437. The relations of the parts of a figure or figures in a plane are not changed by moving the plane containing them from one position to another. 50 (4). 438. A PLANE. A surface such that the straight line joining any two of its points lies entirely in the Surface is a plane. (18.) A plane is unlimited...
Page 451 - If two triangles have the three sides of one equal respectively to the three sides of the other, the triangles are congruent, (sss) REMARK 1.
Page 339 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 391 - O'G O'A' X O'B' O'C' OA X OB X OC V' O'EX O'F O'G O'EX O'FX O'G QED 633. DEF. Similar polyhedrons are polyhedrons that have the same number of faces similar each to each and similarly placed, and have their homologous polyhedral angles equal.
Page 294 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Page 456 - The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference.
Page 414 - Every section of a circular cone made by a plane parallel to the base is a circle. Let the section abed of the circular cone S-ABCD be parallel to the base. To prove that abed is a circle. Proof. Let 0 be the centre of the base, and let o be the point in which the axis SO pierces the plane of the parallel section.

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