Plane and Solid Geometry: Suggestive Method

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Atkinson, Mentzer & Company, 1912 - Geometry - 376 pages
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Page 305 - 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 343 - 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 51 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 223 - ... indefinite length ; as CD. 12. The direction of the line AB means the direction from A toward B; of BA, the direction from B toward A.
Page 352 - 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 302 - 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 288 - The volume of any prism is equal to the product of its base by its altitude.
Page 290 - All these triangles meet in a point called the vertex. The perpendicular distance from the vertex to the plane of the base is the altitude or the height of the pyramid.
Page 361 - A zone is a portion of the surface of a sphere included between two parallel planes.
Page 227 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.

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