Plane and Solid Geometry, Suggestive Method

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Atkinson, Mentzer, 1913 - Geometry - 476 pages
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Page 372 - 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 418 - 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 427 - 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 216 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Page 176 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 295 - If two parallel planes are cut by a third plane, the intersections are parallel. Given II planes MN and PQ cut by plane AD in lines AB and CD, respectively.
Page xxv - 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 429 - 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 384 - The lateral areas, or the total areas, of two similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. H H
Page 317 - The sum of any two face angles of a trihedral angle is greater than the third face angle.

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