Elements of Geometry: Geometry of space

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Harper & Brothers, 1898 - Geometry
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Page 325 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the two bases of the frustum.
Page 309 - A regular pyramid is a pyramid whose base is a regular polygon, and whose vertex lies in the perpendicular erected at the centre of the base.
Page 390 - 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 334 - If a pyramid is cut by a plane parallel to its base, the...
Page 392 - In two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. Let ABC and A'B'C' be two polar triangles. Let the sides AB and AC, produced if necessary, meet the side B'C
Page 426 - The lateral area of a frustum of a cone of revolution is equal to the circumference of a section equidistant from its bases multiplied by its slant height.
Page 268 - The acute angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of the plane.
Page 476 - The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 247 - If a straight line is parallel to a plane, the intersection of the plane with a plane passed through the line is parallel to the line.
Page 527 - The sum of the angles of a triangle is less than two right angles, and the propositions of the last chapter hold without restriction.

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