Elements of Geometry (Google eBook)

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American Book Company, 1896 - Geometry - 540 pages
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Page 40 - If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C...
Page 476 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
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 215 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Page 46 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 389 - 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 148 - ... twice the product of one of these sides and the projection of the other side upon it.
Page 67 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 145 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 157 - The product of two sides of a triangle is equal to the product of the diameter of the circumscribed circle and the altitude upon the third side.

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