Elements of Geometry

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Harper & brothers, 1896 - Geometry - 540 pages
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Page 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Page 5 - If of three quantities the first is greater than the second and the second greater than the third, then the first is greater than the third.
Page 432 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
Page 393 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC...
Page 185 - To construct a square equivalent to the sum of any number of given squares.
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 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 70 - The three medians of any triangle intersect in a common point which is two-thirds of the distance from each vertex to the middle of the opposite side.
Page 474 - The area of any regular polygon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed polygons of half the number of sides.
Page 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.

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