A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry

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J.B. Lippincott, 1872 - Geometry - 368 pages
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Page 245 - It will be shown that every section of a sphere made by a plane is a circle...
Page 128 - The area of a rectangle is equal to the product of its base and altitude.
Page 216 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 129 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 219 - THEOREM. 611. -A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 44 - Every point in the bisector of an angle is equally distant from the. sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Page 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Page 263 - 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 107 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 127 - Any two rectangles are to each other as the products of their bases by their altitudes.

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