Plane and Solid Geometry

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Macmillan, 1901 - Geometry - 370 pages

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Page 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.
Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 209 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Page 31 - The median to the base of an isosceles triangle is perpendicular to the base.
Page 180 - 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 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Page 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 71 - The midpoints of two opposite sides of a quadrilateral and the midpoints of the diagonals determine the vertices of a parallelogram. * Ex.
Page 127 - If a line parallel to one side of a triangle intersects the other two sides, either side is to one of its segments as the other side is to its corresponding segment. For AD:DB = AE : EC.
Page 143 - Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. ED Hyp. In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'.

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