New Plane and Solid Geometry

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D.C. Heath & Company, 1908 - Geometry - 298 pages

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Page 168 - S' denote the areas of two whose radii are R and R', and diameters D and D', respectively. Then, | = "* = = • <337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Page 17 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 138 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 168 - Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii.
Page 50 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.
Page 128 - In any triangle, the product of any two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle, plus the square of the bisector.
Page 265 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Page 282 - A zone is a portion of the surface of a sphere included between two parallel planes.
Page 241 - Every section of a cylinder made by a plane passing through an element is a parallelogram. Given ABCD, a section of cylinder AC, made by plane through element AB.
Page 256 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

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