The Elements of Geometry

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Leach, Shewell & Sanborn, 1894 - Geometry - 378 pages
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Page 165 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 39 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first 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 65 - 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 172 - 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 122 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 355 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 52 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 140 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 123 - In any proportion the terms are in proportion by composition and division ; that is, the sum of the first two terms is to their difference as the sum of the last two terms to their difference.
Page 207 - 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.

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