A Treatise on Special, Or Elementary Geometry

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Sheldon, 1872 - Geometry - 239 pages
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Page 60 - The homologous sides of similar triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides.
Page 137 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 216 - A sphere is a solid, bounded by one continued convex surface, every point of which is equally distant from a point within, called the centre.
Page 145 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Page 113 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Page 116 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 9 - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.
Page 165 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 14 - The logarithm of a quotient equals the logarithm of the dividend minus the logarithm of the divisor.
Page 156 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.

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