A Treatise on Special Or Elementary Geometry

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Sheldon & Company, 1877 - Geometry - 239 pages
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Page 213 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 47 - Similar triangles are to each other as the squares of their homologous sides.
Page 203 - 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 132 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Page 121 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 161 - Oblique lines drawn from a point to a plane, meeting the plane at equal distances from the foot of the perpendicular, are equal; and of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 216 - 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 viii - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.
Page 152 - 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.

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