Elements of Plane and Solid Geometry

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Ginn, Heath, 1882 - Geometry - 398 pages
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Page 120 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Page 42 - 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 191 - In any proportion, the product of the means is equal to the product of the extremes.
Page 178 - Two triangles having 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 165 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 191 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Page 151 - BC : B'C' : : CD : C' D' etc. 278 (the homologous sides of similar polygons arc proportional). ••• AB + BC, etc. : A'B' + B'C', etc. : : AB : A'B', 266 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent). That is P : P
Page 325 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 75 - A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let MB be perpendicular to the radius OA at A.
Page 110 - Two sides of a triangle, and the angle opposite one of them, being given, to construct the triangle. Let A and B be the given sides, and C the given angle.

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