Elements of Plane and Solid Geometry

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Ginn, 1884 - Geometry - 406 pages

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Page 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Page 50 - 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 179 - ... 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 158 - The homologous altitudes of two similar triangles have the same ratio as any two homologous sides. In the two similar triangles ABC and A'B'C', let the altitudes be B 0 and B'O'.
Page 349 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 310 - 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.
Page 157 - A' B'. AB : A'B' : : B С : 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 188 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 115 - From A as a centre, with a radius equal to o, describe an arc ; and from B as a centre, with a radius equal to m, describe an arc intersecting the former arc at C.
Page 137 - ... if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth : or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...

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