An Elementary Geometry: Plane, Solid and Spherical

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1880 - Geometry - 240 pages
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Page 166 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 13 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 41 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 198 - Each side of a spherical triangle is less than the sum of the other two sides.
Page 75 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 203 - In an isosceles spherical triangle, the angles opposite the equal sides are equal. In the spherical triangle ABC, let AB equal AC.
Page 220 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.
Page 136 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Page 199 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Page 162 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. GM is a right section of oblique prism AD', and GM.' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM'. Proof. The lateral edges of GM

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