Metrical Geometry: An Elementary Treatise on Mensuration

Ginn, Heath & Company, 1881 - 232 sider

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Side 222 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 34 - From half the sum of the three sides subtract each side separately. Multiply the half sum and the three remainders together, and extract the square root of the product.
Side 151 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.
Side 109 - COR. 2. The volume of any truncated triangular prism is equal to the product of its right section by one third the sum of its lateral edges.
Side 231 - ... the successive steps from premise to conclusion. In each proposition a concise statement of what is given is printed in one kind of type, of what is required in another, and the demonstration in still another. The reason for each step is indicated in small type between that step and the one following ; and the author thus avoids the necessity of interrupting the process of demonstration to cite a previous proposition.
Side 86 - ... discussion has been carried on, the principal point discussed being the claims of the gramme, the metre, and the second, as against the gramme, the centimetre, and the second, — the former combination having an advantage as regards the simplicity of the name metre, while the latter combination has the advantage of making the unit of mass practically identical with the mass of unit-volume of water — in other words, of making the value of the density of water practically equal to unity.
Side 20 - The perimeters of regular polygons of the same number of sides have the same ratio as their radii or as their apothems. ADB A' D' B' Hyp. P and P' are the perimeters of two regular polygons having the radii OA and O'A', and the apothems OD and O'D', respectively. To prove P:P' = OA: O'A

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