Metrical Geometry: An Elementary Treatise on Mensuration |
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Metrical Geometry! an Elementary Treatise on Mensuration George Bruce Halsted No preview available - 2012 |
Common terms and phrases
15 meters altitude angular points axis B₁ B₂ basal edges base bisects chord circle circular measure circumference circumscribed cone congruent cube cubic centimeters cubic meters curved surface cylinder diagonals diameter distance divided ellipse equal equivalent EXAM Find the area Find the ratio find the volume frustum ƒx³ Given Hence hypothenuse inscribed intersection lateral edges length limit lune mantel medial meters long midpoint Multiply number of degrees number of sides nx² parabola paraboloid parallel planes parallel sides parallelepiped perigon perimeter perpendicular polyhedron prism prismatoid Prismoidal Prismoidal Formula Proof pyramid quader quadrilateral r₁ radians radii radius rectangle regular polygon revolution Rule Scholium sector segment semicircumference slant height solid angle sphere spherical polygon square meters straight line symmetrical tangents tetrahedron trapezoid variable vertex vertices w₁ x₁ Y₁ zoid
Popular passages
Page 220 - 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.
Page 232 - Universities, and is intended for a text-book, and not for an exhaustive treatise. Its peculiarities are the rigorous use of the Doctrine of Limits, as a foundation of the subject, and as preliminary to the adoption of the more direct and practically convenient infinitesimal notation and nomenclature : the early introduction of a few simple formulas and methods for integrating : a rather elaborate treatment of the use of infinitesimals in pure geometry ; and the attempt to excite and keep up the...
Page 32 - 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.
Page 149 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.
Page 107 - 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.
Page 229 - ... 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.
Page 84 - ... 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.
Page 18 - 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