## Metrical Geometry: An Elementary Treatise on Mensuration |

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### Common terms and phrases

altitude angle axis B₁ B₂ base called chord circle circular measure circumference circumscribed common cone congruent constant contains corresponding cube cubic meters curved surface cylinder diagonal diameter difference distance divided double draw edges equal equivalent EXAM expression faces figure find the area find the volume Formula four frustum Given gives half Hence inscribed intersection joining length less limit lune mantel mass mean Multiply number of sides opposite parabola parallel perimeter perpendicular plane polygon polyhedron prism prismatoid Prismoidal Proof prove pyramid quader quadrilateral radii radius ratio rectangle regular polygon right-angled Rule sector segment sides similar slant height solid sphere spherical square meters straight line surface Take tangents tetrahedron third trapezoid triangle twice unit variable vertex whole Y₁

### Popular passages

Page 224 - 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 151 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.

Page 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.

Page 34 - From half the sum of the three sides, subtract each side separately; multiply the half sum and the three remainders together, and the square root of the product will be the area required.

Page 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.

Page 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