# Metrical Geometry; An Elementary Treatise on Mensuration

• Paperback
By (author)

List price: US\$15.85

Currently unavailable

AbeBooks may have this title (opens in new window).

## Description

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1881 edition. Excerpt: ...volume. Eule: Multiply the given volume by the cubed ratio of homologous lines. Vta? Formula: Vi.. Proof: The volumes of two similar solids are as the cubes of any two corresponding dimensions. Ww. 590; (Eu. XI. 33; Cv. VII. 73). Thus, for the sphere, by 88, Note. If a tetrahedron is cut by a plane parallel to one of its faces, the tetrahedron cut off is similar to the first. If a cone be cut by a plane parallel to its base, the whole cone and the cone cut off are similar. Exam. 90. The edge of a cube is 1 meter; find the edge of a cube of double the volume. The cube of the required number is to the cube of 1 as 2 is to 1; or, as3: l::2: l..-. as = 2.... x = 2 = 1-25992+. Ans. Thus a cube, with its edge 1-26 meters, is more than double a cube with edge 1 meter. Exam. 91. The three edges of a quader are as 3, 4, 7, and the volume is 777,924; find the edges. By 72, the volume of the quader, whose edges are 3, 4, 7, is 84; then g4. mm s 260,011, g(S). IRREGULAR SOLIDS. 96. Any small solid may be estimated by placing it in a vessel of convenient shape, such as a quader or a cylinder, and pouring in a liquid until the solid is quite covered; then noting the level, removing the solid, and again noting the level at which the liquid stands. The volume of the solid is equal to the volume of the vessel between the two levels. 97. If the solid is homogeneous, weigh it. Also weigh a cubic centimeter of the same substance. Divide the weight of the solid by the weight of the cubic centimeter. The quotient will be the number of cubic centimeters in the solid. From 73, we have the Formula: Vccm =-. o Exam. 92. A ball 5 centimeters in diameter weighs 431-97 grams. An irregular solid of the same substance weighs 13-2 grams; find its volume. The volume of the