Elements of geometry and trigonometry . MENSURATION OF SOLIDS. 289. Let L=AB, the length ofthe base. /=:GII, tlie length otthe edge. 6 = BC, the breadth oftiie base. h = FG, the altitude ofthe wedge. Then, L —/=AB —GH-AM. Suppose AB, the length of the base, to be equal to GH, thelength of the edge, the solidity will then be equal to half theparallelopipedon having the same base and the same altitude(Book Vll. Prop. VI1.). Hence, the solidity will be equalto ibih (Book VIL Prop. XIV.). If the length of the base is greater than that of the edge,let a section MXG be made parallel to the end BCH.
Elements of geometry and trigonometry . MENSURATION OF SOLIDS. 289. Let L=AB, the length ofthe base. /=:GII, tlie length otthe edge. 6 = BC, the breadth oftiie base. h = FG, the altitude ofthe wedge. Then, L —/=AB —GH-AM. Suppose AB, the length of the base, to be equal to GH, thelength of the edge, the solidity will then be equal to half theparallelopipedon having the same base and the same altitude(Book Vll. Prop. VI1.). Hence, the solidity will be equalto ibih (Book VIL Prop. XIV.). If the length of the base is greater than that of the edge,let a section MXG be made parallel to the end BCH. Thewedge will then be divided into the triangular prism BCH-M,and the quadrangular pyramid G-AMND. The solidity of the prism =]h/tl, the solidity of the pyramid-=-j6//(L—/);* and their sum, {bhl-^^hh{lL—/)=-}M3/ + i6/i2L—lhlr2l=lbk(lL-\-l). if the length of the base is less than the length of the edge,the solidity of tl^ie wedge will be equal to the difference be-tween the prism and pyramid, and we shall have for the solid-ity of the wedge, }J)ld—^hh{
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