Elements of geometry and trigonometry . and ahcdexlSo is that of the pyramid S-ahcdr. (Prop. XV^II.) ;iience two similar pyramids are to each other as the cubes oftheir homologous sides. General Scho/i/nif. The chief propositions of this Book relating to the solill. I/t B represent the base of a pyramid : ][ its altitude: thesolidity of the [)yramid will be B x ,11, or JI x .B, or {WW. Ec;t H represent the altitude of the fn/stum nf a pyramid,having parallel bases A and B ; >/AB will be the mean pro-portional Ix-tween thos(. I>ases ; and the solidity of t!ie frustumwill be iIIx(A !-B ^-V
Elements of geometry and trigonometry . and ahcdexlSo is that of the pyramid S-ahcdr. (Prop. XV^II.) ;iience two similar pyramids are to each other as the cubes oftheir homologous sides. General Scho/i/nif. The chief propositions of this Book relating to the solill. I/t B represent the base of a pyramid : ][ its altitude: thesolidity of the [)yramid will be B x ,11, or JI x .B, or {WW. Ec;t H represent the altitude of the fn/stum nf a pyramid,having parallel bases A and B ; >/AB will be the mean pro-portional Ix-tween thos(. I>ases ; and the solidity of t!ie frustumwill be iIIx(A !-B ^-VAB). In (iiK;, let P and j) repr<*sent the ynlidiiis of tirn simihirprisms or pyrrttnids ; A ami (t, two honiologous edges : then weshall haNe / A : a 166 GEOMETRY. BOOK VIII. THE THREE ROUND BODIES. 1. A cylinder is the solid generated by the revolution of arectangle ABCD, conceived to turn about the immoveableside AB. in this movement, the sides AD, BC, con-tinuing always perpendicular to AB, describeequal circles DHP, CGQ, which are calledthe bases of the cylinde7\ the side CD at thesame time describing the convex surface. The immoveable line AB is called the axisof Lite cylinder. Every section KLM, made in the cylinder,at right angles to the axis, is a circle equal toeither of the bases ; for, w^hilst the rectangleABCD turns about AB, the line KI, perpen-dicular to AB, describes a circle, equal to the base, and thiscircle is nothing else than the section made perpendicular tothe axis at the point I. Every section PQG, made through the axis, is a rectangledouble of the generating rectangle ABCD. 2. A cone is the solid generated by the revolution of a right-angled triangle SAB, conceived to turn about the immoveableside SA. In this movement, the side AB describesa circle BDCE, n
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
