Elements of geometry and trigonometry . 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, named the hase of the cone ;the hypothenuse SB describes the convexsurface of the
Elements of geometry and trigonometry . 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, named the hase of the cone ;the hypothenuse SB describes the convexsurface of the cone. The point S is named the vertex of thecone, SA the axis or the altitude, and SBthe side or the apothem. Every section IlKFI, at right angles tothe axis, is a circle ; every section SDE,through the axis, is an isosceles triangle,double of the generating triangle SAB. 3. If from the cone S-CDB, the cone S-FKII be cut off bya plane parallel to the base, the remaining solid CBIIF is calleda truncated cone, or the frustum of BOOK VIII. 1G7 We may conceive it to be generated by the revolution of atrapezoid ABHG, whose angles A and G are right angles, aboutthe side AG. The immoveable line AG is called the axis oraltitude, of the frustum, the circles BDC, HFK, are its bases, and13H is its side. i. Two cylinders, or two cones, are similar, when theiraxes are to each other as the diameters of their bases. Ô. It in the circle ACD, which forms thebase of a cylinder, a polygon ABCDE bemscribed, a right prism, constructed on thisbase ABCDE, and equal in altitude to thecylinder, is said to be inscribed in the cylin-der, or the cylinder to be circumscribedabout the prism. The edges AF, BG, CTI, ifcc. of the prism,being perpendicular to the plane of the base,are evidently included in the convex sur-face of the cylinder ; hence the prism anddie cylinder touch one another along theseedges. (i. In like manner, if ABCD is a poly-gon, circumscribed about the base of acylinder, a rig
Size: 1363px × 1834px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
