An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in Algebra. Part II, Containing Solid Geometry, with Its Application to the Solution of Problems |
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Page 82
... radii of those bases . A prism is said to be inscribed in a cylinder , when its bases are inscrib- ed in the bases of the cy- linder ; and a prism is said to be circumscribed about FIG . I. FIG . II . a cylinder , when its bases are ...
... radii of those bases . A prism is said to be inscribed in a cylinder , when its bases are inscrib- ed in the bases of the cy- linder ; and a prism is said to be circumscribed about FIG . I. FIG . II . a cylinder , when its bases are ...
Page 84
... to one an- other , when their axes are both perpendicular or equally inclined to their respective bases , and , at the same time , proportional to the radii of those bases . A frustrum of a cone is the lower part of 84 SOLID GEOMETRY .
... to one an- other , when their axes are both perpendicular or equally inclined to their respective bases , and , at the same time , proportional to the radii of those bases . A frustrum of a cone is the lower part of 84 SOLID GEOMETRY .
Page 89
... radii of the same circle ) ; consequently , LI is also equal to IM . Now , if we pass another plane , GHOP , through this cylin- der , still following the direction of its axis , but so as to make any angle we please with the plane ABCD ...
... radii of the same circle ) ; consequently , LI is also equal to IM . Now , if we pass another plane , GHOP , through this cylin- der , still following the direction of its axis , but so as to make any angle we please with the plane ABCD ...
Page 94
... each other ? Ans . They are to each other , in solidity , as the cubes constructed upon the radii , or upon the diameters of their bases . Q. How can you prove this ? A. Let figure I and II represent two simi- lar 94 SOLID GEOMETRY .
... each other ? Ans . They are to each other , in solidity , as the cubes constructed upon the radii , or upon the diameters of their bases . Q. How can you prove this ? A. Let figure I and II represent two simi- lar 94 SOLID GEOMETRY .
Page 95
... radii , CB , cb , for the sake of brevity , be re- presented by R , r , re- FIG . I. FIG . II . H A B spectively , and their heights by H , h . Then , because the solidities of any two cylinders are in proportion to the products of ...
... radii , CB , cb , for the sake of brevity , be re- presented by R , r , re- FIG . I. FIG . II . H A B spectively , and their heights by H , h . Then , because the solidities of any two cylinders are in proportion to the products of ...
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Common terms and phrases
ABCDEF arcs axis basis ABC basis and height bodies calculate called CAVSAS centre cone ABC consequently convex surface corresponding sides cube root cubic contents cubic feet cubic inches diameter distance divided DOCERE draw equal and parallel equal bases equal heights find the solidity foot found by multiplying frustrum GEORGIA LIBRARIES inferences logarithms lower basis manner mean proportional multiplying its basis oblique parallelopiped paral parallel circles parallel planes perpendicular plane angles Plane Geometry plane MN plane parallel polygon PROBLEM prove pyra pyramid ABCD pyramids of equal QUERY radii radius ramid ratio Remark RERVM right angles right cone right cylinder right parallelopiped right prism similar solid angle Solid Geometry SOLUTION spherical spherical angle square feet straight line third three pyramids tiplying triangle AGC triangular prism triangular pyramid truncated prism ungula UNIVERSITY OF GEORGIA upper basis vertex vertices whole pyramid zone