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 v
... Pyramids , Cones , & c , is treated of under a separate head ; because it appeared to me the safest plan , and much ... equal to one another in solidity , when , having equivalent bases , and equal heights , they have also , in every ...
... Pyramids , Cones , & c , is treated of under a separate head ; because it appeared to me the safest plan , and much ... equal to one another in solidity , when , having equivalent bases , and equal heights , they have also , in every ...
Page 47
... equal to the lower basis ABC , and consequently also to the upper one DEF ... same bases and height are equal to one another , since all the sections made parallel to their common bases are equal to that basis , and ... Pyramids 31 32.
... equal to the lower basis ABC , and consequently also to the upper one DEF ... same bases and height are equal to one another , since all the sections made parallel to their common bases are equal to that basis , and ... Pyramids 31 32.
Page 50
... PYRAMIDS . QUERY I. H d ....... a D ... A B If a pyramid ABCDH is cut by a plane parallel to its bases , what ... equal to the corresponding angle in the basis ; because it has been proved ( Section I , page 23 , ) that any two angles ...
... PYRAMIDS . QUERY I. H d ....... a D ... A B If a pyramid ABCDH is cut by a plane parallel to its bases , what ... equal to the corresponding angle in the basis ; because it has been proved ( Section I , page 23 , ) that any two angles ...
Page 55
... pyramids of equal bases and height , are in solidity equal to one another . Let there be two triangular pyramids p , P , whose equal heights DH , dh , we will re- present by the same letter H. Let us further suppose these two pyramids ...
... pyramids of equal bases and height , are in solidity equal to one another . Let there be two triangular pyramids p , P , whose equal heights DH , dh , we will re- present by the same letter H. Let us further suppose these two pyramids ...
Page 56
... equal to one another . And because these two pyramids have not only equal bases and heights , but also throughout the same thickness , ( all sections made parallel to their bases being equal to one another ) , their solidities must be equal ...
... equal to one another . And because these two pyramids have not only equal bases and heights , but also throughout the same thickness , ( all sections made parallel to their bases being equal to one another ) , their solidities must be equal ...
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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