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 26
... ABCDEF . Within that hexagon we will take any point G , and join AG , BG , CG , DG , EG , FG : 1. We shall have as many triangles , AFG , ABG , BCG , & c , formed as there are plane an- gles , ASB , BSC & c , including the solid angle ...
... ABCDEF . Within that hexagon we will take any point G , and join AG , BG , CG , DG , EG , FG : 1. We shall have as many triangles , AFG , ABG , BCG , & c , formed as there are plane an- gles , ASB , BSC & c , including the solid angle ...
Page 27
... ABCDEF . 3. It has just been proved ( in the preceding query ) that of three plane angles , forming a solid angle , any two together are greater than the re- maining third one ; therefore the sum of the two angles BAS , FAS , is greater ...
... ABCDEF . 3. It has just been proved ( in the preceding query ) that of three plane angles , forming a solid angle , any two together are greater than the re- maining third one ; therefore the sum of the two angles BAS , FAS , is greater ...
Page 43
... ABCDEF by its height AG . For every right prism ABCD , & c , may be divided into a number of triangular right prisms AEFMGL , AEDKLG , ACDKGI , ABCIGH , the solidity of each of which is found by multiplying its base by its height ; and ...
... ABCDEF by its height AG . For every right prism ABCD , & c , may be divided into a number of triangular right prisms AEFMGL , AEDKLG , ACDKGI , ABCIGH , the solidity of each of which is found by multiplying its base by its height ; and ...
Page 44
... ABCDEF by the height GA . 1 * * * QUERY II . From the manner in which you calculate the solidity of a triangular right prism , can you now find a rule for calculating that of a trian- gular oblique prism ? Ans . The solidity of a ...
... ABCDEF by the height GA . 1 * * * QUERY II . From the manner in which you calculate the solidity of a triangular right prism , can you now find a rule for calculating that of a trian- gular oblique prism ? Ans . The solidity of a ...
Page 47
... ABCDEF , is cut by a plane GHI , parallel to its basis , what relation can you discover between the section GHI and the basis of the prism ? Ans . The section GHI is equal to the lower basis ABC , and consequently also to the upper one ...
... ABCDEF , is cut by a plane GHI , parallel to its basis , what relation can you discover between the section GHI and the basis of the prism ? Ans . The section GHI is equal to the lower basis ABC , and consequently also to the upper one ...
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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