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 33
... divided into two layers of 10 cubic inches each , and into a third layer containing 10 half cubic inches ; making in the whole 25 cubic inches . * Q. If the measurements of this last parallelopiped were given in feet , yards , poles ...
... divided into two layers of 10 cubic inches each , and into a third layer containing 10 half cubic inches ; making in the whole 25 cubic inches . * Q. If the measurements of this last parallelopiped were given in feet , yards , poles ...
Page 42
... divided ? Ans . These two prisms are equal to one another . Q. Why ? A. Because the five faces , by which the prism ABCEFG is bound , are respectively equal to the five faces , which terminate the prism BCDFGH ; namely : AEGC BFHD ABFE ...
... divided ? Ans . These two prisms are equal to one another . Q. Why ? A. Because the five faces , by which the prism ABCEFG is bound , are respectively equal to the five faces , which terminate the prism BCDFGH ; namely : AEGC BFHD ABFE ...
Page 43
... divided , are equal to each other . Q. What inference can you draw from the truth you have just discovered ? A. 1. The solidity of a triangular right prism is found by multiplying its basis by its height . Thus , the cubic contents of ...
... divided , are equal to each other . Q. What inference can you draw from the truth you have just discovered ? A. 1. The solidity of a triangular right prism is found by multiplying its basis by its height . Thus , the cubic contents of ...
Page 44
... divided a right parallelopiped into two equal right prisms , we might divide an oblique parallelopiped into two equal oblique prisms ; * and as the whole solidity of an oblique parallelopiped is equal to that of a right paral- lelopiped ...
... divided a right parallelopiped into two equal right prisms , we might divide an oblique parallelopiped into two equal oblique prisms ; * and as the whole solidity of an oblique parallelopiped is equal to that of a right paral- lelopiped ...
Page 45
... divided into a number of triangular prisms ; the solidities of which are found by multiply- ing their bases by their common height . Q. And what other truths can you infer with regard to the ratios , which the solidities of any two ...
... divided into a number of triangular prisms ; the solidities of which are found by multiply- ing their bases by their common height . Q. And what other truths can you infer with regard to the ratios , which the solidities of any two ...
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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