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" ... is equal to one. third of the product of its base and altitude (P. XVI., C. 2) ; hence, the sum of the volumes of the triangular pyramids, is equal to one-third of the product of the sum of their bases by their common altitude. But the sum of the... "
A Secondary Arithmetic - Page 163
by John Charles Stone - 1908
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...bases by their common altitude. But the sum of the triangular pyramids is equal to the given pyramid, and the sum of their bases is equal to the base of the given pyramid : hence, the volume of the given pyramid is equal to onethird of the product of its base...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...bases by their common altitude. But the sum of the triangular pyramids is equal to the given pyramid, and the sum of their bases is equal to the base of the given pyramid: hence, the volume of the given pyramid is equal to onethird of the product of its base...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...bases by their common altitude. But the sum of the triangular pyramids is equal to the given pyramid, and the sum of their bases is equal to the base of the given pyramid : hence, the volume of the given pyramid is equal to one. third of the product of its...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...bases by their common altitude. But the sum of the triangular pyramids is equal to the given pyramid, and the sum of their bases is equal to the base of the given pyramid : hence, the volume of the given pyramid is equal to one third of the product of its...
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Solid Geometry, with Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1919 - 240 pages
...non-adjacent edges. The altitudes of the triangular prisms are the same as that of the given prism, and the sum of their bases is equal to the base of the given prism. Now use § 197 and complete the proof. 199. COROLLARY 1. The product of the base and altitude...
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Solid Geometry, with Problems and Applications

Herbert Ellsworth Slaught - Geometry, Solid - 1919 - 244 pages
...non-adjacent edges. The altitudes of the triangular prisms are the same as that of the given prism, and the sum of their bases is equal to the base of the given prism. Now use § 197 and complete the proof. 199. COROLLARY 1. The product of the base and altitude...
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