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" Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions. "
Elements of Geometry: With Practical Applications to Mensuration - Page 199
by Benjamin Greenleaf - 1863 - 320 pages
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...parallelograms having equal altitudes are to each other as their bases ; and, in general, parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION VI. — THEOREM. 227. Tlie area of any triangle is equal to the product of its base by...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 pages
...the same base, or equivalent bases, are to each other as their altitudes. 491. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. 492. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by passing...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...be proved. V \L ^ \ F \Q f* \ \ * 0\ A D \ I ^ \ ] 3 C : : AB : . AO. 196 PROPOSITION XIII. THEOBEM. Any two rectangular parallelopipedons are to each other as the products of their bases and altitudes ; that is^ as the products of their three dimensions. Let AZ and AG be any two - rectangular...
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New Elementary Algebra: in which the First Principles of Analysis are ...

Benjamin Greenleaf - 1863 - 338 pages
...57. 5. If a -f- x : a — x : : 11 : 7, what is the ratio of a to x '! Ans. 9 : 2. 6. Triangles are to each other as the products of their bases by their altitudes. The bases of two triangles are to each other as 17 to 18, and their altitudes as 21 to 23 ; required...
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Elements of Geometry and Trigonometry

C. Davies - 1867 - 342 pages
...any two rectangular parallelopipedons are to each other as the product of their three dimensionsSck We are consequently authorized to assume, as the measure...a rectangular parallelopipedon, the product of its three dimensionsIn order to comprehend the nature of this measurement, it Of Parallelopipedonasolid...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1868 - 338 pages
...the same base, or equivalent bases, are to each other as their altitudes. 491. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. 492. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by passing...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 319 pages
...two rectangular parallelopipedons are to each other as the product of their three dimensions. Sch. We are consequently authorized to assume, as the measure...a rectangular parallelopipedon, the product of its three dimensions. In order to comprehend the nature of this measurement, it is necessary to reflect,...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...bases ; triangles having equal bases are to each other as their altitudes ; and any two triangles are to each other as the products of their bases by their altitudes. PROPOSITION VI.— THEOREM. 17. The area of a trapezoid is equal to the produet of its altitude by...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...bases; which was to be proved. \ • w A i \L \ \ A 3 : : AB : E D I \ 3 1. AO. PROPOSITION THEOPvEM. Any two rectangular parallelopipedons are to each other as the products of their bases and altitudes ; that is, as the products of their three dimensions. Let AZ and AG be any two rectangular...
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A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...are to each other as their altitudes ; of equal altitudes, as their bases ; and in general they are to each other as the products of their bases by their altitudes. PROPOSITION TII. 325. Theorem. — The area of a trapezoid is equal to the product of its altitude...
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