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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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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 238 pages
...cutting a pyramid are as the squares of their distances from the vertex. (39 ; II. 31.) 75. Pyramids are to each other as the products of their bases by their altitudes. (51.) 76. Pyramids with equivalent bases are as their altitudes ; with equal altitudes, as their bases....
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 566 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 VII. 325. TJieorem. — The area of a trapezoid is equal to the product of its altitude...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...dimensions. 71. In a cube the square of a diagonal is three times the square of an edge. 72. Prisms are to each other as the products of their bases by their altitudes. (25.) 74. Polygons formed by parallel planes cutting a pyramid are as the squares of their distances...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...parallelograms having equal bases are to each other as their altitudes; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V.—THEOREM. 13. The area of a triangle is equal to half the product of its bate and altitude....
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Mensuration of lines, surfaces, and volumes

David Munn - 1873
...their bases ; triangles having equal bases are toeach other as their altitudes, and two triangles are to each other as the products of their bases by their altitudes. PROP. IV. — To find the area of a triangle, -when the three sides are given. In the triangle ABC,...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 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. THEOREM VI. 189. The area of any triangle is equal to the product of its base by half its altitude....
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...proved. ,< -i \ .' \ \K \L \ E "i A D A \ I M \ : : AB : . i J t AO. PROPOSITION XHI. THEOREM. 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 Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 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. THEOREM VI. 189. The area of any triangle is equal to the product of its base by half its altitude....
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Harvard Examination Papers

1875 - 164 pages
...cases. 2. To make a square which is to a given square in a given ratio. 3. Prove that two rectangles are to each other as the products of their bases by their altitudes. What follows if we suppose one of the rectangles to be the unit of surface ? 4. Prove that two similar...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...bases ; pyramids having equivalent bases are to each other as their altitudes; and any two pyramids are to each other as the products of their bases by their altitudes. Cor. 3. Similar pyramids are to each other as the cubes of their homologous edges. • Scholium. The...
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