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" Any two rectangles are to each other as the products of their bases by their altitudes. "
Elements of Geometry and Conic Sections - Page 60
by Elias Loomis - 1849 - 226 pages
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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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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 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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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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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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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 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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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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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1864 - 506 pages
...incommensurable, denote the area by k', the base by 6', and the altitude by a'. Then, since by Geometry any two rectangles are to each other as the products of their bases and altitudes, we have k : k' :: ab : a'b'. But k — ah, .-. k' = a'b'. 159. Problem. To find the...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...rectangles ABCD, AE FD, having equal altitudes, are to each other as their bases AB, AE. THEOREM IV. 185. Any two rectangles are to each other as the products of their bases multiplied by their altitudes. Let ABCD, AEGF be two DC rectangles ; then will ABCD be toAEGFusAB multiplied...
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Mensuration of lines, surfaces, and volumes

David Munn - 1873 - 160 pages
...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 - 1874 - 206 pages
...rectangles AB CD, A EFD, having equal altitudes, are to each other as their bases A B. AE. THEOREM IV. 185. Any two rectangles are to each other as the products of their bases multiplied by their altitudes. Let AB CD, AEGF be two 5- ° ° rectangles ; then will ABCD be i to...
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