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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 Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 442 pages
...'rove. ) j 1 t. AC We ar rec 1' 1 У E' t AD •i G' PROPOSITION II. THEOREM. 315. Two rectangles are to each other as the products of their bases by their altitudes. Let A and R' be two rectangles, having for their bases b and b', and for their altitudes a and a'....
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...parallelopipeds having equal altitudes are to each other as their bases. VI. Theorem. Any two parallelopipeds are to each other as the products of their bases by their altitudes. HYPOTII. P and p are two parallelopipeds whose bases are B and &, and whose altitudes are A and a respectively....
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New Elementary Algebra: Designed for the Use of High Schools and Academies

Benjamin Greenleaf - Algebra - 1879 - 322 pages
...= 57. 5. If a -f- x : a — x : : 11 : 7, what is the ratio of a to xl 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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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...have (II. 21, 24) \ h F V \ \ \ B \ \ \ ! ft \ ! \ V \ THEOREM IX. 34. Rectangular parallelopipeds are to each other as the products of their bases by their altitudes. Let AB, CD, be rectangular parallelopipeds, then Produce the edge EA to G making EG equal to FC; if...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 382 pages
...parallelopipedons having the same altitude are to each other as their bases. PROPOSITION XVI. THEOREM. A ny two rectangular parallelopipedons are to each other...as the products of their bases by their altitudes, or as the products of their three dimensions. For, having placed the two solids, AG, AZ, so that their...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...and C' 0'. Then АACB = ВXС0 =^_x_CO_, 326 Л A' С' B' A' B' X C' 0' A' B' C" O' (two A are to each other as the products of their bases by their altitudes). But -- = , 297 A'B' С'O' (the homologous altitudes of similar A have the same ratio as their homologous...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...one-half of any parallelogram having an equal base and an equal altitude. Cor. II.—Any two triangles are to each other as the products of their bases by their altitudes. For, let T and T' denote two triangles whose bases are b and b', and whose altitudes are a and a'....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1885 - 540 pages
...altitudes, are to each other as their bases ; which was to be proved. BOOK VII. PROPOSITION XIII. 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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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 346 pages
...two rectangular parallelopipedons are to each othrr as the product of their three dimensions. Sch. We are consequently authorized to assume, as the measure...of a rectangular parallelopipedon, the product of it8 throe dimensions. In order to comprehend the nature of this measurement. ii V l \ . X \z \ A \...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...prove that -A^- = -^MA'B'C' A'B'2 Draw the altitudes CD and C'D'. Then since any two triangles are to each other as the products of their bases by their altitudes ( 329), we have ABC AB x CD AB CD x A'B'C' A'B' x C'D' A'B' C'D' But the homologous altitudes of...
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