 | 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.... | |
 | 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,... | |
 | 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.... | |
 | 1875 - 256 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... | |
 | Elias Loomis - Conic sections - 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... | |
 | George Albert Wentworth - Geometry - 1877 - 436 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'.... | |
 | William Henry Harrison 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.... | |
 | 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... | |
 | 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... | |
 | Charles Scott Venable - 1881 - 380 pages
...part of the prism having the same base and the same altitude. COR. 2. First. — Any two pyramids are to each other as the products of their bases by their altitudes. Secondly. — Two pyramids having the same altitude are to each other as their bases. Thirdly. —... | |
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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. 
