| 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'.... | |
| 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.... | |
| 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 - 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... | |
| 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... | |
| 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'.... | |
| 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... | |
| 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 \... | |
| 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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