| Elias Loomis - 1880 - 456 pages
...the same method employed in B. Ill, Pr. 14. Therefore two rectangles, etc. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their bases by their altitudes. gle ABCD to the rectangle AEGF is the same with the ratio of the product of AB by AD to the product... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...Scholium. By rectangle in these propositions is meant surface of the rectangle. ' THEOREM XV. v 38. Any two rectangles are to each other as the products of their bases by their altitudes. LetABCD,DJ£FGbe two rectangles ; then A BCD :DEFG=AD XD Place the two rectangles so that „ the angles... | |
| George Albert Wentworth - 1881 - 266 pages
...Euclid's Def., § 272 QED 1 1 1 Í j L t. AC We ar г to ) ¡rove TCC PROPOSITION II. THEOREM. 315. Two rectangles are to each other as the products of their bases by their altitudes. _____ J b b' Ь Let Л and R' be two rectangles, having for their bases b and b', and lor their altitudes... | |
| 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. —... | |
| 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'.... | |
| George Albert Wentworth - 1884 - 264 pages
...altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles are to each other as the products of their bases and altitudes. 178. Theorem. Area of a rectangle = base X altitude. 179. Theorem. Area of a square... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...equal to AE : hence, ABCD : AEFD :: AB : AE ; which was to be proved. H E C B PROPOSITION IV. THEOREM. Any two rectangles are to each other as th-e products of their bases and altitudes. Let ABCD and AEGF be two rectangles: then ABCD is to AEGF, as ABxAD is to AExAF. For,... | |
| Charles Davies - Geometry - 1886 - 352 pages
...to any other rectangles whose bases are whole numbers : hence, AEFD : EBCF : : AE : EB. THEOREM VI. Any two rectangles are to each other as the products of their bases and altitudes. DC Let ABCD and AEGF be two rectangles : then will ABCD : AEGF : ABxAD : AFxAE For,... | |
| William Chauvenet - Geometry - 1887 - 342 pages
...Corollary. Two rectangles having equal bases are to each other as their altitudes. PROPOSITION III. Any two rectangles are to each other as the products of their bases by their altitudes. PROPOSITION IV. The area of a rectangle is equal to the product of its base and altitude. PROPOSITION... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...Corollary. Two rectangles having equal bases are to each other as their altitudes. PROPOSITION III. Any two rectangles are to each other as the products of their bases by their altitudes. PROPOSITION IV. The area of a rectangle is equal to the product of its base and altitude. PROPOSITION... | |
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