 | George Albert Wentworth - Geometry - 1877 - 416 pages
...0'. T, J_ i] . ' И Л AСB ABХ CO AB v CO /\ Д A' C'B' A' HX C' 0' A' B' " С" 0' ' (two ÊÎ are to each other as the products of their bases by their altitudes). AB = CO A'B' "" C7^' 326 But § 297 (¿Ae homologous altitudes of similar A have the same ratio as... | |
 | 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
...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 - Geometry, Modern - 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'.... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...consequently, it must be 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,... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...the unit of length. To prove that the area of A, referred to B as the unit, is equal to ax b. Since any two rectangles are to each other as the products of their bases by their altitudes (§ 318), we have A _a xb B~ 1 x 1 = ax b. A But since B is the unit of surface, — is the area of... | |
 | 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,... | |
| |
Any two rectangles are to each other as the products of their bases by their altitudes. 
