 | 1875 - 256 pages
...Proof in both 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... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...incommensurable, denote the area by k', the base by b', and the altitude by a'. Then, since by Geometry any two rectangles are to each other as the products of their bases and altitudes, we have k : k' : : ab : a'b'. But k = ab, .-. k' = a'b'. 159. Problem. To find tJie... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...in its base multiplied by the number of linear units in its altitude, which was to be proved. Cor. Any two rectangles are to each other as the products of their bases and altitudes ; if their bases are equal, they are to each other as their altitudes. Scho. The product... | |
 | Richard Wormell - 1876 - 268 pages
...rectangles are contained in each ; that is, as the number of units in their bases. The surfaces of two rectangles are to each other as the products of their bases and heights. Proof.— Let the rectangles be placed so that their sides are on two straight lines at... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...1 ' 1 ° to i 1 '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 Frothingham Bradbury - Geometry - 1877 - 262 pages
...37. Scholium. By rectangle in these propositions is meant surface of the rectangle. THEOREM XV. 38. Any two rectangles are to each other as the products of their bases by their altitudes. LetABCD,DEFGbe two rectangles ; then Place the two rectangles so that ^ i, ^ the angles at D are vertical,... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...Euclid's Def., § 272 QED 1 ' 1 ; to г 1 'rove ) j rec 1 t. AС Wear PROPOSITION II. THEOREM. 315. Two rectangles are to each other as the products of their bases by their altitudes. ______ j b V Ь Let R and R' be two rectangles, having for their bases b and b', and for their altitudes... | |
 | 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 - 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.... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
