 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...rectangles ABCD, AE FD, having equal altitudes, are to each other as their bases AB, AE. THEOREM IV. 185. Any two rectangles are to each other as the products of their bases multiplied by their altitudes. Let ABCD, AEGF be two DC rectangles ; then will ABCD be toAEGFusAB multiplied... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...rectangles AB CD, A EFD, having equal altitudes, are to each other as their bases A B. AE. THEOREM IV. 185. Any two rectangles are to each other as the products of their bases multiplied by their altitudes. Let AB CD, AEGF be two 5- ° ° rectangles ; then will ABCD be i to... | |
 | 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 area of a parallelogram.... | |
 | 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.... | |
 | 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 of two lines... | |
 | 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 right... | |
 | Elias Loomis - Conic sections - 1877 - 458 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. , Let ABCD, AEGF be two rectangles ; the ratio of the rectangle ABCD to the rectangle... | |
 | 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... | |
 | 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',... | |
 | 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... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
