 | David Munn - 1873 - 160 σελίδες
...their bases ; triangles having equal bases are toeach other as their altitudes, and two triangles are to each other as the products of their bases by their altitudes. PROP. IV. — To find the area of a triangle, -when the three sides are given. In the triangle ABC,... | |
 | Benjamin Greenleaf - 1874 - 206 σελίδες
...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... | |
 | 1875 - 256 σελίδες
...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 - 1875 - 284 σελίδες
...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 - 1876 - 412 σελίδες
...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 σελίδες
...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 - 1877 - 436 σελίδες
...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 - 1877 - 262 σελίδες
...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 - 1877 - 426 σελίδες
...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 - 1877 - 458 σελίδες
...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... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
