 | 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... | |
 | 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... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...that which is said to be compounded of the ratios of JTto L and of L to M; [V. Def. A. therefore K has to M the ratio which is compounded of the ratios of the sides. Now the parallelogram AC is to the parallelogram CH as2?<7isto CG; [VI. 1. but BC is to CG as K is... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...Wherefore, ex aequali, K is to M, as the parallelogram AC is to the parallelogram CF (V. 22). But K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. Wherefore, equiangular parallelograms, &c. QED OUunime. — because there are three parallelograms... | |
 | 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',... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...the parallelogram CF, having the angle BCD equal to the angle ECO: the parallelogram AC shall have to the parallelogram CF the ratio which is compounded of the ratios of their sides. Let BC and CG be placed in a straight line ; therefore DC and CE are also in a straight... | |
 | 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... | |
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K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products... 
