 | George Albert Wentworth - 1889 - 264 pages
...Definitions. Equivalent figures, area of a figure, units of area, transformation of a figure. 176. Theorem. Two rectangles having equal bases are to each other as their altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles... | |
 | George Albert Wentworth - 1889 - 276 pages
...Definitions. Equivalent figures, area of a figure, units of area, transformation of a figure. 176. Theorem. Two rectangles having equal bases are to each other as their altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...rectangles may bo considered as their bases, and their bases as their altitudes, therefore : Tlie areas of rectangles having equal bases are to each other as their altitudes. NOTE —In these propositions the words " rectangle," " triangle," etc., are often used to denote the " area of the rectangle, "... | |
 | William Chauvenet - 1893 - 340 pages
...PROPOSITION II. Two rectangles having equal altitudes are to each other as their bases. Corollary. Two rectangles having equal bases are to each other as their altitudes. PROPOSITION III. Any two rectangles are to each other as the products of their bases by their altitudes.... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...will approach the limit -—. 300. COR. Since either side of a rectangle may be taken as the base, it follows that Two rectangles having equal bases are to each other at their altitudes. PROPOSITION II. THEOREM. 301. Any two rectangles are to each other as the products... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...X b' [Two rectangles having equal altitudes are to each other as their bases.] And —,-=-,' §378 [Two rectangles having equal bases are to each other as their altitudes.] Multiplying, A. J\. R axt> RX ba — x — =— x— , X R' V a' or QED R X t R' a a PROPOSITION IV.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Ax. a Hence the rectangles coincide throughout and are equal. § 1 5 QED PROPOSITION II. THEOREM 378. Two rectangles having equal bases are to each other as their altitudes. GIVEN — two rectangles AC and A'C, having equal bases, AD and A'D'. rect. AC AB To PROVE rect. A'C... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...areas of two rectangles having equal altitudes are to each other as their bases. 361. Cor. The areas of two rectangles having equal bases are to each other as their altitudes. 362. The areas of two rectangles are to each other as the products of their bases by their altitudes.... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...i ' \ \ \ \ l 1 i 1 ! F Tf QED 246. COR. Since either side of a rectangle may be taken as the base, it follows that Two rectangles having equal bases are to each other as their altitudes. PROPOSITION II. THEOREM. 247. Any tivo rectangles are to each other as the products of their bases... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...are incommensurable. 169 Use the method of proof given in Prop. 79, and consult Prop. 55, Cor. COB. Two rectangles having equal bases are to each other as their altitudes. Proposition 163. Theorem. 199. Any two rectangles are to each other as the products of their bases... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R... 
