| George Albert Wentworth - Geometry - 1888 - 264 pages
...are constantly equal, and each approaches a limit, the limits arc equal). a ED 361. COB. The areas of **two rectangles having equal bases are to each other as their altitudes.** For AB and AE may be considered as the altitudes, AD and AD as the bases. PROPOSITION II. THEOREM.... | |
| 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... | |
| William Chauvenet - 1893 - 340 pages
...equivalent. 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.... | |
| 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.... | |
| 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... | |
| 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.... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...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... | |
| Edward Brooks - Geometry, Modern - 1901 - 278 pages
...and „, , rect. AC AB We have — 7 — r^=-r^recLAF AE Or ABCD : AEFD = AB : AE. II. 16. COR. — **Two rectangles having equal bases are to each other as their altitudes.** For their altitudes may be regarded as bases, and their bases as altitudes. PROPOSITION III. — THEOREM.... | |
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