| William Chauvenet - Geometry - 1871 - 380 pages
...(III. 15). 4. Corollary. Since AD may be called the base, and AB and AE the altitudes, it follows that **two rectangles having equal bases are to each other as their altitudes.** Note. In these propositions, by " rectangle" is to be understood " surface of the rectangle." PROPOSITION... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...(III. 15). 4. Corollary. Since AD may be called the base, and AB and AE the altitudes, it follows that **two rectangles having equal bases are to each other as their altitudes.** Note. In these propositions, by " rectangle" is to be understood "surface of the rectangle." PROPOSITION... | |
| George Albert Wentworth - 1881 - 266 pages
...near they approach their limits ; rect. AF .-. their limits are equal, namely, = ., § 199 rect. AC **AB QED 314. COROLLARY. Two rectangles having equal...two rectangles, with the same base, or equal bases,** are to each other as their altitudes. GEOMETRY. — BOOK IV. ANOTHER DEMONSTRATION. Let A С and A'... | |
| George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...their limits ; rect AF .'. their limits are equal, namely, are always equal AE §199 rect. AC AB a ED **314. COROLLARY. Two rectangles having equal bases...two rectangles, with the same base, or equal bases,** are to each other as their altitudes. ANOTHER DEMONSTRATION. Let AC and A' C' be two rectangles of... | |
| Webster Wells - Geometry - 1886 - 392 pages
..._ AD 153 317. COROLLARY. 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. 318. Any two rectangles are to each other as the products of their bases by... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 342 pages
...AE Therefore, by II., Theorem, Doctrine of Limits, ABCD AB AEFD AE' (v. II., 42, and III., 14.) 6. **COROLLARY. Two rectangles having equal bases are to each other as their altitudes.** Note. In these propositions, by " rectangle" is to be understood " surface of the rectangle." PROPOSITION... | |
| William Chauvenet - Geometry - 1887 - 331 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 - Geometry - 1888 - 260 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 - 270 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... | |
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