| 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 - Mathematics - 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 - Geometry - 1877 - 436 pages
...approach their limits ; rect. AF are always equal .'. their limits are equal, namely, AE rect. AC §199 **AB QED 314. COROLLARY. Two rectangles having equal...two rectangles, with the same base, or equal bases,** aro to each other as their altitudes. GEOMETRY. BOOK ANOTHER DEMONSTRATION. Let A С and A' C' be two... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...near they approach their limits ; rect. AF .-. their limits are equal, namely, AE rect, AC AB §199 **QED 314. COROLLARY. Two rectangles having equal bases...two rectangles, with the same base, or equal bases,** aro to each other as their altitudes. GEOMETRY. — BOOK IV. ANOTHER DEMONSTRATION. Let A С and A'... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...approach their limits ; rect. AF are always equal .'. their limits are equal, namely, AE rect. AC AB §199 **QED 314. COROLLARY. Two rectangles having equal bases...rectangles AD and AD, the altitudes will be AB and** AE But we have just shown that these two rectangles are to each, other as AB is to A E. Hence two rectangles,... | |
| George Albert Wentworth - Geometry - 1882 - 442 pages
...they approach their limits ; rect. AF .'. their limits are equal, namely, AE rect. AC AB §199 ''a. ED **314. COROLLARY. Two rectangles having equal bases...equal bases, are to each other as their altitudes.** I ii I i 176 GEOMETRY. BOOK IV. ANOTHER DEMONSTRATION. Let AC and A' C' be two rectangles of equal... | |
| George Albert Wentworth - Geometry - 1884 - 422 pages
...their limits ; rect. AF are always equal .'. their limits are equal, namely, 199 = AE rect. A~C ~~ ТB' **QED 314. COROLLARY. Two rectangles having equal bases...equal bases, are to each other as their altitudes.** ANOTHER DEMONSTRATION. Let A С and A' C" be two rectangles of equal altitudes. P С О PI D' £' F'... | |
| 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, William Elwood Byerly - 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.... | |
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