 | William Chauvenet - 1871 - 380 σελίδες
...(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 - 1872 - 382 σελίδες
...(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 - 1877 - 416 σελίδες
...their limits ; rect. AF AE ТB are always equal , their limits are equal, namely, 199 rect. A С QED 314. COROLLARY. Two rectangles having equal bases...equal bases, are to each other as their altitudes. GEOMETRY. • — BOOK IV. ANOTHER DEMONSTRATION. Let A С аad A' C' be two rectangles of equal altitudes.... | |
 | George Albert Wentworth - 1877 - 436 σελίδες
...their limits ; rect. AF are always equal .'. their limits are equal, namely, AE rect. AC §199 AB 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 ANOTHER DEMONSTRATION. Let A С and A' C' be two... | |
 | George Albert Wentworth - 1877 - 416 σελίδες
...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 - 1882 - 442 σελίδες
...near they approach their limits ; rect. AF .'. their limits are equal, namely, AE rect. AC AB §199 ''a. ED 314. COROLLARY. Two rectangles having equal...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... | |
 | Webster Wells - 1886 - 392 σελίδες
..._ 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 - 1887 - 331 σελίδες
...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.... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 342 σελίδες
...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... | |
 | George Albert Wentworth - 1888 - 264 σελίδες
...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.... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
