 Two rectangles are to each other as the products of their bases and altitudes. For if R = a6, and R  Plane Geometry - Page 194by Webster Wells, Walter Wilson Hart - 1915 - 309 pagesFull view - About this book
 | George Washington Hull - Geometry - 1807 - 408 pages
...variables are equal, Then lim. = lira. , § 140 EFGH EF Or =. QED EFGH EF i \ K BE M 223. COE. — Two rectangles having equal bases are to each other as their altitudes. Since either side of a rectangle may be taken as its base. PROPOSITION III. THEOREM. 224. Any two rectangles... | |
 | 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
...rect. AF are always equal .'. their limits are equal, namely, AE rect. AC §199 AB QED 314. COROLLARY. Two rectangles having equal bases are to each other as their altitudes. By considering the bases of these two rectangles AD and AD, the altitudes will be AB and A E. But we... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...their limits ; rect. AF .-. their limits are equal, namely, = ., § 199 rect. AC AB QED 314. COROLLARY. Two rectangles having equal bases are to each other as their altitudes. By considering the bases of these two rectangles AD and AD, the altitudes will be AB and A E. But we... | |
 | 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 - 331 pages
...its limit. AE AE Therefore, by II., Theorem, Doctrine of Limits, (,11,42, 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 - 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 - 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... | |
 | 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... | |
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