Books Books Any two rectangles are to each other as the products of their bases by their altitudes. Elements of Plane and Solid Geometry - Page 175
by George Albert Wentworth - 1877 - 398 pages ## A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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... ## A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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... ## Elements of Geometry

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'... ## Elements of Geometry

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... ## The Elements of Geometry

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... ## Chauvenet's Treatise on Elementary Geometry

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... ## Chauvenet's Treatise on Elementary Geometry

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.... ## A Text-book of Geometry

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.... ## Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

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... 