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" Any two rectangles are to each other as the products of their bases by their altitudes. "
Elements of Geometry - Page 175
by George Albert Wentworth - 1881 - 250 pages
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A Text-book of Geometry

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....
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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...
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Exercise Manuals, Issue 3

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...
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Elementary Geometry

William Chauvenet - 1893 - 340 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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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...areas of two rectangles having equal altitudes are to each other as their bases. 361. Cor. The areas of two rectangles having equal bases are to each other as their altitudes. 362. The areas of two rectangles are to each other as the products of their bases by their altitudes....
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Ax. a Hence the rectangles coincide throughout and are equal. 1 5 QED PROPOSITION II. THEOREM 378. Two rectangles having equal bases are to each other as their altitudes. GIVEN — two rectangles AC and A'C, having equal bases, AD and A'D'. rect. AC AB To PROVE rect. A'C...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...X b' [Two rectangles having equal altitudes are to each other as their bases.] And —,-=-,' 378 [Two rectangles having equal bases are to each other as their altitudes.] Multiplying, A. J\. R axt> RX ba — x — =— x— , X R' V a' or QED R X t R' a a PROPOSITION IV....
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...i 1 ! F Tf QED 246. COR. 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. 247. Any tivo rectangles are to each other as the products of their bases...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...are incommensurable. 169 Use the method of proof given in Prop. 79, and consult Prop. 55, Cor. COB. Two rectangles having equal bases are to each other as their altitudes. Proposition 163. Theorem. 199. Any two rectangles are to each other as the products of their bases...
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Plane Geometry: A Complete Course in the Elements of the Science

Edward Brooks - Geometry, Modern - 1901 - 278 pages
...and „, , rect. AC AB We have — 7 — r^=-r^recLAF AE Or ABCD : AEFD = AB : AE. II. 16. COR. — Two rectangles having equal bases are to each other as their altitudes. For their altitudes may be regarded as bases, and their bases as altitudes. PROPOSITION III. — THEOREM....
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