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" Two rectangles having equal altitudes are to each other as their bases. "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 79
by Benjamin Greenleaf - 1862 - 490 pages
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...equal, n FD E' D' Dem. Prove by superposition, noting the coincidence PROPOSITION II 240. Theorem. Two rectangles having equal altitudes are to each other as their bases. a Appl. Cons. E a A kI—:H : L t JI.D Case I. When the bases are commensurable. ^ = ^ ABEF AF measure...
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Elements of Geometry: Plane geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...[If two variables are always equal and each approaches a limit, the limits are equal.] QED 379. COR. Two rectangles having equal altitudes are to each other as their bases. PROPOSITION III. THEOREM 380. Any two rectangles are to each other as the products of their bases and...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 556 pages
...[If two variables are always equal and each approaches a limit, the limits are equal.] QED 379. COR. Two rectangles having equal altitudes are to each other as their bases. Hint. — AD and A' D' may be regarded as the altitudes, and AB and A' B' as the bases. PROPOSITION...
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 50 pages
...polygon, to construct a polygon similar to the given polygon. BOOK IV. THEOREMS. 360. The 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....
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...altitude. 221. COR. 2.—Triangles having equal bases and equal altitudes are equivalent. PROPOSITION II. THEOREM. 222. Two rectangles having equal altitudes are to each other as their bases. CASE I.— When the bases are commensurable. D ,c Given—ABCD and EFGH any two rectangles having equal...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 250 pages
...a triangle similar to a given triangle. ( 262.) BOOK IT. AREAS OF POLYGONS PROP. I. THEOREM. 299. Two rectangles having equal altitudes are to each other as their bases. Note. The words "rectangle," "parallelogram," "triangle," etc., in the propositions of Book IV., mean...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...terminal points of the former. Thus A'B' 1-1 e projection of AB on XX'. PROPOSITION I. THEOREM. 245. Two rectangles * having equal altitudes are to each other as their bases. D 0 0 Let the two rectangles be AC and AF, having the same altitude AD. m 4.1, , AECD AB To prove that...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...a triangle similar to a given triangle. ( 262.) BOOK IV. AREAS OF POLYGONS PROP. I. THEOREM. 299. Two rectangles having equal altitudes are to each other as their bases. Note. The words " rectangle," " parallelogram," " triangle," etc., in the propositions of Book IV.,...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 240 pages
...segments of the same parallel lines as the respective bases of the other. Proposition 162. Theorem. 198. Two rectangles having equal altitudes are to each other as their bases. CASE I. When the bases are commensurable. CASE II. Wlten the bases are incommensurable. 169 Use the...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...are often used for ' ' area of rectangle, " " area of triangle, ' ' etc. PROPOSITION I. THEOREM. 395. Two rectangles having equal altitudes are to each other as their bases. Let the rectangles AC and AF have the same altitude AD. To prove that rect. AC : rect. AF = base AB...
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