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" Any two rectangles are to each other as the products of their bases by their altitudes. "
Elements of Geometry and Conic Sections - Page 60
by Elias Loomis - 1857 - 226 pages
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...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. PROPOSITION IV. The area of a rectangle is equal to the product of its base and altitude. PROPOSITION...
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Examination Papers for the Academic Year ...

Examinations - 1893 - 408 pages
...angle B is twice A, and C is three times B; find the number of degrees in each angle. 3 4 Prove that any two rectangles are to each other as the products of their bases and altitudes. . 5 5 Find the side of a square which shall be equal in area to the sum of two rectangles...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1893 - 270 pages
...be considered as the altitudes, AD and AD as the bases. PROPOSITION II. THEOREM. 362. The areas of two rectangles are to each other as the products of their bases by tJieir altitudes. Let It and Ji' be two rectangles, having for their bases I and '/', and for their...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 398 pages
...either side of a rectangle may be taken as the base, it follows that PROPOSITION II. THEOREM. 301. Any two rectangles are to each other as the products of their bases by their altitudes. Let A and B be any two rectangles, having the altitudes a and a', and the bases b and b', respectively....
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...their bases, and rectangles having equal bases are to each other as their altitudes. 244. Theorem. Two rectangles are to each other as the products of their bases and altitudes. 245. Theorem. The area of a rectangle is equal to the product of its base and its altitude....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1895 - 450 pages
...two rectangular parallelopipeds, etc. PROPOSITION X. THEOREM. Any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes. Let AG, AQ be two rectangular par- M allelopipeds, of which the bases are the rectangles ABCD, AIKL, and...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...uu AF ABCD_ (iu ABEF as in Proposition XI, Bk. II, and Proposition X, Bk. Ill PROPOSITION III 242. Theorem. Any two rectangles are to each other as the products of their bases by their altitudes. Appl. Cons. Dem. b Prove M = abN~a'b' Construct rectangle P, as indicated Ma — = — Pa' | 1 M ab...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...a linear unit. To PROVE — area of 7? = a X b, provided U is the unit of area. 380 R_a x& Z7 ixi" [Two rectangles are to each other as the products of their bases by their altitudes.] But -— = area of R. U §374 [The area of a surface is the ratio of that surface to the unit surface.]...
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...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. 363. The area of a rectangle is equal to the product of its base and altitude. 365. The area of a parallelogram...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...linear unit. To PROVE — area of R = a X b, provided U is the unit of area. R axb = axb. §380 U ixi [Two rectangles are to each other as the products of their bases by their altitudes.] But — = area of R. U §374 [The area of a surface is the ratio of that surface to the unit surface.]...
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