 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...and C' 0'. Then АACB = ¿ВXС0 =^_x_CO_, § 326 Л A' С' B' A' B' X C' 0' A' B' C" O' (two A are to each other as the products of their bases by their altitudes). But -- = , § 297 A'B' С'O' (the homologous altitudes of similar A have the same ratio as their homologous... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...one-half of any parallelogram having an equal base and an equal altitude. Cor. II.—Any two triangles are to each other as the products of their bases by their altitudes. For, let T and T' denote two triangles whose bases are b and b', and whose altitudes are a and a'.... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...prove that -A^- = -^MA'B'C' A'B'2 Draw the altitudes CD and C'D'. Then since any two triangles are to each other as the products of their bases by their altitudes (§ 329), we have ABC AB x CD AB CD x A'B'C' A'B' x C'D' A'B' C'D' But the homologous altitudes of... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...to be understood " surface of the rectangle." PROPOSITION III.—THEOREM. 7. Any two rectangles are to each other as the products of their bases by their altitudes, Let E and R' be two rectangles, k and k their bases, h and h ' their altitudes; then E _ k XA R ' Jfx... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...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 their altitudes. r s L_ b V b i Let R and R' be two rectangles, having for their bases b and b', and for their altitudes... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...is the same as that of the first ? Proposition 2. Theorem. 358. The areas of any two rectangles are to each other as the products of their bases by their altitudes. Hyp. Let R and R' be two rectangles, b and b' their bases, a and a' their altitudes, R a X b To prove... | |
 | Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1892 - 544 pages
...criticism, it will be necessary to reproduce the demonstration given. To prove that two rectangles are to each other as the products of their bases by their altitudes. R and R' are two rectangles, having for their bases b and b' and for their altitudes a and a'. It is... | |
 | William Chauvenet - 1893 - 340 pages
...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... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...altitudes ; triangles having equal altitudes are to each other as their bases ; any two triangles are to each other as the products of their bases by their altitudes. 371. The area of a trapezoid is equal to one-half the sum of the parallel sides multiplied by the altitude.... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...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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Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions. 
