 | Webster Wells - Geometry - 1886 - 392 pages
...as their bases ; two triangles having equal bases are to each other as their altitudes ; and any two triangles are to each other as the products of their bases by their altitudes. PROPOSITION VI. THEOREM. 331. The area of a trapezoid is equal to one-half the sum of its parallel... | |
 | 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 - 414 pages
...the same parallels, the area of the triangle is half that of the parallelogram. 369. COR. 3. Any two triangles are to each other as the products of their bases by their altitudes ; therefore triangles having equal bases are to each other as their altitudes, and triangles of equal... | |
 | 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
...other as their 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.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...— 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.]... | |
 | 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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... two triangles are to each other as the products of their bases by their altitudes. 
