 | 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... | |
 | 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... | |
 | 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.... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...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 —... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...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 altitudes. GIVEN—any two rectangles, R and R', their bases being b and b', and altitudes a and... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...A' D' may be regarded as the altitudes, and AB and A' B as the bases. PROPOSITION III. THEOREM 380. Any two rectangles are to each other as the products of their bases and altitudes. V GIVEN — any two rectangles, R and R', their bases being b and b', and altitudes... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | New York (State). Legislature. Senate - Government publications - 1897 - 1306 pages
...4-5 State and prove a theorem, the conclusion of which is, the triangles are similar. 6-7 Prove that any two rectangles are to each other as the products of their bases and altitudes. 8 Derive an expression for the area of a regular triangle whose side is s. 9 State in... | |
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K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products... 
