| William Chauvenet - 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 - 386 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 - 393 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 - Geometry - 1896 - 50 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.... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 556 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, Plane - 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... | |
| George Washington Hull - Geometry - 1897 - 408 pages
...second parallelogram, with a and b its altitude and base respectively. COR. 1.—Two parallelograms are **to each other as the products of their bases by their altitudes.** For P= A X B, and p — a X b (§ 229). COR. 2.— Two parallelograms having equal bases are to each... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...rectangle is equal to the product of its base and altitude. It is known (from 247) that two rectangles are **to each other as the products of their bases by their altitudes** ; therefore, but S is the unit of area ; hence R = h x b. 249. COB. If h = b, then R = bxb = b*. But... | |
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