 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...rectangles are contained in each ; that is, as the number of units in their bases. The surfaces of two rectangles are to each other as the products of their bases and heights. 279. Let the rectangles be placed so that their sides are on two straight lines at right-angles,... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...rectangles, &c. PROPOSITION IV. THEOB3M. Any two rectangles are to each other as the products of then bases by their altitudes. Let ABCD, AEGF be two rectangles...AD, to thj product of AE by AF; that is, ABCD : AEGF :: ABx AD : Having placed the two rectangles so that the angles at A are veitical, pro'duce the sides... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...bases ; 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. 17. The area of a trapezoid is equal to the produet of its altitude by... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...parallelograms having equal bases are to each other as their altitudes; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V.—THEOREM. 13. The area of a triangle is equal to half the product of its bate and altitude.... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...are to each other as their altitudes ; of equal altitudes, as their bases ; and in general they are to each other as the products of their bases by their altitudes. PROPOSITION TII. 325. Theorem. — The area of a trapezoid is equal to the product of its altitude... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...cutting a pyramid are as the squares of their distances from the vertex. (39 ; II. 31.) 75. Pyramids are to each other as the products of their bases by their altitudes. (51.) 76. Pyramids with equivalent bases are as their altitudes ; with equal altitudes, as their bases.... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...dimensions. 71. In a cube the square of a diagonal is three times the square of an edge. 72. Prisms are to each other as the products of their bases by their altitudes. (25.) 74. Polygons formed by parallel planes cutting a pyramid are as the squares of their distances... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...are to each other as their altitudes ; of equal altitudes, as their bases ; and in general they are to each other as the products of their bases by their altitudes. PROPOSITION VII. 325. TJieorem. — The area of a trapezoid is equal to the product of its altitude... | |
 | Aaron Schuyler - Measurement - 1864 - 506 pages
...incommensurable, denote the area by k', the base by 6', and the altitude by a'. Then, since by Geometry any two rectangles are to each other as the products of their bases and altitudes, we have k : k' :: ab : a'b'. But k — ah, .-. k' = a'b'. 159. Problem. To find the... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...rectangles ABCD, AE FD, having equal altitudes, are to each other as their bases AB, AE. THEOREM IV. 185. Any two rectangles are to each other as the products of their bases multiplied by their altitudes. Let ABCD, AEGF be two DC rectangles ; then will ABCD be toAEGFusAB multiplied... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
