 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...any two rectangles having equal altitudes, are to each other as their bases. PROPOSITION IV. THEOEEM. Any two rectangles are to each other as the products of their bases and altitudes. Let ABCD, AEGF, be two rectangles ; then will the rectangle, ABCD : AEGF :: ABxAD : AExAF. Having placed... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...to any other rectangles whose bases are whole numbers : hence, AEFD : EBCF : : AE : EBTHEOREM VIAny two rectangles are to each other as the products of their bases and altitudesLet ABCD and AEGF be two rectangles : then will ABCD : AEGF - : ABxAD : AFxAE For, having... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...any two rectangles having equal altitudes, are to each other as their bases. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their bases and altitudes. Let ABCD, AEGF, be two rectangles; then will the rectangle, ABCD : AEGF :: ABxAD : AExAF. Having placed... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...have the proportion ABCD : AEFD : : AB : AE. Therefore, two rectangles, &c. PROPOSITION IV. THEORSM. Any two rectangles are to each other as the products of their bases by their altitudes. Let ABCD, AEGF be two rectangles ; the ratio of the rectangle ABCD to the rectangle... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...equal to AE : hence, ABCD : AEFD : : AB : AE ; which was to be proved. 98 PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their bases and altitudes. Let AB CD and AEGF be two rectangles : then will ABCD be to AEGF, as AB x AD is to AE x AF. For, place... | |
 | Richard Wormell - Geometry, Modern - 1868 - 286 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,... | |
 | 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,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...propositions, by " rectangle" is to be understood "surface of the rectangle." PROPOSITION II— THEOREM. 5. Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R' be two rectangles, k and k' their bases, h and h' their A altitudes;... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...propositions, by "rectangle" is to be understood " surface of the rectangle." PROPOSITION II.—THEOREM. 5. Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R' be two rectangles, k and k' their bases, h and h' their 4 altitudes;... | |
 | 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 area of a parallelogram.... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
