 | James Hayward - Geometry - 1829 - 218 pages
...its height, and CE X CG is the product of the base of the rectangle CEFG by its height. Therefore — Two rectangles are to each other as the products of their bases by their heights. 159. It is usual to estimate areas by square feet, square yards, square rods, &c.... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...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 of their bases multiplied by their altitudes. SCHOLIUM. Hence the product of the base by the altitude may be assumed... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...ABCD, AEFD, of the same altitude, are to each other as theii bases AB, AE. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their bases multiplied by their altitudes. Let ABCD, AEGF, be two rectangles ; then will the rect angle, ABCD :... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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 of their bases multiplied by their altitudes. SCHOLIUM. Hence the product of the base by the altitude may be assumed... | |
 | Nathan Scholfield - 1845 - 894 pages
...Hence, rectangles having the same altitude are to each other as their bases. H PROPOSITION VI. THEOREM. Any two rectangles are to each other as the products of their bases multiplied by their altitudes. Let ABCD, AEGF, be two rectangles ; then will the rectangle, ABCD :... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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 of their bases multiplied by their altitudes. SCHOLIUM. Hence the product of the base by the altitude may be assumed... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...have the proportion ABCD : AEFD : : AB : AE. Therefore, two rectangles, &c. PROPOSITION IV. THEOREM. 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... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...ABCD, AEFD, of the same altitude, are to each other as their bases AB, AE. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their base* multiplied by their altitudes. Let ABCD, AEGF, be two rectangles ; then will the rectangle, ABCD... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...to any other rectangles whose bases are whole numbers : hence, AEFD : EBCF : : AE i EB. THEOREM VI. Any two rectangles are to each other as the products of their bases and altitudes. Let ABCD and AEGF be HD two rectangles : then will ABCD : AEGF :: ABxAD • AFxAE For, having placed... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...to any other rectangles whose bases are whole numbers : hence, AEFD : EBCF : : AE : EB. THEOREM VI. Any 'two rectangles are to each other as the products of their bases and altitudes. Let ABCD and AEGF be JI D two rectangles : then will ABCD : AEGF : : ABxAD E B : AFxAE For, having... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
