 | 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,... | |
 | 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... | |
 | 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 :... | |
 | 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... | |
 | Euclid, John Playfair - Geometry - 1853 - 336 pages
...parallelogram CF ; ex aequali (22. 5.), K is to M, as the parallelogram AC to the parallelogram CF ; but K has to M the ratio which is compounded of the ratios of...any two rectangles are to each other as the products 0f their bases multiplied by their altitudes. SCHOLIUM. Hence the product of the base by the altitude... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...parallelogram CF ; ex oequali (22. v.), K is to M, as the parallelogram AC to the parallelogram CF : but K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. Wherefore, equiangular parallelograms, etc. QED PROPOSITION XXIV. THEOR. Tlie parallelograms about... | |
 | Euclides - Geometry - 1853 - 176 pages
...f : ex œquali (v. 22), k is to Щ, as the parallelogram a С to the parallelogram С f : but k has to m the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram a С has to the parallelogram С f the ratio which is compounded of the ratios of the sides. Wherefore,... | |
 | 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.... | |
 | John Playfair - Geometry - 1855 - 334 pages
...parallelogram CF ; ex aquali (22. 5.), K is to M, as the parallelogram AC to the parallelogram CF; but K has to M the ratio which is compounded of the ratios of the sides; therefore also the parallelogram AC Las to the parallelogram CF the ratio which is compounded of the ratios of the sides. DR Coa. Hence,... | |
| |
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... 
