 | John Playfair - Geometry - 1836 - 148 pages
...parallelogram CF ; (16. 4.) 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, &c. QED PROP. XXIV. THEOR. The parallelograms about the diameter... | |
 | 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 : AEGF : : AB.AD : AF.AE. . Having... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the parallelogram CF; K is to M, as the parallelogram AC to the parallelogram CF (V. 22) ; but K has to M the ratio which is compounded of the ratios of...ratio which is compounded of the ratios of the sides. COB. 1. — The rectangles under the corresponding terms of two analogies are proportional. For let... | |
 | Euclides - Geometry - 1841 - 378 pages
...therefore, ex aequali,* K is to M, as the * 22 - 5 ' parallelogram AC to the parallelogram CF: but K has to M the ratio which is compounded of the ratios of the sides; therefore the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the... | |
 | Euclides - 1842 - 316 pages
...aequali (10. Pr.), к is to м, as the parallelogram AC to the parallelogram c F : but к has to м the ratio which is compounded of the ratios of the...ratio which is compounded of the ratios of the sides. Wherefore equiangular parallelograms, &c. QED PROP. XXIV. THEOR. THE parallelograms about the diameter... | |
 | Euclid - Geometry - 1845 - 218 pages
...CF ; ex requali f, K is to t 22. «. 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, &c. QED PROPOSITION XXIV. THEOR. — The parallelograms about... | |
 | Euclides - 1845 - 546 pages
...parallelogram GF; ex aequali, K is to M, as the parallelogram AC to the parallelogram CF: (v.22.) 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, &c. QED PROPOSITION XXIV. THEOREM. Parallelograms about the... | |
 | 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 : AEGF::AB.AD : AF.AE. B Having placed... | |
 | Euclides - 1846 - 292 pages
...therefore, ex asquali, the parallelogram AC is to the parallelogram CF as K to M : But K is to M in the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC is to the parallelogram CF in the ratio which is compounded of the ratios of the sides. Wherefore,... | |
 | 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... | |
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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... 
