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Books Books 1 - 3 of 3 on ... F is greater than E, but not greater than D (V. Def. 7). Because E and D are....  
" ... F is greater than E, but not greater than D (V. Def. 7). Because E and D are equimultiples of B and A, and E is less than D . (Const). Therefore B is less than A (V Ax. 4) Therefore, of two magnitudes, &o QED PBOP. XI. THEOREM. Ratios that are equal... "
Elements of Trigonometry, and Trigonometrical Analysis, Preliminary to the ... - Page 55
by Augustus De Morgan - 1837 - 230 pages
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...QED PEOP. XI. (THEouEM.)—Ratios that are equal to the same ratio, are equal to one another. If A is to B as C is to D, and C is to D as E is to F, then A is to 3 as E is to F. Take of A, C, and E, any equimultiples whatever, G, H, and...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...magnitudes, &o QED PBOP. XI. THEOREM. Ratios that are equal to the same ratio, are equal to one another. If A is to B as C is to D ; and C is to D, as E is to F. A is to B, aa E is to F. Take of A. C, and E, any equimultiples whatever, G, H, and K...
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Plato's Republic: A Study

Stanley Rosen - Philosophy - 2008 - 423 pages
...two unequal parts A and 8, and A is divided into parts c and d, whereas 8 is divided into e and f. A is to B as c is to d, and c is to d as e is to /". One of the first two parts stands for the visible domain, and the other for the intelligible...
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