| Euclid - 1835 - 513 pages
...H, K ; _ p v/ B - D L- - M -- Nand of B, D, F any equimultiples whatever L, M, N: Then, because A is **to B as C is to D, and as E to F** ; and G, H, K are equimultiples of A, C, E, and L, M, N equimultiples Book v. of B, D, F ; if G be... | |
| Euclides - Geometry - 1841 - 351 pages
...equimultiples whatever G, H, K; and of B, D, F any equimultiples whatever L, M, N: then because A is **to B, as C is to D, and as E to F;** and that G, H, K are equimultiples of A, C, E, and L, M, N equimultiples of B, D, F; therefore if G... | |
| Euclid - Geometry - 1845 - 199 pages
...PROPOSITION XI. THEOR. — Ratios that are the same to the same ratio, are the same to one another. **Let A be to B, as C is to D ; and as** C to D, so let E be to F : A is to B, as E to F. Take of A, C, E, any equimultiples whatever G, H,... | |
| Euclid, James Thomson - Geometry - 1845 - 352 pages
...whatever G, H, K : and of B, D, F any like multiples whatever L, M, N : then (V. def. 5) because A is **to B, as C is to D, and as E to F,** and that G, H. K are like multiples of A, C, E ; and L, M, N like multiples of B, D, F ; if G be greater... | |
| Euclides - 1845
...QED PROPOSITION XI. THEOREM. Ratios that are the same to the same ratio, are the same to one another. **Let A be to B as C is to D ; and as** C to D, so let E be to F. QA Then A shall be to B, as E to F. Take of A, C, E, any equimultiples whatever... | |
| Euclides - 1846
...equimultiples whatever G,H,K, and of B, D, F any equimultiples whatever L, M, N : Then, because A is **to B as C is to D and as E to F,** and that G, H, K are equimultiples of A, C, E, and L, M, N equimultiples of B, D, F, therefore, if... | |
| Royal Military Academy, Woolwich - Mathematics - 1853
...PROPOSITION XI. Tin,' M;. Ratios that are tJie same to the same ratio, are the same to one another. **Let A be to B, as C is to D ; and as** C to D, so let E be to F : A is to B, as E to F. Take of A, C, E, any equimultiples whatever G, H,... | |
| Euclides - Geometry - 1853 - 147 pages
...PROPOSITION XI. — THEOREM. Ratios that are the same to the same ratio are the same to one another. **LET a be to b as c is to d ; and as** c to d so let e be to f ; a is to b as e to f. Take of a, c, e, any equimultiples whatever g, h, k... | |
| Robert Potts - Geometry, Plane - 1860 - 361 pages
...QED PROPOSITION XI. THEOREM. Ratios that are the same to the same ratio, are the same to one another, **Let A be to B as C is to D ; and as** C to D, so let E be to F. Then A shall be to B, as E to F. ACE L . MN Take of A, C, E, any equimultiples... | |
| Euclides - 1864
...QED PROPOSITION XI. THEOREM. Ratios that are the tame to the same ratio, are the same to one another **Let A be to B as C is to D ; and as** C to D, so let E be to F. Then A shall be to B, as E to F. GH KBD FLM NTake of A, C, E, any equimultiples... | |
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