 | Euclid - 1876 - 240 pages
...Cis> A, or Ais> C. PROPOSITION XL THEOREM. — If ratios are equal to the same ratio, they are equal to one another. Let A be to B as C is to D ; and also let C be to D as E is to F ; then shall A be to B as E is to F. HA CBD FL II N (a) V. Def. 5.... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...magnitude, &c. QED PROPOSITION XL THEOREM. Satins 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. 8Tako of A, C, E, any equimultiples whatever... | |
 | Euclides - 1878 - 398 pages
...Simson's edition. PROPOSITION V. (EucL v. 11.) Ratios that are the same to (he same ratio, are the same tc one another. Let A be to B as C is to D, and E be to F as C is to D. Then must A be to B a$ E is to F. Take of A, C, S any equimultiples mA, mC,... | |
 | James Hamblin Smith - Euclid's Elements - 1879 - 378 pages
...edition. PROPOSITION V. (Eucl. v. 11.) Ratios that are the same to the same ratio, are the same tc ont another. Let A be to B as C is to D, and E be to F as C is to D. Then must AbetoBasEisttf F. ' Take of A, C, E any equimultiples mA, mC, mE,... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...magnitude &o. QED PROPOSITION 11. 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 let C be to D as E '•& to> : A shall be to B as ^ is to F. H ------ KC - EB - • D L - M Take of... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...A. [V. .Aascmi 4. PROPOSITION 11. 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 Z>, and let C be to D as E is to F : A shall be to B as E is to F. A B LTake of A, C, E any equimultiples... | |
| |
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. 
