 | Euclid - 1876 - 240 σελίδες
...PROPOSITION D. THEOREM. — If the first lie to the second ai the third to the fourth, and if the first lie a multiple or submultiple of the second, the third...same multiple or submultiple of the fourth. Let A be to B as C is to D; and first let A be a multiple of B, then C shall be the same multiple of D. DEMONSTRATION.... | |
 | Isaac Todhunter - 1880 - 426 σελίδες
...taken separately, be proportionals, they si mil also be proportionals when taken jointly; that is, {f the first be to the second as the third to the fourth, the first and second together shall be to the second as the third and fourth toy ether to the fourth.... | |
 | Euclid, Isaac Todhunter - 1883 - 428 σελίδες
...taken separately, lie proportionals, they shall also be proportionals when taken jointly; that is, {f the first be to the second as the third to the fourth, the first and second together shall be to the second as the third and fourth together to the fourth.... | |
 | Euclides - 1884 - 434 σελίδες
...mB, by inversion. V. A PROPOSITION C. THEOREM. If the first term of a proportion be a multiple or a submultiple of the second, the third is the same multiple...of the fourth. Let A : B = C : D, and first let A = mB : it is required to prove C = mD. Of A and C take equimultiples by any number as 2, and of B and... | |
 | Euclides - 1885 - 340 σελίδες
...therefore T = -;. doa PROP. D. — THEOREM (SrasoN). If the first be to the second as the third is to the fourth, and if the first be a multiple or submultiple...is the same multiple or submultiple of the fourth. 1. Let a : b : : c : d, and let as be a multiple of b, then c is the same multiple of d. Dem. — Let... | |
 | Euclid, John Casey - 1885 - 340 σελίδες
...therefore T = -3. dod PROP. D. — THEOREM (SIMSON). If the first be to the second as the third is to the fourth, and if the first be a multiple or submultiple...is the same multiple or submultiple of the fourth. 1. Let a : b : : c : d, and let a be a multiple of b, then c is the same multiple of d. Dem. — Let... | |
 | Joseph Battell - 1903 - 722 σελίδες
...the fourth, the first is to the second as the third to the fourth. PROPOSITION C. ' If the first is to the second as the third to the fourth ; and if the first is a multiple or a part of the second, the third is the same multiple or the same part of the fourth.'... | |
 | Euclid - 1908 - 456 σελίδες
...pair multiplied by unity]. To prove the partial converse we begin with Prop. D. If the first be to t)u second as the third to the fourth, and if the first be a multiple or part of the second, the third is the same multiple or the same part of the fourth. Let A be to B as... | |
 | Euclid - 452 σελίδες
...pair itself, ie the pair multiplied by unity]. To prove the partial converse we begin with Prop. D. If the first be to the second as the third to the fourth, and if the first be a multiple or part of the second, the third is the same multiple or the same part of the fourth. Let A be to B as... | |
| |
IF the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same part of the fourth... 
