 | Euclid - 1826 - 234 pages
...the multiple of the third to the multiple of the fourth." " Prop. 3. If the first of four magnitudes be to the second as the third to the fourth, and if any like aliquot parts whatever be taken of the first and third, and any like aliquot parts whatever... | |
 | Euclides - 1826 - 226 pages
...then delivers the propositions, which are the following: " Prop. 2. If the first of four magnitudes be to the second as the third to the fourth, and if any equimultiples whatever of the first and third be taken, and also any equimultiples of the second... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...is to B, as C is to D. Therefore, if the first be the same multiple, &c. QED PROP. D. THEOR. See N. If the first be to the second as the third to the fourth, and if theJirst be a multiple, or a part of the second; the third is the same multiple, or the same part of... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...magnitudes, taken separately, be proportionals, they are also proportionals when taken jointly : that is, if the first be to the second as the third to the fourth, the first and second together are to the second as the third and fourth together to the fourth. Let... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...demonstrated, A : C : : B : D, and inversely (A. 5.) C : A: : D : B. Therefore, &c. QED PROP. C. THEOR. If the first be to the second as the third to the...the same multiple or the same part of the fourth. Let A : B : : C : D, and first let A be a multiple of B, C is the same multiple of D, that is, if A=mB.C=mD.... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...demonstrated, A : C : : B : D and inversely (A. 5.) C: A : : D : B. Therefore, &c. QED PROP. C. THEOR. If the first be to the second as the third to the fourth ; and if the first le a multiple or a part of the second, the third is the same multiple or the same part of the fourth.... | |
 | Euclides - 1834 - 518 pages
...to D. Therefore, if the first be the same multiple, &c. QED PROPOSITION D. THEOR. — If the Jlrst be to the second as the third to the fourth, and if the. Jirsl be a multiple, or a part of the second ; the third is the same multiple, or the same part of... | |
 | Euclid - 1835 - 540 pages
...separately, be proportionals, See N. they will also be proportionals when taken jointly ; — that is, if the first be to the second, as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth.... | |
 | Mathematics - 1836 - 488 pages
...taken separately, be proportionals, they will also be proportionals when taken joint, ly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second as the third and fourth together to the fourth.... | |
 | 1841 - 488 pages
...taken separately, be proportionals, they shall also be proportionals when taken jointly — that is, if 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, is to the fourth.... | |
| |
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... 
