| John Playfair - Euclid's Elements - 1806 - 320 pages
...demonstrated, A : C : : B : D ; therefore, inversely0, 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 be a multiple or a part of the second, the third is the same multiple or the same... | |
| John Mason Good - 1813 - 714 pages
...of the last two has to the other of these. Prob. XVIII. Theor. If magnitudes, taken separately, he **proportionals, they shall also be proportionals, when...to the fourth, the first and second together shall** he to the second, as the third and fourth together to the fourth. Prop. XIX. Theor. If a whole magnitude... | |
| Charles Butler - Mathematics - 1814 - 540 pages
...clear, one or two more particulars will require an explanation. If four numbers are proportionals, **that is, if the first be to the second as the third to the fourth,** then will the first be to the third аз the second to the fourth; and this accounts for the usual... | |
| Euclides - 1814 - 560 pages
...is to B, as C is to D: Therefore, if the first be the same multiple, A. &c. QED CD H PROP. D. THEOR. **IF the first be to the second as the third to the** s«- N. fourth, and if the first be a multiple or part of the second ; the third is the same multiple,... | |
| Euclides - 1816 - 588 pages
...&c. QED PROP. XVIII. THEOR. .. ; • v'i M IF magnitudes, taken separately, be proportional sj See N. **they shall also be proportionals when taken jointly, that is, if the first be to the second,** a§ thethirdhto the fourth, the first and second together shall be to the second, as the third and... | |
| Bewick Bridge - Algebra - 1818 - 254 pages
...с : b : d, and b : d :; a.: c. cd cd, с а Тн. 5. "If there be six proportional quantities, and **the " first be to the second as the third to the fourth** ; and the third " to the fourth as the fifth to the sixth ; then will the first " be to the second... | |
| John Playfair - 1819 - 354 pages
...Therefore, &c. Q, ED PROP. XVIII. THEOR. If magnitudes, taken separately, be proportionals, they will **also be proportionals -when taken jointly, that is,...third to the fourth, the first and second together** will be to the second, as the third and fourth together to the fourth. If A : B : : C : D, then, by... | |
| John Mason Good - 1819 - 800 pages
...the same ratio which the remaining one of the last two has to the other of these. Prop. XV11I. Theor. **If magnitudes, taken separately, be proportionals,...proportionals, when taken jointly, that is, if the first** lie to the second, as the third to the fourth, the first and second together shall be to the second,... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...Therefore, &c. Q, ED PROP. XVIII. THEOR. If magnitudes, taken separately, be proportionals, they will **also be proportionals when taken jointly, that is, if the first be to the** seconrf at the third to the fourth, the first and second together will be to the second, as the third... | |
| Euclid, Robert Simson - Geometry - 1821 - 514 pages
...Therefore (5. def. 5.), as AE is to tB, so is CF to FD. If then magnitudes, &c. QED PROP. XVIII. THEOR. > **IF magnitudes, taken separately, be proportionals,...proportionals when taken jointly, that is, if the** hrst be to the second, as the third to the fourth, the first and second together shall be to the second,... | |
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