| Robert Simson - Trigonometry - 1806 - 518 pages
...H— DEF C— H— ill PROP. A. THEOR. IF the first of four magnitudes has to the second the See N. **same ratio which the third has to the fourth ; then, if the first be greater than the** second, the third is also greater than the fourth; and, if equal, equal; if less, less. Take any equimultiples... | |
| John Playfair - Euclid's Elements - 1806 - 311 pages
...D. Therefore wA>nB, and wE<nF ; wherefore A : B>E : Fa. Therefore, &c. QED PROP. XIV. THEOR. Bookv. **IF the first have to the second the same ratio which the third has to the fourth,** and if the first be greater than the third, the second will be greater than the fourth; if equal, equal;... | |
| Euclid - Geometry - 1810 - 518 pages
...FH — F. Wherefore, as E • is to F, so is G to Hb. But, when four magnitudes are proportionals, **if the first be greater than the third, the second shall be** c!4. 5. greater than the fourth; and if equal, equal; if less, lessc. Wherefore, if E be greater than... | |
| John Mason Good - 1813
...shall all the antecedents taken together he to all the consequents. Prop. XIII. Theor.If the 6rst has **to the second the same ratio which the third has to the fourth,** hut the third to the fourth a greater ratio than the fifth has to the sixth ; the first shall also... | |
| Euclides - 1814 - 558 pages
...magnitudes, &c. QED PROP. A. THEOR. Bonx V. IF the first of four magnitudes has to the second SeeN. **the same ratio which the third has to the fourth ; then, if the first be greater than the** second, the third is also greater than the fourth; and if equal, equal; if less, less. Take any equimultiples... | |
| Charles Butler - Mathematics - 1814 - 528 pages
...smaller numbers ? OF PROPORTION ". 53. Four quantities are said to be proportionals, when the first has **to the second the same ratio which the third has to the fourth** ; that is, when the first is the same multiple, part, or parts of the second that the third is of the... | |
| Charles Butler - 1814
...terms in the form of a fraction . therewhen four quantities are proportionals, that is, when the has **to the second the same ratio which the third has to the** ih, it follows, that the fraction constituted by the terms of first ratio, -will be equal to the fraction... | |
| Charles Hutton - Astronomy - 1815 - 686 pages
...then delivers the propositions, which are the following: " Prop. 1. If the first of four magnitudes **have to the second, the same ratio which the third has to the fourth ; then, if the first be** equal to the second, the third is equal to the fourth; if greater, greater; if less, less." " Prop.... | |
| Euclides - 1816 - 528 pages
...magnitudes, &c. QED OF EUCLID. PROP. A. THEOR. 121 Boo* V. IF the first of four magnitudes has to the secon9 **the same ratio which the third has to the fourth ; then, if the first be greater than the** second, the third is also greater than the fourth ; and if equal, equal ; if less, leps. i Take any... | |
| John Playfair - 1819 - 317 pages
...Therefore mAy»B, and mE/f »F, wherefore, . A : B7E : F (def. 1. 5.). Therefore, &r, QED PROP. XIV. THEOR. **If the first have to the second the same ratio which the third has to the fourth,** and if the first be greater thkn the third, the second shall be greater than the fourth ; if equal,... | |
| |