 | Robert Simson - Trigonometry - 1806 - 546 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 - Mathematics - 1806 - 320 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 - 554 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 - 714 pages
...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 - 560 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 - 582 pages
...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 - 588 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 - 354 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,... | |
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THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the... 
