 | Robert Simson - 1806 - 546 σελίδες
...has a greater ratio to the second, than the fifth has to the sixth. PROP. XIV. THEOR. SeeN. a 8. 5. IF the first has to the second the same ratio which the third has to the fourth; then, if the first be greater than the third, the second shall be greater than the fourth; and if equal,... | |
 | John Playfair - 1806 - 320 σελίδες
...demonstration be extended to any number of magnitudes. Therefore, &c. QED PROP. XXIV. THEOR. IF the first have to the second the same ratio which the third has to the fourth, and the fifth to the second the same ratio which the sixth has to the fourth ; the first and fifth... | |
 | John Mason Good - 1813 - 714 σελίδες
...shall also have to the second a greater ratic than the filth lias to the sixth. Prop. XIV. Tlieor. If the first has to the second, the same ratio which the third has to the fourth ; then, if the first be greater than the third, the second shall be greater than the fourth; and if... | |
 | Charles Butler - 1814 - 582 σελίδες
...its 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 - 1815 - 686 σελίδες
...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;... | |
 | Euclides - 1816 - 588 σελίδες
...first has a greater ratio to the second, than the fifth' has to the sixth. PROP. XIV. THEOR. See N. IF the first has to the second, the. same ratio which the third has to the fourth ; then, if the first be greater than the third, the second shall be greater than the fourth; and if... | |
 | John Playfair - 1819 - 350 σελίδες
...the demonstration be extended to any nuinber of magnitudes. Therefore, &c. Q, ED . PROP. XXIV. THEOR. If the first has to the second the same ratio which the third has to thefourtli ; and the fifth to the second, the same ratio which the sixth has to the fourth ; the first... | |
 | John Playfair - 1819 - 354 σελίδες
...demonstration be extended to any number of magnitudes. Therefore, &c. Q, ED PROP. XXIV. THEOR. Ifthefirst has to the second the same ratio which the third has to the fourth; and the fifth to the second, the same ratio which the sixth has to tht fourth ; the first and fifth,... | |
 | John Mason Good - 1819 - 800 σελίδες
...the words, "ex a.-quali in proportione pertúrbala;'' or " ex 3-qno pertúrbate." Prop. XXIV. Theor. If the first has to the second the same ratio which the third lus to the fourth ; and the fifth to the second, the taro« n .« which the sixth has to the fouiui;... | |
 | Miles Bland - 1821 - 898 σελίδες
...the first three of which are in arithmetic and the last three in harmonic progression ; prove that the first has to the second the same ratio which the third has to the fourth. ч 18. The sum of three terms of an harmonic progression, whose first term is -, is = — ; determine... | |
| |
If the first has to the second the same ratio which the third has to the fourth... 
