 | John Playfair - Mathematics - 1806 - 320 pages
...second the same ratio which the third, together with the fourth, have to the fourth, the first will have to the second the same ratio which the third has to the fourth. If A+B : B : : C+D : D, then, by division, A : B : : C : D. Take mA and nB any multiples of A and B,... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...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 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... | |
 | 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;... | |
 | Euclides - 1816 - 588 pages
...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 - 354 pages
...second the same ratio which the third, together •ycith the fourth, has to the fourth, the first will have to the second the same ratio which the third has to the fourth. If A+B : B : : C+D : D, then by division A : B : : C : D. Take mA and nB any multiples of A and B,... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...; therefore (def 5. 5.) A : B : : A+C+E : B+D+F. Therefore, &c, QED PROP. XIII. THEOR. If thejlrst have to the second the same ratio which the third has to tht fourth, but the third to the fourth a greater ratio than the fifth has to the sixth ; the first... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...that GB is of E. If therefore two magnitudes,. &c. QED PROP. A. THEOR. 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 greater then the second, the third is also greater than the fourth; and 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... 
