 | James Ryan - Algebra - 1824 - 550 pages
...A : D : : E : H. In like manner we may proceed for any number of magnitudes. QED tt PROP. xxiv. I/ the first has to the second the same ratio which the third has to the fouttY\ -, *a& v\» fe.Wtv \x> V^^ wtcond the same ratio vrtucVi V\ia %vs.\Xx \\a& \» fourth; the... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...5.) And «cause us В is to C, so is D to E, and that H, K are equimultiples of PROP. XXIV. THEOR. If the first has to the second the same ratio which the third has lo the fourth ; and the fifth lo the second, the same ratio which the sixth has to the fourth ; the... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...: B+D+F. Therefore &e. QED PROP. XIII. THEOR. If the first have to the seeond the same ratio whieh the third has to the fourth, but the third to the fourth a greater ratio than the fifth has to the sixth ; the first has also to the seeond a greater ratio than the fifth has to the sixth.... | |
 | Euclid - 1826 - 234 pages
...delivers the propositions, which are the following : "Prop. i. 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 - 1826 - 226 pages
...second a less ratio than the third has to the fourth." "Prop. i. 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... | |
 | James Ryan - Algebra - 1826 - 430 pages
...therefore A : D : : E : H. In like manner we may proceed for any number of magnitudes. QED PROP. XXIV. If the first has to the second the same ratio which the tbird has to the fourth ; and the fifth to the second the same ratio s*v which the sixih has to the... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...number of magnitudes. Therefore, if there be any number, &c. QED PROP. XXIV. THEOR. See N. If the fast has to the second the same ratio which the third has to the fourth : and the f1fth to the second, the same ratio which the sixth has to the fourth ; the fast and. fifth... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...and so on, whatever be the number of magnitudes. PROPOSITION XXIV. THEOREM. (503) 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 Warren - 1828 - 174 pages
...opposite direction are called negative quantities. (12.) DEF. The first of four quantities is said to have to the second the same ratio which the third has to the fourth; when the first has in length to the second the same ratio which the third has in length to the fourth,... | |
 | Euclid, Robert Simson - Geometry - 1829 - 548 pages
...are A, C, E together to B, I>, F together. Wherefore, if any number, &c. QED • PROP. XIII. THEOR. IF the first has to the second the same ratio which...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... | |
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If the first has to the second the same ratio which the third has to the fourth... 
