 IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last.  An elementary course of practical mathematics - Side 184av James Elliot - 1860Uten tilgangsbegrensning - Om denne boken
 | Robert Simson - 1806 - 546 sider
...Therefore, if there be any number, &c. QED PROP. XXIII. THEOR, IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio, the first shall have to the last of the first magnitudes the same ratio which the first of the... | |
 | John Playfair - 1806 - 320 sider
...number of magnitudes. QED Therefore, &c. PROP. XXIII. THEOR. IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio, the first will have to the last of the first magnitudes the same ratio which the first of the... | |
 | John Mason Good - 1813 - 714 sider
...the words " ex aequali,'' or " ex aequo." Prop. XXIII. Theor. If there be any number of mae -itudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the... | |
 | Charles Butler - 1814 - 528 sider
...ranks. This is called EX JE&UALI IN PROPORTIONS ORDINATA, or simply EX JESUO ORDINATO. Euclid 22, 5. 82. If there be any number of quantities, and as many others, which taken two and two in cross order are proportionals, namely, the first to the second of the first rank, as the last but one... | |
 | Euclides - 1816 - 588 sider
...•>!« ' . l:i •! : . I. I .1 * . PROP. XXIII. THEOR. SeeN. IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the... | |
 | John Playfair - 1819 - 354 sider
...: : E : F, then A : D : : E : H. For, since A, B, C are three magnitudes, and F, G, H other three, which taken two and two, in a cross order, have the same ratio, by the first case, A : C : : F : H. But C : D : : E : F, therefore, again, by the first case,... | |
 | James Ryan - 1824 - 550 sider
...whatever be the number of magnitudes. QED 3«J PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and two in a cross order, have the same ratio ; the 6rst shall have to the last of the first magnitudes the same ratio which the first of the... | |
 | James Ryan, Robert Adrain - 1824 - 542 sider
...whatever be the number of magnitudes. QED PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, which, taken two and two in a cross order have the same ratio •; the 6rst shall have to the last of the first magnitudes the same ratio which the first of... | |
 | Peter Nicholson - 1825 - 1046 sider
...to F: A is to D. as E to H. Because А, В, С, яге three magnitudes, and F, G, H, other three, which, taken two and two in a cross order, have the same ratio ; by the first case, A is to C, as F to H: But с is to D, as E to F ; wheretbre again. by the... | |
 | Robert Simson - 1827 - 546 sider
...<.] r tHyp. •11.5. tHyp. Next, let there be four magnitudes A, B, C, D, and other four E, F, G, H, which taken two and two in a cross order have the same ratio, viz. A to B, as G to H; B to C, as F to G ; and C to D, asEtoF: A shall be to D, as E to H.... | |
| |
