 | Euclid - 1822 - 222 sider
...each other, if they be such that the less can be multiplied so as to exceed the greater. See ff. 5. Magnitudes are said to be in the same ratio, the first to the second as the third to the fourth, when any submultiple whatsoever of the first is contained in the second,... | |
 | Euclides - 1826 - 226 sider
...Magnitudes are said to have a proportion to one another, which multiplied can exceed each other. 5. Magnitudes are said to be in the same ratio, the 'first to the second as the third to the fourth, when the equimultiples of the first and third compared with the equimultiples... | |
 | Euclid - 1826 - 234 sider
...Magnitudes are said to have a proportion to one another, which multiplied can exceed each other. 5. Magnitudes are said to be in the same ratio, the first to the second as the third to the fourth, when the equimultiples of the first and third compared with the equimultiples... | |
 | Euclides - 1833 - 304 sider
...no determinate ratio to its diagonal, for the value of one is unity and of the other the */2. .">. Magnitudes are said to be in the same ratio, the first to the second as the third to the fourth, when, as often as any submultiple whatever of the first is contained in... | |
 | Euclides - 1855 - 230 sider
...Algebra; and with the view of removing this objection, Elrington has substituted the following, namely, " Magnitudes are said to be in the same ratio, the first to the second as the third to the fourth, when any submultiple whatsoever of the first is contained in the second,... | |
 | Euclid - 1859 - 150 sider
...XXаiгXаffккi/юг, írartpov íKa.Ttpov if Ира uiгípíxy, í) «/ia tffa y, s"/ ¿'/ia tXXeíirç KaraXXr;Xa. Magnitudes are said to be in the same ratio, the first to the second as the third to the fourth ; when any equimultiples whatsoever of the first and third, compared with... | |
 | Eucleides - 1860 - 396 sider
...; and with the view of removing this objection, Elrington has substituted the following, namely, " Magnitudes are said to be in the same ratio, the first to the second as the third to the fourth, when any submultiple whatsoever of the first is contained in the second,... | |
 | Euclides - 1861 - 464 sider
...are said to have a ratio to one another, when the less can be multiplied so as to exceed the other. "Magnitudes are said to have a ratio to one another, which are able on being multiplied to exceed one another." — EUCLID. « In Geometry, multiplication is only... | |
 | Euclid - 1868 - 138 sider
...iro\\air\aaiaafiov, екarfpov fKuTBpov jj аfia inrepk%y, jj afia laa y, i) ¡ífia éXXeiirp KaráXXqXa. Magnitudes are said to be in the same ratio, the first to the second as the third to the fourth; when any equimultiples whatsoever of the first and third, compared with... | |
 | 1917 - 330 sider
...ratio is a sort of relation in respect of size between two magnitudes of the same kind. DEFINITION 4. Magnitudes are said to have a ratio to one another...capable when multiplied of exceeding one another. DEFINITION 5. Let A, B, X, Y be four magnitudes, A of the same kind as B, X of the same kind as Y.... | |
| |
Magnitudes are said to have a ratio to one another which are capable, when multiplied, of exceeding one another. 
