| Euclid - 1822 - 179 pages
...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
...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, Phillips - 1826 - 180 pages
...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
...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
...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,... | |
| Joseph Allen Galbraith - 1859
...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
...; 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
...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
...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... | |
| Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - Mathematics, Greek - 1908
...II. 8 3. A ratio is a sort of relation in respect of size between two magnitudes of the same kind. 4. **Magnitudes are said to have a ratio to one another...capable, when multiplied, of exceeding one another.** 5. Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth,... | |
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