| 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,... | |
| 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 - 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... | |
| 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 - 1840
...be of the same kind) when one of them may be multiplied (numerically) till it exceeds the other. 5. **Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when,** any equimultiples whatsoever being taken of the first and third, and any equimultiples whatsoever of... | |
| Encyclopedias and dictionaries - 1841
...quantities given by Euclid is as follows : — ' Magnitudes are said to have the same ratio to one another, **the first to the second, and the third to the fourth, when** equimultiples of the first and third, and equimultiples of the second afld fourth, whatever the multiplications... | |
| 1841
...quantities given by Euclid is as follows : — ' Magnitudes are said to have the same ratio to one another, **the first to the second, and the third to the fourth, when** equimultiples of the first and third, and equimultiples of the second and fourth, whatever the multiplications... | |
| Euclides - 1846
...said to have a ratio to one another, when the less can be multiplied so as to exceed the greater. 5. **Magnitudes are said to be in the same ratio, the first to the second, and the third to the fourth, when** any submultiple whatsoever of the first is contained in the second, as often as an equi- submultiple... | |
| 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... | |
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