| Euclid - 1822 - 179 pagina’s
...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...equi-submultiple of the third is contained in the fourth.** 6. Magnitudes which have the same ratio are called proportionals. See N. 7. If a submultiple of the... | |
| 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 of the second second, than... | |
| Euclid, Phillips - 1826 - 180 pagina’s
...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 of the second second, than... | |
| 1832
...farmore easy of application — namely, that four magnitudes are proportional, when a submitltiple **of the first is contained in the second, as often...equi-submultiple of the third is contained in the fourth.** This definition includes the case of the incominensurables, one too important to be omitted. To the... | |
| Euclid, Thomas Elrington - 1833 - 183 pagina’s
...multiplied so as to exceed the greater. 5. Magnitudes are said to be in the same ratio, the See N. **first to the second as the third to the fourth, when...equi-submultiple of the third is contained in the fourth.** 6. Magnitudes which have the same ratio are called proportionals. 7. If a submultiple of the first... | |
| 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 the second, so often is an equi-submnltiple... | |
| 1837 - 230 pagina’s
...next definition, is here assumed* as the distinction of quantities which have a ratio. DEFINITION V. **Magnitudes are said to be in the same ratio the first to the second,** and the third to the fourth : when the same multiples of the first and third being taken, and also... | |
| 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,... | |
| Philip Kelland - 1843 - 147 pagina’s
...one. We thus arrive at Euclid's definition ; " Four magnitudes are said to be in the same proportion, **the first to the second as the third to the fourth, when** equimultiples of the first and third being taken, and also equimultiples of the second and fourth,... | |
| 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,... | |
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