 | Euclid - 1822 - 222 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...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 - 226 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 of the second second, than... | |
 | Euclid - 1826 - 234 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 of the second second, than... | |
 | England - 1832 - 868 pages
...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 - Euclid's Elements - 1833 - 216 pages
...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 - 304 pages
...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... | |
 | Augustus De Morgan - Calculus - 1837 - 268 pages
...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 - 192 pages
...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 - Algebra - 1843 - 168 pages
...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 - 272 pages
...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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Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike... 
