 | Euclid - 1822 - 222 pages
...to 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 - 1826 - 234 pages
...4. 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 - 226 pages
...4. 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 - Euclid's Elements - 1833 - 216 pages
...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 any submultiple whatsoever...the first is contained in the second, as often as an equi-submultiple of the third is contained in the fourth. 6. Magnitudes which have the same ratio are... | |
 | 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... | |
 | 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 of the second and fourth, with any... | |
 | Euclides - 1840 - 192 pages
...to 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...the second and the third to the fourth, when, any equimultiples whatsoever being taken of the first and third, and any equimultiples whatsoever of the... | |
 | Encyclopedias and dictionaries - 1841 - 1040 pages
...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 - 524 pages
...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 - 1855 - 230 pages
...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,... | |
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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... 
