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Boeken Boek 1 - 10 van 101 over Magnitudes are said to be in the same ratio, the first to the second and the third....
" 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... "
The Elements of Euclid with Many Additional Propositions and Explanatory Notes - Pagina 20
door Eucleides - 1860
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The First Six Books with Notes

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...
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Euclid's Elements of geometry, transl. To which are added ..., Boeken 1-6

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...
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Elements of Geometry, Containing the First Six Books of Euclid

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...
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The Athenaeum

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...
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The first six books of the Elements of Euclid: with notes

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...
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The Elements of geometry [Euclid book 1-3] in general terms, with ..., Deel 3

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...
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Elements of Trigonometry, and Trigonometrical Analysis, Preliminary to the ...

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...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

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,...
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Lectures on the Principles of Demonstrative Mathematics

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,...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

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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