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Books Books 1 - 10 of 105 on 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... "
Elements of Trigonometry, and Trigonometrical Analysis, Preliminary to the ... - Page 30
by Augustus De Morgan - 1837 - 230 pages
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The First Six Books with Notes

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

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...
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Euclid's Elements of geometry, transl. To which are added ..., Books 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...
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The Elements of geometry [Euclid book 1-3] in general terms, with ..., Part 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...
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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, and any equimultiples whatsoever of...
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Penny Cyclopaedia of the Society for the Diffusion of Useful ..., Volumes 19-20

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...
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The Penny Cyclopaedia of the Society for the Difussion of Useful ..., Volume 19

Society for the Difussion of Useful Knowledge - 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...
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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, as often as an equi- submultiple...
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The Elements of Euclid, with many additional propositions, and explanatory ...

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,...
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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Euclides - 1859
...XXаiгXаffккi/юг, rartpov Ka.Ttpov if Ира uiгpxy, ) /ia tffa y, s"/ '/ia tXXeir 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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