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Books Books 1 - 10 of 57 on Magnitudes are said to have a ratio to one another which are capable, when multiplied,....
" Magnitudes are said to have a ratio to one another which are capable, when multiplied, of exceeding one another. "
The Teaching of Geometry - Page 229
by David Eugene Smith - 1911 - 339 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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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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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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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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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

Joseph Allen Galbraith - 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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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...; 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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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...are said to have a ratio to one another, when the less can be multiplied so as to exceed the other. "Magnitudes are said to have a ratio to one another, which are able on being multiplied to exceed one another." — EUCLID. In Geometry, multiplication is only...
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Manual of Euclid, Books 4-6

Euclid - 1868
...iro\\air\aaiaafiov, екarfpov fKuTBpov jj аfia inrepk%y, jj afia laa y, i) fia XXeiirp KarXXqXa. 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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Books 3-9

Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - Mathematics, Greek - 1908
...II. 8 3. A ratio is a sort of relation in respect of size between two magnitudes of the same kind. 4. Magnitudes are said to have a ratio to one another...capable, when multiplied, of exceeding one another. 5. Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth,...
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