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Books Books 41 - 50 of 97 on The first of four magnitudes is said to have the same ratio to the second, which....
" The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple... "
A system of practical mathematics; being no.xvi. of a new series of school-books - Page 111
1845
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third are taken,...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...magnitude, they cannot be said to be of the same Hud, and so cannot have any ratio to each other. V. The first of four magnitudes is said to have the same ratio to the ęcond, which the third has to the fourth, when any equimultiples whatsoever of the first and third...
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The principles and practice of arithmetic

John Hind - 1856
...is stated in the fifth Book of Euclid's Elements, that "Proportion is the Similitude of Ratios ; and the first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatever of the first and third being taken,...
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Practical Arithmetic, by Induction and Analysis

Joseph Ray - Arithmetic - 1857 - 336 pages
...PROPORTION. ART. 197. Proportion is an equality of ratios. Four numbers are proportional, when the first has the same ratio to the second that the third has to the fourth. Thus, the two ratios, 2 : 4 and 3 : 6, form a proportion, iince | = £, each being equal to 2. ART....
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A Treatise on Elementary and Higher Algebra

Theodore Strong - Algebra - 1859 - 551 pages
...multiple is in like manner greater, equal to, or less tJian the fourth; then the first quantity has the same ratio to the second that the third, has to the fourth. This proposition is substantially the same as the famous Definition V. of Book V. of Euclid ; see R....
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...magnitudes are proportional Or, to bring it still nearer to the language of Euclid's definition: — The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...ratio that the third has to the/owrM. 11. Magnitudes are said to be proportionals when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth ; and so on, whatever...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...which one is infinitely small and the other infinitely large. V. — Definition of Proportion. — The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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The propositions of the fifth book of Euclid proved algebraically

George Sturton Ward - 1862
...multiplied so as to exceed the other. This is the criterion of magnitudes being of the same kind. V. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth when, any equimultiples whatsoever of the first and third being taken,...
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