| 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,... | |
| 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** «cond, which the third has to the fourth, when any equimultiples whatsoever of the first and third... | |
| 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,... | |
| 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.... | |
| 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.... | |
| 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,... | |
| 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,... | |
| 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... | |
| 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,... | |
| 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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