| Euclides - 1846
...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 whatever of the first and third being taken,... | |
| John Playfair - Euclid's Elements - 1846 - 317 pages
...multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or the first has **the same ratio to the second that the third has to the fourth.** We are now arrived very nearly at Euclid's definition ; for, let A, B, C, D be four proportionals,... | |
| Frederic A. Adams - Arithmetic - 1846 - 212 pages
...tho value is not altered ; it is still 2. PROPORTION. If there are four numbers, and the first has **the same ratio to the second that the third has to the fourth,** the four numbers are said to be in proportion. Thus the numbers 2:1:: 12 : 6, are in proportion. The... | |
| Euclides - 1848
...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,... | |
| Edward Hughes - 1849
...9. 18. 12. 12. 18. 4. 48. Suppose any four terms to be proportional, that is, the first term shall **have the same ratio to the second that the third has to the fourth** ; for example : 8 : 12: : 10 : 15. Let us multiply the two means together 1 2 X 10=1 20, and also the... | |
| Rufus Putnam - Arithmetic - 1849 - 264 pages
...proportion consists of two equal ratios. When four numbers are so related to each other, that the first has **the same ratio to the second that the third has to the fourth,** they constitute a proportion. Thus the numbers 4, 5, Í2, 15, form a proportioH, because the ratio... | |
| James B. Dodd - 1850
...PROPORTION consists in an equality of ratios. Four quantities are in proportion, when the first has **the same ratio to the second, that the third has to the fourth.** Thus, the numbers 6, 3, 8, 4, are in proportion; since the ratio of 6 to 3 is §=2, and the ratio of... | |
| Euclides - Geometry - 1853 - 147 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,... | |
| James B. Dodd - 1853
...PROPORTION consists in an equality of ratios. Four quantities are in proportion, when the first has **the same ratio to the second, that the third has to the fourth.** Thus, the numbers 6, 3, 8, 4, are in proportion; since the ratio of 6 to 3 is f=2, and the ratio of... | |
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