 | Euclid, John Playfair - 1846 - 334 σελίδες
...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 - 1846 - 230 σελίδες
...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... | |
 | Edward Hughes - 1849 - 162 σελίδες
...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 - 1849 - 402 σελίδες
...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 - 276 σελίδες
...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... | |
 | James B. Dodd - 1853 - 398 σελίδες
...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... | |
 | John Hind - 1856 - 346 σελίδες
...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, and any equimultiples whatever of the second said fourth ; if the multiple of the... | |
 | Joseph Ray - 1857 - 348 σελίδες
...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 - 1859 - 570 σελίδες
...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.... | |
 | Euclides - 1860 - 288 σελίδες
...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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The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples... 
