| Euclid, James Thomson - Geometry - 1837 - 390 pages
...the sixth, is of the fourth D. If, therefore, &c. PROP. IV. THEOR. IF the first of four magnitudes **have the same ratio to the second which the third has to the fourth** ; then any like multiples whatever of the first and third have the same ratio to any like multiples... | |
| John Playfair - Geometry - 1837 - 318 pages
...7nB=77inC, and by hypothesis A=mB, therefore A=7nnC. PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** and if any equimultiples whatever be taken of the first and third, and any whatever of the second and... | |
| John Hind - Algebra - 1837 - 539 pages
...there being taken any equimultiples whatever of the first and third, and any equimultiples whatever **of the second and fourth : if the multiple of the first be** greater than the multiple of the second, the multiple of the third will be greater than that of the... | |
| John Hind - Arithmetic - 1840 - 224 pages
...in iheJifth Book of Euclid's Elements, that " Proportion is the Similitude of Ratios; and theJirst **of four magnitudes is said to have the same ratio...the third has to the fourth, when any equimultiples** whatever of the^rst and third being taken, and any equimultiples whatever of the second anA fourth... | |
| Euclides - 1840
...multiples or submultiples which are equal, those pairs of numbers are proportional, or the first has **the same ratio to the second which the third has to the fourth.** But it must be remembered that there are incommensurable magnitudes, the relative values of which,... | |
| Oliver Byrne - Euclid's Elements - 1841 - 98 pages
...understand this definition before proceeding further. с 2 PROP. IV. THEO. If the first of four magnitudes **have the same ratio to the second, which the third has to the fourth,** then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| Oliver Byrne - Ratio and proportion - 1841 - 98 pages
...a, artd (m — n) b с = b, when m — n = 1. PROP. A. THEO. If the first of the four magnitudes has **the same ratio to the second, which the third has to the fourth,** then, if the first be greater than the second, the third is also greater than the fourth ; and if equal,... | |
| Euclides - Geometry - 1841 - 351 pages
...the fourth. If, therefore, the first, &c. QED PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth;** then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| Euclides - 1842
...the ratio of the third to the fourth. Definition of proportion according to Euclid, (Def. V., Book " **The first of four magnitudes is said to have the same...second and " fourth ; if the multiple of the first be** equal to, greater " than, or less than the multiple of the second, the multiple " of the third is also... | |
| Wales Christopher Hotson - 1842
...:: a + c + e ... : 6 + d +/... 149. Geometrical Definition of Proportion. (Euclid, book v. def. 5). **The first of four magnitudes is said to have the same...first and third being taken, and any equimultiples** whatsover of the second and fourth ; if the multiple of the first, be less than that of the second,... | |
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