 | William Whewell - 1837 - 226 pages
...GEOMETRY. ELEMENTS or GEOMETRY. EUCLID, Books *i, *II, *III, IV. Book v. *Definition of Proportion. The first of four magnitudes is said to have the same...second which the third has to the fourth, when^ — any eq'wi-multiples whatsoever of the Jirst and third being taken, and any equi-multiples whatsoever of... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 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 - Euclid's Elements - 1837 - 332 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 - 584 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 - 252 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 - 192 pages
...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 - Mathematics - 1841 - 144 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 - Mathematics - 1841 - 140 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 - 378 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 - 316 pages
...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... | |
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The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any... 
