| Pierce Morton - 1830 - 584 pages
...having the same ratio to two others В and D, of the same kind with the former two respectively. Def. 7. **The first of four magnitudes is said to have the same ratio to the** se* By the word " corresponding" here used, it U R«TÍy iat«*nded to point out the fact of there... | |
| Euclid - 1833 - 216 pages
...ought to be defined, is still a subject of controversy among geometers. Euclid defines them thus : **The first of four magnitudes is said to have the same...being taken, and any equimultiples whatsoever of the** second and fourth being taken, the equi-multiples of the first and third either together exceed, are... | |
| Robert Simson - 1835 - 544 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. y. **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 whatsoever of the first and third being taken,... | |
| Euclid - 1835 - 540 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. y. **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 whatsoever of the first and third being taken,... | |
| 1835 - 684 pages
...equal to, or less than the corresponding magnitude of the other ; and conversely (ax. 1, 2, 3, 4).* • **"The first of four magnitudes is said to have the same ratio** tu the second, which the third has to the fourth, when any equimultiples whatsoever of the first and... | |
| 1836 - 488 pages
...oft as there are units in the product of these two numbers. IV. 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 tcriken of the first and third, and any whatever of the second... | |
| 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 - 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 - 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 - 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... | |
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