| Euclid, Robert Simson - Geometry - 1829 - 516 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** scoond, which the third has to the fourth, when any equimultiples whatsoever of the first and third... | |
| George Peacock - Algebra - 1830 - 685 pages
...be equal to that of the second, the multiple of the third will be equal to that of the fourth : and **if the multiple of the first be less than that of the second, the multiple of the third** will be less than that J of the fourth. It is this proposition which is deduced as a necessary consequence... | |
| Pierce Morton - Geometry - 1830 - 272 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 - Euclid's Elements - 1833 - 183 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...equimultiples whatsoever of the second and fourth** being taken, the equi-multiples of the first and third either together exceed, are equal to, or are... | |
| Euclides - 1834
...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...taken, and any equimultiples whatsoever of the second** arid rt fourth, if the multiple of the first be less than that of li T.* • * the second, the multiple... | |
| Euclid - 1835 - 513 pages
...less, that is, ' when the ' greater contains the less a certain number of times ex' actly.' III. ' **Ratio is a mutual relation of two magnitudes of the...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,... | |
| Robert Simson - Trigonometry - 1835 - 513 pages
...less, that is, ' when the ' greater contains the less a certain number of times ex' actly.' III. ' **Ratio is a mutual relation of two magnitudes of the...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,... | |
| Mathematics - 1835
...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... | |
| Mathematics - 1836 - 472 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 - Mechanics - 1837 - 182 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... | |
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