 | Pierce Morton - 1830 - 584 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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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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 whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple... 
