| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 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 second,** which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
| John Playfair - Euclid's Elements - 1806 - 311 pages
...ratio that the third has to the fourth. VI. Magnitudes are said to be proportionals, when the first has **the same ratio to the second that the third has to the fourth** ; and the third to the fourth the same ratio which the fifth has to the sixth, and so on, whatever... | |
| Sir John Leslie - Geometry, Analytic - 1809 - 493 pages
...exactly resemble the changes usually effected in the reduction of equations. According to Euclid, " **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,... | |
| Euclides - Euclid's Elements - 1816 - 528 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,** which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,... | |
| Sir John Leslie - Geometry - 1817 - 432 pages
...resemble exactly the changes usually effected in the reduction of equations. According to Euclid, " **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,... | |
| John Playfair - Circle-squaring - 1819 - 333 pages
...multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or the first has **the same ratio to the second that the third has to the fourth.** We are now arrived very nearly at Euclid's definition ; for, let A, B, C, D be four proportionals,... | |
| Euclid - 1822 - 179 pages
...be defined, is still a subject of controversy among geometers. Euclid defines them thus: The Jirst **of four magnitudes is said to have the same ratio to the second,** which the third has to the fourth, when any equi-multiples whatsoever of the Jirst and third being... | |
| George Crabb - Industrial arts - 1823
...the ratio of 6 to 2 is the same as that of 15 to 5, which is expressed thus : as 6 : 2 : : 15 : 5. **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,... | |
| James Ryan - Algebra - 1824 - 516 pages
...that the ratio of C to D is less than the ratio of A to B. The Fifth Definition according to Euclid. **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... | |
| James Ryan - Algebra - 1824 - 516 pages
...that the ratio of C to D is less than the ratio of A to B. The Fifth Definition according to Euclid. **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,... | |
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