 | Robert Simson - 1806 - 546 σελίδες
...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 - 1806 - 320 σελίδες
...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 - 1809 - 542 σελίδες
...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 - 1816 - 588 σελίδες
...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 - 1817 - 456 σελίδες
...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 - 1819 - 350 σελίδες
...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 - 222 σελίδες
...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 - 1823 - 704 σελίδες
...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, Robert Adrain - 1824 - 542 σελίδες
...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 - 1824 - 550 σελίδες
...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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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... 
