| Euclides - 1863 - 122 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...whatsoever of the first and third being taken, and** auy equimultiples whatsoever of the second and fourth; if the multiple of the first b« IMS than that... | |
| Euclides - 1864 - 448 pages
...being any integers, no, no, ' or mAl : na, : : mAt : no,. That is, if the first of four magnitudes has **the same ratio to the second which the third has to the fourth** ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| Euclides - 1865 - 402 pages
...has to the second a greater ratio than the fifth has to the sixth . . . . . V. 13. 10. If the first **have the same ratio to the second which the third has to the fourth** ; then if the first be greater than the third, the second is greater than the fourth ; and if equal,... | |
| Robert Potts - 1865 - 528 pages
...is to G, so is Fto H. (v. def. 5.) Therefore, if the first, &c. QED CoR. Likewise, if the first has **the same ratio to the second, which the third has to the fourth,** then also any equimultiples whatever of the first and third shall have the same ratio to the second... | |
| Euclid, Isaac Todhunter - 1867 - 426 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. **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 whatever of the first and the third being... | |
| Euclid, Isaac Todhunter - 1867 - 424 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. **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 whatever of the first and the third being... | |
| Euclid - 1868 - 138 pages
...Sivripov Kai rfrápruv, кaQ' ùiroiovovv iro\\air\aaia.afièv, rbv àvrbv ejfi Xóyo»< If the first has **the same ratio to the second which the third has to the fourth;** any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of... | |
| Robert Potts - 1868 - 434 pages
...fourth D. If, therefore, the first, &c. QED PROPOSITION IV. THEOREM. If the first of four magnitudes hat **the same ratio to the second which the third has to the fourth** ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| James Hamblin Smith - 1869 - 412 pages
...representing the ratios must be equal. Euclid's test is given in Book v. Def. 5, where it stands thus : " **The first of four magnitudes is said to have the same...being taken and any equimultiples whatsoever of the** second and fourth : " If the multiple of the first be less than that of the second, the multiple of... | |
| James Hamblin Smith - 1870 - 478 pages
...representing the ratios must be equal. Euclid's test is given in Book Y. Def. 5, where it stands thus: " **The first of four magnitudes is said to have the same...being taken and any equimultiples whatsoever of the** second and fourth : " If the multiple of the first be less than that of the second, the multiple of... | |
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