| Euclides - 1864
...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
...greater ratio to the second, than the fifth has to the sixth. PROP. XIV.— THEOREM. If tlie first has **the same ratio to the second which the third has to the fourth** ; then, if the first be greater than the third, the second shall be greater than the fourth ; and if... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...whatever of the first and the third being taken, and any equimultiples whatever of the second and the **fourth, if the multiple of the first be less than...of the third is also less than that of the fourth,** and if the multiple of the first be equal to that of the second, the multiple of the third is also... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...multiple of the third is also equal to that of the fourth, and if the multiple of the first be greater **than that of the second, the multiple of the third is also** greater than that of the fourth. 6. Magnitudes which have the same ratio are called proportionals.... | |
| Euclid - 1868 - 141 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 - 410 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
...multiple of the third is also equal to that of the fourth : or, " If the multiple of the first be greater **than that of the second, the multiple of the third is also** greater than that of the fourth." We shall now shew, first, how to deduce Euclid's test of the equality... | |
| James Hamblin Smith - Algebra - 1870
...test is given in Book v. Def. 5, where it stands thus: " The first of four magnitudes is said to have **the same ratio to the second which the third has to...equimultiples whatsoever of the first and third being** takeu and any equimultiples whatsoever of the second and fourth : " If the multiple of the first be... | |
| James Hamblin Smith - 1870
...of the third is also equal to that of the fourth: or, • " If the multiple of the first be greater **than that of the second, the multiple of the third is also** greater than that of the fourth." • . We shall now shew, first, how to deduce Euclid's test of the... | |
| James Hamblin Smith - Algebra - 1872 - 398 pages
...test is given in Book v. Def. 5, where it stands thus: " The first of four magnitudes is said to have **the same ratio to the second which the third has to...whatsoever of the first and third being taken and** auy equimultiples whatsoever of the second and fourth : " If the multiple of the first be less than... | |
| |