| 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... | |
| 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... | |
| James Hamblin Smith - Algebra - 1870
...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...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 - Algebra - 1872 - 398 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...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... | |
| André Darré - 1872
...only one hitherto devised that applies equally to commensurable and incommensurable quantities ; " **the first of four magnitudes is said to have the same ratio to the second,** that the third has to the fourth, when any equi-multiples whatsoever of the first and third being taken,... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...be proportionals, and any equimultiples be taken of the first and third, and also any equimultiples **of the second and fourth, if the multiple of the first be** greater than that of the second, the multiple of the third must be greater than that of the fourth... | |
| Euclid, Lewis Carroll - Euclid's Elements - 1874 - 62 pages
...third is also greater than that of the fourth. The Algebraical Definition answering to this would be ' **The first of four magnitudes is said to have the same...the second which the third has to the fourth, when** the first is the same multiple, part, or fraction of the second which the third is of the fourth '... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...be compared with one which differs from the latter by less than any assignable quantity. DEFINITION. **The first of four magnitudes is said to have the same...the second which the third has to the fourth when,** if the first be divided into any number whatever of equal parts and the third be divided into the same... | |
| Charles Lutwidge Dodgson - 1874
...third is also greater than that of the fourth. The Algebraical Definition answering to this would be ' **The first of four magnitudes is said to have the same...the second which the third has to the fourth, when** the first is the same multiple, part, or fraction of the second which the third is of the fourth '... | |
| Euclides - 1874
...ratio to the second, than the fifth has to the sixth. PROPOSITION 14.— Theorem. If the 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 ; ana if... | |
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