| James Hamblin Smith - 1870 - 452 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...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 - 1872 - 454 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 - 226 pages
...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,... | |
| Euclid, Lewis Carroll - 1874 - 80 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 '... | |
| Charles Lutwidge Dodgson - 1874 - 96 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 - 1874 - 400 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... | |
| Euclides - 1874 - 342 pages
...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... | |
| William Alexander Willock - 1875 - 196 pages
...OAv OB, be proportional, and the following statement hold good:— If there be four magnitudes, and **any equimultiples whatsoever of the first and third...being taken, and any equimultiples whatsoever of the** second and fourth being taken, if the equimultiples of the first and third together exceed, or are... | |
| Euclid - 1876 - 240 pages
...Or, to bring it still nearer to the language of Euclid's definition: — The first of four magnitades **is said to have the same ratio to the second, which...equimultiples whatsoever of the first and third being taken,** the second is contained as often in the equimultiple of the first, as the fourth is contained in the... | |
| Robert Potts - 1876 - 446 pages
...any integers, m,*l. mA. or m/ll : na, : : m/f, : na,. That i«, 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 game ratio to any equimultiples... | |
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