 | Robert Potts - 1868 - 434 pàgines
...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 - 1870 - 452 pàgines
...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 pàgines
...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 pàgines
...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 - 1872 - 376 pàgines
...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 - 1874 - 80 pàgines
...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 pàgines
...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 pàgines
...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 pàgines
...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 pàgines
...OAv OB, be proportional, and the following statement hold good:— If there be four magnitudes, and any equimultiples whatsoever of the first and third...equimultiples whatsoever of the second and fourth being taken, if the equimultiples of the first and third together exceed, or are equal to, or are less... | |
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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... 
