 | James Hamblin Smith - 1870 - 478 páginas
...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...whatsoever of the first and third being taken and any equimultiples whatsoever of the second and fourth : " If the multiple of the first be less than... | |
 | James Hamblin Smith - 1870 - 452 páginas
...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 páginas
...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...second and fourth : " If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth : or,... | |
 | André Darré - 1872 - 226 páginas
...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,... | |
 | Francis Cuthbertson - 1874 - 400 páginas
...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... | |
 | Euclid, Lewis Carroll - 1874 - 80 páginas
...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 páginas
...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 - 342 páginas
...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... | |
 | Euclid - 1876 - 240 páginas
...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 páginas
...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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The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple... 
