 | Euclides - 1855 - 230 pagina’s
...integers or fractions. Thus — = 3, and - = 3, therefore the numbers 15, 5, 9, and 3 are said 15 9 t> U to be in proportion; and this is usually expressed...the first is contained in the second, as often as au equi-submultiple of the third is contained in the fourth." On the other hand, many of the most able... | |
 | Euclid - 1859 - 150 pagina’s
...XXаiгXаffккi/юг, írartpov íKa.Ttpov if Ира uiгípíxy, í) «/ia tffa y, s"/ ¿'/ia tXXeíirç KaraXXr;Xa. Magnitudes are said to be in the same ratio, the first...to the second as the third to the fourth ; when any equimultiples whatsoever of the first and third, compared with any equimultiples whatsoever of the... | |
 | Euclides - 1861 - 464 pagina’s
...greater than that of the second, the multiple of the third is also greater than that of the fourth. " Magnitudes are said to be in the same ratio, the first to the second, and the third to the fourth, — when the equimultiples of the first and third, being at the same time... | |
 | Euclid - 1868 - 138 pagina’s
...iro\\air\aaiaafiov, екarfpov fKuTBpov jj аfia inrepk%y, jj afia laa y, i) ¡ífia éXXeiirp KaráXXqXa. Magnitudes are said to be in the same ratio, the first...to the second as the third to the fourth; when any equimultiples whatsoever of the first and third, compared with any equimultiples whatsoever of the... | |
 | Euclid - 1872 - 284 pagina’s
...said to have a ratio to one another, when the less can be multiplied so as to exceed the greater. 5. Magnitudes are said to be in the same ratio, the first to the second, and the third to the fourth, when any submultiple whatsoever of the first is contained in the second,... | |
 | William Alexander Willock - 1875 - 196 pagina’s
...the first as the fourth to the third. This is evident from the first test. For, since a submultiple of the first is contained in the second as often as...equisubmultiple of the third is contained in the fourth, it follows that a submultiple of the second is contained in the first as often as an equisubmultiple... | |
 | Euclid - 1876 - 240 pagina’s
...fault with because it beans no resemblance to the common notions of the similitude of ratios emJdoyed in Arithmetic or Algebra; and with the view of removing...geometers have maintained that the fifth book of Euclid is u masterpiece of skilful reasoning ; and that none of the attempts which have been made to supersede... | |
 | Homersham Cox (the younger) - 1885 - 254 pagina’s
...very theorems it is desired to prove. Euclid,s definition of proportion is as follows : Quantities are said to be in the same ratio, the first to the second and the third to the fourth when equal multiples of the first and third are at the same time greater... | |
 | Euclid - 1908 - 456 pagina’s
...said to have a ratio to one another which are capable, when multiplied, of exceeding one another. 5. Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and... | |
 | David Eugene Smith - 1911 - 370 pagina’s
...are said to have a ratio to one another which are capable, when multiplied, of exceeding one another. Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and... | |
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Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike... 
