 | Euclides - 1841 - 378 pagina’s
...together, have to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to the other, the same...one of the last two has to the other of these. Let A6, BE, CD, DP be the magnitudes, taken jointly, which are proportionals; that is, as AB to BE, so... | |
 | Oliver Byrne - 1841 - 144 pagina’s
...together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...remaining one of the last two has to the other of these. then will ф : 0 " 0 : О' Take M ф ^- m 0, to each add M 0, then we have M^ + M 0 c- « 0 + M 0'... | |
 | Euclides - 1845 - 546 pagina’s
...together have to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...taken jointly which are proportionals ; that is, as AB to BE, so let CD be to DF. Then they shall also be proportionals taken separately, viz. as AE to EB,... | |
 | Euclid - 1845 - 218 pagina’s
...together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...jointly, which are proportionals ; that is, as AB to BE, so is CD to DF : they shall also be proportionals taken separately ; viz. as AE to EB, so CF... | |
 | Euclides - 1846 - 292 pagina’s
...together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...two has to the other of these. Let AB, BE, CD, DF be four magnitudes which, taken jointly, are proportionals, that is, let AB be to BE as CD to DF : they... | |
 | Euclides - 1848 - 52 pagina’s
...together have to one of them, the same ratio which two others have to one of these the remaining one of the first two shall have to the other the same...remaining one of the last two has to the other of these. PROP. XVIII. THEOREM. If magnitudes, taken separately, be proportionals, they shall also be proportionals... | |
 | Euclides - 1853 - 176 pagina’s
...together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...the last two has to the other of these. LET ab, be, С d, df be the magnitudes taken jointly which are proportionals ; that is, as ab to be so is Сd to... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pagina’s
...together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same ratio which the remaining one of the last lwo has to the other of these. Let AB, BE, CD, DF be the magnitudes, taken jointly, which are proportionals... | |
 | Euclides - 1855 - 230 pagina’s
...together have to one of them the same ratio which tieo others hare to one of these, the remaining one of the first two shall have to the other the same...CD to DF ; they shall also be proportionals taken separately, viz. as AE is to EB so is CF to FD. AB ; therefore GK is the same multiple of GA c AB that... | |
 | Robert Potts - 1860 - 380 pagina’s
...together haw to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...taken jointly which are proportionals ; that is, as AB to BE, so let CD be to DF. Then they shall also be proportionals taken separately, viz. as AE to EB,... | |
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IF magnitudes, taken jointly, be proportionals, they shall also be proportionals when taken separately ; that is, if two magnitudes together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall... 
