| Euclides - 1841
...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 - 98 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'... | |
| Robert Simson - 1845 - 199 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... | |
| Robert Potts - 1845
...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,... | |
| Euclides - 1846
...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
...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
...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, Thomas Stephens Davies, Stephen Fenwick, William Rutherford - 1853
...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
...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 - 361 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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