| Euclid, Robert Simson - 1781 - 466 pagina’s
...have to the ,other, the fame ratio which the remaining one of the laft two has to the other of thefe. **Let AB, BE; CD, DF be the magnitudes taken jointly which are proportionals ; that is, as AB** to BE, fo is CD to DF ; they fhall alfo be proportionals taken feparately, viz. as AE to EB, fo CF... | |
| Euclid - 1781 - 520 pagina’s
...have to the other the fame ratio which the remaining one of the laft two has to the other of thefe. **Let AB, BE, CD, DF be the magnitudes taken jointly which are proportionals ; that is, as AB** to BE, fo is CD to DF; they fhall alfo be proportionals taken feparately, viz. as AE to EB, fo CF to... | |
| Robert Simson - 1804
...have to the other, the fame ratio which the remaining one of the laft two has to the other of thefe. **Let AB, BE; CD, DF be the magnitudes taken jointly which are proportionals ; that is, as AB** to BE, fo is CD to DF ; they fhall alfo be proportionals taken feparately, viz. as AE to EB, fo CF... | |
| Euclid, Robert Simson - 1806 - 518 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...AB, BE, CD, DF be the magnitudes taken jointly which** arc proportionals; that is, as AB to BE, so is CD to DF ; they shall also be proportionals taken separately,... | |
| Euclid - 1810 - 518 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 is CD to DF; they shall also be proportionals taken separately, viz. as AE to KB, so CFtoFD.... | |
| John Mason Good, Olinthus Gilbert Gregory - 1813
...together have to one of them the same ratio which t»o 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.** Prob. XVIII. Theor. If magnitudes, taken separately, he proportionals, they shall also be proportionals,... | |
| Euclides - 1816 - 528 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 is CD to DF : they shall also be proportionals taken separately, viz. as AE to EB, so CF... | |
| James Ryan - 1824 - 516 pagina’s
...together have to one of them the same ratio which two others have to oneof 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.** DEMONSTRATION. By hypothesis we have A + B : B : : C-fD : D, and we are to prove that A : B : : C :... | |
| James Ryan - 1824 - 516 pagina’s
...have to one of them the same ratio which two o\\\ets,\\&NeAo of these, the remaining oue ot the 10 **the other the same ratio which the remaining one of the last two has to the other of these.** DEMONSTRATION. By hypothesis we have A + B : B : : C + D : Dt and we are to prove that A : B : : C... | |
| Peter Nicholson - 1825 - 372 pagina’s
...to one of them the same ratio which two others have to one oj these, the remaining one of the ßrtt **two shall have to the other the same ratio which the remaining** ene of the last two has to i/te other of these. Let AB, BE, CD, DF be the magnitudes taken jointly... | |
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