 | Euclid - 1781 - 552 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 - 1781 - 534 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... | |
 | Robert Simson - 1804 - 530 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... | |
 | Robert Simson - 1806 - 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...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 - 554 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 - 1813 - 714 pagina’s
...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 - 588 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, Robert Adrain - 1824 - 542 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 - 550 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 - 1046 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... | |
| |
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... 
