| James Ryan - 1826 - 383 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.** DEMONSTRATION. By hypothesis we have A+B : B : : C+D : D,.and we are to prove that A : B : : C : D.... | |
| Robert Simson - 1827 - 513 pagina’s
...to one of them the same ratio which two others have to one of these, the remaining one of the fast **two shall have to the other the same ratio which the...taken jointly which are proportionals; that is, as AB** to BE, so let CD be to DF : they shall also be proportionals taken separately, viz. as AE to EB, so... | |
| Euclid, Dionysius Lardner - 1828 - 324 pagina’s
...of them the same ratio which two others have to one of these, the remaining one of the first two has **to the other the same ratio which the remaining one...of the last two has to the other of these. Let AB,** EC, CD, DF be the magnitudes takenjointly which are proportionals •. that is, AB : BE = CD : DF:... | |
| Euclid, Robert Simson - 1829 - 516 pagina’s
...the same ratio which two others have to one of these, the remaining one of the first two shall Jiave **to the other the same ratio which the remaining one...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... | |
| Euclides - 1834
...to one of these, the remaining one of the Jirsl two shall have to the other, the same ratio rvhich **the remaining one of the last two has to the other...jointly, which are proportionals ; that is, as AB** to BE, so let CD be- ** N to DF : they shall also be proportionals taken separately ; viz. as AE to... | |
| Euclid, Robert Simson - 1835 - 513 pagina’s
...them the same ratio which two others have to one of these, the remaining one of the first two will **have to the other the same ratio which the remaining one of the** latter two has to the other of these. Let AB, BE, CD, DF be the magnitudes taken jointly which are... | |
| Euclid, Robert Simson - 1835 - 513 pagina’s
...them the same ratio ivhich two others have to one of these, the remaining one of the first two will **have to the other the same ratio which the remaining one of the** latter two has to the other of these. Let AB, BE, CD, DF be the magnitudes taken jointly which are... | |
| Euclid - 1838 - 416 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... | |
| Euclid - 1838 - 416 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...magnitudes 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,... | |
| Dionysius Lardner - 1838 - 332 pagina’s
...of them the same ratio which two others have to one of these, the remaining one of the first two has **to the other the same ratio which the remaining one...magnitudes taken jointly which are proportionals : that is,** AB : BE = CD : D If : they shall also be proportionals taken separately, viz. AE : EB = CF : FD. Take... | |
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