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Boeken Boek 11 - 20 van 43 over IF magnitudes, taken jointly, be proportionals, they shall also be proportionals....
" 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... "
The Elements of Euclid with Many Additional Propositions and Explanatory Notes - Pagina 51
door Eucleides - 1860
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An Elementary Treatise on Algebra: Theoretical and Practical ...

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....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

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...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

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:...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

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...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

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...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

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...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

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...
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The Elements of Euclid

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...
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The Elements of Euclid

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,...
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The First Six Books of the Elements of Euclid: With a Commentary and ...

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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