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" 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 - Page 49
by Eucleides - 1860
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1781 - 534 pages
...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...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 pages
...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...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,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 554 pages
...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....
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Pantologia. A new (cabinet) cyclopŠdia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...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,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...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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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...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 :...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...to one of them the same ratio which two others have to one oj these, the remaining one of the ▀rtt 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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