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" IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. "
An Elementary Treatise on Algebra: Theoretical and Practical - Page 498
by James Ryan, Robert Adrain - 1824 - 516 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 488 pages
...B, F. Therefore as A is to B, fo is E to Fa. Wherefore ratios that, &c. Q^ED PROP. XII. THEO R. TF any number of magnitudes be proportionals, as one of the antecedents is to its confequcnt, fo fhall all the antecedents taken together be to all the confequents. Let any number of...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 534 pages
...B, F : Therefore, as A is to B, fo is E to F". Wherefore ratios that, &c. Q^ED PROP. XII. THEO R. TF any number of magnitudes be proportionals, as one of the antecedents is to its confequent, fo fhall all the antecedents taken together be to all the cor.fequents. Let any number...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...B, F : Therefore, as A is to B, fo is E to F*. Wherefore ratios that, &c. Q^ED PROP. XII. THEO R. / "IF any number of magnitudes be proportionals, as one \ of the antecedents is to its confequent, fo fhal! all the antecedents taken together be to all the cpnfeqtients. Let any number...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...any whatever of B and F ; therefore A : B : : E : F. Therefore, &c. Q., ED PROP. PROP. XII. THEO R. IF any number of magnitudes be proportionals, as one of the antecedents is to its confequent, fo (hall all the antecedents taken together be to all the confequents. If A:B::C:D, andC:D::E:F;...
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The Elements of Mathematical Analysis, Abridged: For the Use of Students ...

Nicolas Vilant - Algebra - 1798 - 196 pages
...Ratios that are die lame to the fame ratios, are the fame to one tlier. PROPOSITION XII,— THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its confequent, fo ihall all the antecedents taken together be to all the confequents. Hyp- | A : B=C :...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 374 pages
...A is to B, fo a is E to F. Wherefore, &c. Q^ ED PROP. I J3 contains B; PROP. XII. THEOR. .BooK v-. IF any number of magnitudes be proportionals, as one of the antecedents is to its confequent, fo {hall all the antecedents taken together be to all the confequents. Let any number of...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 pages
...of B, F. Therefore as A is to B, fo is E to F •. Wherefore ratios that, &c. . D. PROP. XII. THEOR. IF any number of magnitudes be proportionals, as one of the antecedents is to its confequent, fo fhall all the antecedents taken together be to all the eonfequents. Let any number of...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair, Euclid - Circle-squaring - 1804 - 468 pages
...of B and F ; therefore A : B : : E : F a. Therefore, &c. Q^ ED Book V. *— * - ' PROP. XII. THE OR. IF any number of magnitudes be proportionals, as one of the antecedents is to itsconfequent, fb are all the antecedents, taken together, to all the confequents. If A : B : : C :...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...of B, F : therefore, as A is to B so is E to F. Wherefore, ratios that, &c. QED PROP. XII. THEOR. IF any number of magnitudes be proportionals, as one...antecedents taken together be to all the consequents. Let any number of magnitudes A, B, C, D, E, F be proportionals ; that is, as A is to B so C to D, and...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...wF any whatever of B and F ; therefore A : B : : E : Fa. Therefore, &c. QED Bookv. PROP. XII. THEOR. IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so are all the antecedents, taken together, to all the cdnsequents. If A : B : : C : D, and C : D : :...
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