 | Robert Simson - 1762 - 488 pàgines
...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... | |
 | Robert Simson - 1775 - 534 pàgines
...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... | |
 | Euclid - 1781 - 552 pàgines
...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... | |
 | Euclid, John Playfair - 1795 - 462 pàgines
...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;... | |
 | Nicolas Vilant - 1798 - 196 pàgines
...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 :... | |
 | Alexander Ingram - 1799 - 374 pàgines
...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... | |
 | Robert Simson - 1804 - 530 pàgines
...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... | |
 | John Playfair, Euclid - 1804 - 468 pàgines
...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 :... | |
 | Robert Simson - 1806 - 546 pàgines
...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... | |
 | John Playfair - 1806 - 320 pàgines
...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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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. 
