| 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... | |
| 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... | |
| 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... | |
| 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;... | |
| 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 :... | |
| 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... | |
| 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... | |
| 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 :... | |
| 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... | |
| 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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