 | Euclides - 1846 - 292 pages
...any whatever of B, F ; therefore, AistoBasEistoF. Wherefore, Ratios that S$c. QEI>. PROP. XII. THEOR. If any number of magnitudes be proportionals, as one of the antecedents is to its conseifuent, so shall all the antecedents taken together be to all the consequents. Let any number... | |
 | University of Cambridge - 1849 - 560 pages
...triangle. How may a circle be described touching one side and the produced parts of the other two? 6. 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. What restriction... | |
 | Harvey Goodwin - Mathematics - 1851 - 196 pages
...triangle. How may a circle be described touching one side and the produced parts of the other two ? 6. 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. What restriction... | |
 | Euclides - Geometry - 1853 - 176 pages
...any whatever of b, f : therefore, as a is to b, so is e to f (v. def. 5). Wherefore, ratios, &c. QED PROPOSITION XII. — THEOREM. If any number of magnitudes...proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. LET any number of... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...therefore, as A is to B, so is E to F (5 Def. v.). Wherefore, ratios that, etc. QED PROPOSITION XII. THEOB. 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. Let any number of... | |
 | Euclid, John Playfair - Geometry - 1853 - 336 pages
...and nB, »F any whatever of B and F ,• therefore A : B : : E : F (def. 5. 5.). PROP. XII. THEOR. ff any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so arc all the antecedents, taken together, to all the consequents. If A : B : C : D, and... | |
 | Euclides - 1855 - 270 pages
...of B and F. Therefore, A is to B .¿s E is to F (V. Def. 5). Wherefore, ratios that, &c. QED PROP. XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so are all the antecedents taken together to au the consequents. Let any numbsr of magnitud«... | |
 | Euclides - 1855 - 230 pages
...therefore A : B :: E : F A _ C C _ E D ~ F ; .. , AE therefore - = -, PROPOSITION XII. THEOREM.—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 taken together. Let... | |
 | Euclides - 1860 - 288 pages
...whatever of A and E ; and nB, riF any whatever of B and F ; therefore A : B : : E : F (V. Def. 10). PROPOSITION XII. THEOREM. If any number of magnitudes...proportionals, as one of the antecedents is to its consequent, so is the sum of all the antecedents to that of the consequents. Given A : B : : C : D,... | |
 | Eucleides - 1860 - 396 pages
...B — D; and because C : D :: E : F, C _ E D ~~ F! therefore — = ^, and therefore A : B :: E : F PROPOSITION XII. THEOREM. — If any number of magnitudes...proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together he to all the consequents taken together. Let... | |
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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. 
