 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...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...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,... | |
 | Euclid, John Playfair - 1853 - 336 σελίδες
...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 C . D : . E... | |
 | Euclides - 1855 - 230 σελίδες
...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...antecedents taken together be to all the consequents taken together. Let any number of magnitudes A, B, C, D, E, F, be proportionals ; that is, as A is... | |
 | Euclides - 1855 - 270 σελίδες
...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« A, B, С,... | |
 | Eucleides - 1860 - 396 σελίδες
...E : F, C _ E D ~~ F! therefore — = ^, and therefore A : B :: E : F PROPOSITION XII. THEOREM. — If any number of magnitudes be proportionals, as one...consequent, so shall all the antecedents taken together he to all the consequents taken together. Let any number of magnitudes A, B, C, D, E, F, be proportionals... | |
 | Euclides - 1860 - 288 σελίδες
...nB, riF any whatever of B and F ; therefore A : B : : E : F (V. Def. 10). PROPOSITION XII. THEOREM. If any number of magnitudes be 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, and C : D : :... | |
 | Robert Potts - 1860 - 380 σελίδες
...as A is to B, so is E to F. (v. def. 5.) Wherefore, ratios that, &c. QED PROPOSITION XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents it to Us consequent, so shall all the antecedents taken together be to all the consequents. Let any... | |
 | Euclides - 1861 - 464 σελίδες
...Thus also, if A : B > or < C : D, and C : D = E : F, then A : B > or < E : F. PROP. XII. — THEOB. If any number of magnitudes be proportionals, as one...antecedents taken together be to all the consequents. Cos. Pst. 1, V. DEM. Def. 5, V. Definition of Proportion. 1, V. If any no. of Ms he equims of as many,... | |
 | George Sturton Ward - 1862 - 104 σελίδες
...therefore - = -; о а and because с : d : : e : f, therefore - = - : therefore -¡ = 7, b Í PROPOSITION XII. If any number of magnitudes be proportionals,...antecedents taken together be to all the consequents. a, b ; c,d ; e, f. Let a : b ; ; с : d :: e :f. Then shall a : b ;: a + c+ e : b+ d+f. Because a :... | |
 | Euclides - 1864 - 448 σελίδες
...is to B, so is E to F. (v. def. 5.) Wherefore, ratios that, &o. q. i;. i,. PROPOSITION XII. THEOREM. 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,... | |
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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. 
