 | John Mason Good - 1813 - 714 pages
...XI. Theor. Ratios that are the same to thr same ratio, are the same to one onother. Prop XII. Theor. If any number of magnitudes be proportionals, as one of the antecedents is to it? consequent, so shall all the antecedents taken together he to all the consequents. Prop. XIII.... | |
 | Euclides - 1816 - 588 pages
...of B, F : Therefore, as A is to B, so is E to Fa. Wherefore, ratios that, &c. QED PROP. XII. THEOIl. 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... | |
 | John Playfair - 1819 - 354 pages
...whatever of B and F ; therefore A : B : : E : F (def. 5. 5.). Therefore, &c. QED 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 consequents. If A : B : : C : D,... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...whatever of B andF ; therefore A : B : : E : F (def. 5. 5.). Therefore, &c. Q, ED . x PROP. XII. THEOR. If any number of magnitudes be proportionals, as one of the antecedents ii to its consequent, so are all the antecedents, taken together, to all the consequents. If A : B... | |
 | James Ryan - Algebra - 1824 - 550 pages
...the same reason-^r —7=7! c \j therefore 4-=§-, that is, A : B : : E : F. 1) r QED /Z-. PROP. XII. 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. DEMONSTRATION. By... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...as C to D, therefore-g=jj, EC for the same therefore g-=-, that is, A : B : : E : F. QED PROP. XII. 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. DEMONSTRATION. By... | |
 | John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...the segments of the other. 4. Inscribe an equilateral and equiangular hexagon in a gives circle. 5. 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. 6. If magnitudes... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...therefore * * 5 Def. 5. as A is to B, so is E to F. Wherefore, ratios that, &c. «. ED PROP. XII. THEOR. 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, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...This proposition is to ratios what Axiom I. Book I. is to magnitudes. PROPOSITION XII. THEOREM. (489) 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 consequents. Let any number of magnitudes... | |
 | Euclid - 1835 - 540 pages
...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 of the antecedents is to its consequent, so are all the antecedents, taken together, to all the consequents. Let any number of magnitudes... | |
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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. 
