 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...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 A, B, C,... | |
 | John Playfair - 1832 - 358 σελίδες
...any 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, no are all the antecedents, taken together, to all the consequents. If A:B: : C: D, and C: D: : E:... | |
 | Euclides - 1834 - 518 σελίδες
...ratios that, &c. QED PROPOSITION XII. t. THEOR. — If any number of magnitudes be proportionals, af v one of the antecedents is to its consequent, so shall...all the . / antecedents taken together, be to all lhe consequents. Let any number of magnitudes A, B, C, D, E, F be proportionals ; that is, as A is... | |
 | James Ryan, Robert Adrain - 1835 - 388 σελίδες
...•=-, S3 JU EC for the same reason -Fr=fr- ; therefore f D ~=^-t that is, A : B : : E : FQED 1) r PROP. XII. If any number of magnitudes be proportionals,...consequents ; and we are to prove that as rA is to A, so is rA-f rB+rC to A+B+C. rA The ratio of rA to A is expressed by -r=r, and the ratio of A. rA+rB+rC to... | |
 | Robert Simson - 1835 - 544 σελίδες
...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 A, B,... | |
 | Euclid - 1835 - 540 σελίδες
...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 A, B,... | |
 | 1836 - 488 σελίδες
...magnitude, is the least of the two. XI. Ratios that are equal to the same ratio are equal to one another. XII. 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. XIII. If the first have to the second... | |
 | John Martin Frederick Wright - 1836 - 776 σελίδες
...the segments of the other. 4. Inscribe an equilateral and equiangular hexagon in a given circle. 5. If any number of magnitudes be proportionals, as one...of the antecedents is to its consequent, so shall au the antecedents taken together be to all the conséquents. 6. If magnitudes taken jointly be proportionals,... | |
 | Andrew Bell - 1837 - 290 σελίδες
...nB, nF, 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. If A:B::C:D,andC:D::E:F;A:B:':A + C +... | |
 | Euclides - 1840 - 192 σελίδες
...E ; and wB, nF any whatever of B and F ; therefore, A : B : : E : F (v. Def. 5). 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, 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. 
