 | Giovanni Ferraro - Mathematics - 2007 - 392 pages
...number of magnitudes are proportional, then one of the antecedents is to one of the consequents as the sum of the antecedents is to the sum of the consequents (see Euclid [E]). In modern symbols, if sn = X/«=i ai, then ai : o2 = (sn - an) . (sn - ai)Hence,... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Modern - 1912 - 356 pages
...d = a : c. 3. d : b = c : a. 7. c : a = d : b. 4. d : c = b : a. 8. c : d = a : b. 361. Theorem IV. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. aceo Proof. If T — i — "7.— 7 ? let # represent the value of each bdfh of the ratios. Then a... | |
 | Edinburgh Mathematical Society - Electronic journals - 1888 - 154 pages
...the terms D, E, F are proportional. Since A : B = B : C, by composition A + B:B = B + C:G; therefore the sum of the antecedents is to the sum of the consequents in the same ratio, that is, A + 2B + C:B + C = B + C:C. Now D = A + 2B + C, E = B + C, and F = C ;... | |
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In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. 
