Books Books 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. Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages ## The Rise and Development of the Theory of Series up to the Early 1820s

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,... ## Plane Geometry

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... 