 | James McMahon - 1903 - 382 pages
...ratios, all the magnitudes being of the same kind, then as any of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents. Given A :B — A' :B' = A" : B"; to prove A : B = A + A' + A" : B + B' + B". From the... | |
 | Euclid - 1908 - 456 pages
...separando, a, - a.. a, -a. aa a, whence, since, as one of the antecedents is to one of the consequents, so is the sum of all the antecedents to the sum of all the consequents, [vn. 12] a* + «»-i +...+«] ai which gives (Zj + «,+ ...+ aB, or £„. If, to compare... | |
 | Euclid - 452 pages
...a„-! a1 we have, separando, whence, since, as one of the antecedents is to one of the consequents, so is the sum of all the antecedents to the sum of all the consequents, [vn. 1 2] a„ + <*„_,+ ...-*-a! a, which gives al + <t( + ... H- an, or Sn. If, to... | |
 | London univ - 1874 - 778 pages
...any number of quantities be m continued proportion, as one of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents. 9. Prove the rule for finding the sum to n terms of an Arithmetic Series of which the... | |
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When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. 
