 | Bézout - 1825 - 258 sider
...: 3 is to the second : : 2 is to the third. Now, we have seen (186) that the sum of the antecedent? is to the sum of the consequents, as any one antecedent is to its consequent : we can then say here, that the sum 9 of the three parts proportional to the parts that we seek, is... | |
 | Thomas Sherwin - 1841 - 314 sider
...= dq, e =fq, g = hq. Adding these equations q, or Dividing by 6 + d+f+h a-\-c-4-e-\-gac - ' In any series of equal ratios, the sum of the antecedents is to the sum of the consequents, as any one of the antecedents is to its consequent. 16. If a : b = c : d, and e :f= g : h, that is, — = —... | |
 | Thomas Sherwin - 1841 - 320 sider
...antecedents, is to the sum or difference of the consequents, as either antecedent is to its consequent ; the sum of the antecedents is to the sum of the consequents, as the difference of the antecedents is to the difference of the consequents; also, the sum of the, antecedents... | |
 | Charles William Hackley - 1851 - 536 sider
...A4 : A4' : : be : be' : : cd : cd', &c. PLANE SAILING. therefore, since by the theory of proportion the sum of the antecedents is to the sum of the consequents as any one antecedent is to its consequent, A* : A6' : : A4 + be + cd + &c., : A4' + be' + cd' + >fec. But AJ + be + cd + Ac., is the whole distance... | |
 | William Smyth - 1851 - 272 sider
...-f- d : d. Comparing this with the proposed, we derive the following principle : In every proportion, th~e sum of the antecedents is to the sum of the consequents, as any one anetcedent is to its consequent. In like manner it may be shown, that the difference of the antecedents... | |
 | William Smyth - 1856 - 264 sider
...-\-d : d. Comparing this with the proposed, we derive the following principle : In every proportion, the sum of the antecedents is to the sum of the consequents as any one antecedent is to its consequent. Let there be next a series of quantities, a, b, c, d, e, f, g h... forming, two and two, a series of... | |
 | Samuel Alsop - 1856 - 152 sider
...§1O«5. If any number of like magnitudes be proportionals, one antecedent will be to its consequent as the sum of the antecedents is to the sum of the consequents. Let a : Ъ : : с : d : : e :f, then a:b::a-\-c-{-e:b-{-d -)-/• For since a : b : : с : d, and a... | |
 | William Smyth - 1858 - 386 sider
...the proposed, we derive the following principle : In every proportion, the sum of the antecedents u to the sum of the consequents as any one antecedent is to its consequent. Let there be next a series of quantities, a, b, c, d, e, f, g h . . . forming, two and two, a series... | |
 | Olinthus Gregory - 1863 - 482 sider
...there be a series of equal ratios represented by f we shall have - « - * - V - ««• T • - Tj Therefore, in a series of equal ratios, the sum of...its consequent. If there be two proportions, as 30 : 1 5 : : 6 : 3, and 2 : 3 : : 4 : 6, then multiplying them term by term we shall have 30 x 2 : 15... | |
 | Adrien Marie Legendre - 1863 - 464 sider
...shall have, A±PA : B±*-B :: C ±2,0 : 2>±^D; PEOPOSITION XI. THEOEEM. In any continued proportion, the sum of the antecedents is to the sum of the consequents, as any antecedent to its corresponding consequent. From the definition of a continued proportion (D. 3), A... | |
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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. 
