 | Thomas Sherwin - Algebra - 1841 - 314 pages
...= 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 - Algebra - 1841 - 320 pages
...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... | |
 | William Smyth - Algebra - 1851 - 272 pages
...last the same principle, we have and thus in order, whatever the number of equal ratioS. Therefore, in a series of equal ratios, the sum of the antecedents is to the sum of the consequents, as any one antecedent is to its consequent. Let us take next the two proportions If we now multiply these... | |
 | Charles William Hackley - Trigonometry - 1851 - 536 pages
...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... | |
 | Samuel Alsop - Algebra - 1856 - 148 pages
...§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... | |
 | Olinthus Gregory - 1863 - 480 pages
...series of equal ratios represented by f we shall have - « - * - V - ««• T • - Tj Therefore, in a series of equal ratios, the sum of the antecedents is to the sum of the consequents, as any one antecedent is to its consequent. If there be two proportions, as 30 : 1 5 : : 6 : 3, and 2 : 3... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...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 : B : : 0... | |
 | Edward Brooks - Geometry - 1868 - 288 pages
...THEOREM XII. If any number of quantities are in proportion, any antecedent will be to its consequent as the sum of the antecedents is to the sum of the consequents. Let A:B:: C: D:\E\F, etc. A : B : : E : F; we have A x .D = S X C, and AXF= B X E; adding to these,... | |
 | Charles Davies - Geometry - 1872 - 466 pages
...have, DD* A±*-A : *± P -B :: C±$C : D ± *D; PBOPOSITION XI. THEOREM. 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. : B : : C... | |
 | Aaron Schuyler - Navigation - 1873 - 536 pages
...give the continued proportions: AB : AE : : BC : BF :: CD : CG. AB : EB :: BC : FC :: CD : GD. Since the sum of the antecedents is to the sum of the consequents as one antecedent is to its consequent, we have, AD : AE+BF + CG : : AB : AE. NAVIGATION. Now let a right... | |
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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. 
