 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.  Complete Algebra - Σελίδα 188των Herbert Ellsworth Slaught, Nels Johann Lennes - 1917 - 624 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Thomas Sherwin - 1841 - 314 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | William Smyth - 1851 - 272 σελίδες
...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... | |
 | Samuel Alsop - 1856 - 152 σελίδες
...§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... | |
 | Adrien Marie Legendre - 1863 - 464 σελίδες
...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... | |
 | Olinthus Gregory - 1863 - 482 σελίδες
...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... | |
 | Edward Brooks - 1868 - 284 σελίδες
...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 - 1872 - 464 σελίδες
...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 - 1873 - 536 σελίδες
...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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