 | 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... | |
 | William Smyth - 1851 - 272 σελίδες
...: c : : b -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... | |
 | Charles William Hackley - 1851 - 524 σελίδες
...Geom.), Aft : Aft' : : 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, A6 : A&' : : A& + be + cd + <fec., : A&' + be' + cd' + <fec. But... | |
 | 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
...and, n — 1 ± —' , we 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
...and, n = 1 ± —,, we shall 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... | |
 | Cincinnati (Ohio). Board of Education - 1873 - 352 σελίδες
...moins son foyer, sa famille ; on s'accoutumne il s'en passer; on a son chez-soi partout. GEOMETRY. 1. In any continued proportion the sum of the antecedents is to the sum of the_ consequents, as any antecedent is to its consequent. Prove. 2. If two circumferences intersect... | |
| |
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. 
