| George Washington Hull - Geometry - 1807 - 408 pages
...In a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents an **any antecedent is to its consequent. Let a : b= c : d = e** :/. Let r = the common ratio, Then r = r> ar>da == or- (1) b '- = r, and c = dr. (2) 7=r, ande=/r.... | |
| 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 - 372 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 - 150 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 - 482 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 - 455 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 - 294 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 - 464 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 - 482 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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