| Bézout - 1825 - 236 páginas
...: 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... | |
| Olinthus Gregory - 1834 - 427 páginas
...If there be a series of equal ratios represented by | = 'Ts = - we sa ave = « = f = У = Therefore, **in a series of equal ratios, the sum of the antecedents...there be two proportions, as 30 : 15 : : 6 : 3, and 2** : 3 : : 4 : 6, then multiplying them term by term we shall have 30 x 2 : 15 x 3 : :6 x4:3 x 6, which... | |
| Olinthus Gregory - 1838 - 427 páginas
..._ 1111 "~T~ * v~f~ 14-f- ou ., f. I. - A p IT« = .3 ° we shall have 3 . 5 . 7 + i5 = I % — I = **V &cTherefore, in a series of equal ratios, the sum...there be two proportions, as 30 : 15 : : 6 : 3, and 2** : 3 : : 4 : 6, then multiplying them term by term we shall have 30 X 2 : 15X3::6X4:3X6, which is evidently... | |
| Thomas Sherwin - 1841 - 300 páginas
...= 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 - 300 páginas
...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 - 372 páginas
...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 - 236 páginas
...-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
...-\-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 - 135 páginas
...§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
...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... | |
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