 | John Radford Young - 1827 - Liczba stron: 228
...contradicts the hypothesis. PROPOSITION V. THEOREM. If any number of homogeneous magnitudes be proportional, as one antecedent is to its consequent, so is the sum of the antecedents to the sum of the consequents. First, let there be four magnitudes, or the proportion... | |
 | John Playfair - 1829 - Liczba stron: 210
...division, conversion, and mixing. If several quantities be proportional, as one of the antecedents is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. If four quantities be proportional, and if the first and second be multiplied or divided by any quantity,... | |
 | John Radford Young - 1832 - Liczba stron: 408
...uc eg/, &c. ' aei, &c. : bfk, &c. : : eg/, &c. : dhm, &c. THEOREM 7. In any number of equal ratios, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. A /7 f A Let the ratios be - = - = - = &c. : Put - = a ; then b = aa, ace a ' d = Cq,f= eq, &c. and,... | |
 | Euclid - 1833 - Liczba stron: 216
...magnitudes proportional (A to B as C to D), as one of the antecedents is to its consequent (A to B), so is the sum of all the antecedents to the sum of all the consequents (sum of A and C to sum of B andD.) For, if there be taken a and c equi-submultiples of A and C, the... | |
 | 1836 - Liczba stron: 488
...How — the ratio of lesser inequality ? If, in several couplets the ratios are equal, what ratio has the sum of all the antecedents to the sum of all the consequents ? How ¡я a ratio of greater inequality affected by adding the same quantity to both terms ? How —... | |
 | James Bryce - 1837 - Liczba stron: 322
...: ôrta : : d : d±c, and b±a:b::d±c:d. 178. V. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the...antecedents to the sum of all the consequents. Let there be any number of proportionals, a:b::c:d::e:f; then ad=bc, and afz=be; also ab = ba; therefore,... | |
 | John Hind - 1837 - Liczba stron: 584
...or, a(6 + d +/+ &c.) = b(a + c + e + &c.): , , aa + c + e + &c. whence, - = : b 6 + d+/+&c. that is, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. Similarly, if a : b = b : c = c : d = &c., we shall have aa + b + c + &c. 6 b + c + d + &c. ' (J f*... | |
 | Andrew Bell - 1837 - Liczba stron: 290
...10). PROPOSITION XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so is the sum of all the antecedents to that of the consequents. If A:B::C:D,andC:D::E:F;A:B:':A + C + E: B + D + F. nB + wD + «F ; and if... | |
 | Euclides - 1838 - Liczba stron: 264
...otherwise than proportional. PROP. V. THEOR. If any number of homogeneous magnitudes be proportional, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. First, let there be four magnitudes, A being one antecedent, B its consequent ; C the other antecedent,... | |
 | John Radford Young - 1839 - Liczba stron: 332
...&c. cgl, &c. ' aei, &c. : bfk, &c. : : cgl, &c. : dhm, &c. THEOREM 7. In any number of equal ratios, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. Т Ï /• • Let the ratios be - = - = - = &c. : Put - = a ; ace a then b — aq, d = cq, f= eq,... | |
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When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. 
