 | Sir John Leslie - Geometry, Analytic - 1809 - 542 pages
...named inverse, or ptrturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. Let A:B::C:D::E:F::6:H; then A:B::A+C +E+G:B... | |
 | Enoch Lewis - Algebra - 1826 - 180 pages
...the latter, = - r, or a+b : as-b : : c+d : c*rd. 65. 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. Let a : b : : c :'d : : e :f : : g : h, &c.,... | |
 | George Lees - 1826 - 276 pages
...alternately, a+b : a — ,b::c+d: c — d. 117. WJien any number of quantities are proportionals, i as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. Let a : b : : c : d : : e :f, &c. Then shall... | |
 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...contradicts the hypothesis. PROPOSITION V. THEOREM. If any number of homogeneous magnitudes be proportional, as one antecedent is to its consequent, so is the...of the antecedents to the sum of the consequents. First, let there be four magnitudes, or the proportion A : B : : C : D, then also A : B : : A + C :... | |
 | John Radford Young - Algebra - 1832 - 408 pages
...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 sum of all the antecedents to the sum of all the consequents. A /7 f A Let the ratios be - = - = - = &c. :... | |
 | John Radford Young - Geometry, Modern - 1833 - 238 pages
...apply to magnitudes 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 siim of the consequents. First, let there be four magnitudes, or the proportion A : B : : C : D, then... | |
 | John Hind - Algebra - 1837 - 584 pages
...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 sum of all the antecedents to the sum of all the consequents. Similarly, if a : b = b : c = c : d = &c., we... | |
 | James Bryce - Algebra - 1837 - 322 pages
...: 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 sum of all the antecedents to the sum of all the consequents. Let there be any number of proportionals, a:b::c:d::e:f;... | |
 | Euclides - 1838 - 264 pages
...otherwise than proportional. PROP. V. THEOR. If any number of homogeneous magnitudes be proportional, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. First, let there be four magnitudes, A being... | |
 | John Radford Young - 1839 - 332 pages
...&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 sum of all the antecedents to the sum of all the consequents. Т Ï /• • Let the ratios be - = - = - =... | |
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And as one of the antecedents is to its consequent, so is the sum of the antecedents to the sum of the consequents; [V. 
