...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...

...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.,...

...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...

...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 :...

...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. :...

...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...

...: 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;...

...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...

...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...

...&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 - = - = - =...