| Isaac Dalby - Mathematics - 1807 - 476 pages
...15 9 5 3 13<5. In a rank of proportionals standing in order, two and two. — As any antecedent is **to its consequent, so is the sum of all the antecedents to** the sum of all the consequents. Let the proportionals be 3 : 5 : : 9 : 15 : : 36 : 60. Then 3 : 5 (or... | |
| John Leslie - Geometry, Analytic - 1809 - 542 pages
...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 + D+F+H. Because A : B... | |
| Sir John Leslie - Geometry - 1817 - 454 pages
...perturbate, 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 : : G : H; then A : B : : A+C+E+G : B+D+F+H.... | |
| Robert Patterson - Arithmetic - 1819 - 156 pages
...antecedents will = « — g, and the sum of all the consequents = s — I : but as one of the antecedents is **to its consequent, so is the sum of all the antecedents, to** the sum of all the consequents-)-. That is, / : IR : : s — g : * — /. Ilente - — Rg l- Theor.... | |
| Thomas Keith - Arithmetic - 1822 - 332 pages
...: A — B :: c : C — D. , IB. 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. Thus, if A : B :: C : D :: E : F :: G : H, &c. Then A : B :: A+C+E+G... | |
| George Lees - 1826 - 266 pages
...— ,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 a:b:: «+c+c+&c. : b+d+f+&c.... | |
| Enoch Lewis - Algebra - 1826 - 166 pages
...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., then (art. 62.) ad=bc,... | |
| John Playfair - Geometry - 1829 - 186 pages
...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... | |
| James Bryce - Algebra - 1837 - 322 pages
...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; then ad=bc,... | |
| John Hind - Algebra - 1837 - 539 pages
...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 shall have aa + b + c... | |
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