| John Parsons - Algebra - 1705 - 284 pages
...THEOREM 7. In Proportional Quantities how many foever they be, as one Antecedent is to its Confeqnenti fo is the Sum of all the Antecedents to the Sum of all the Confequents, As if A : a :: B : i :: C : c :: D : i/, &c. then will ^ : d :: ,4+B+C+D, &C. . a+b+c+d, &c. For fince... | |
| John Ward - Algebra - 1724 - 242 pages
...fo many Quantities are in continued Proportion 5 it will always be, As one of the Antecedents : Is to its Confequent : : So is the Sum of all the Antecedents : To the Sum of all the Confequents. T, . . . . . bb bbb bbbb That is, a : b : : a4- b + — -\ -4- : 1 ' a aa ' aaa ,bb bbb bbbb_ bbbbb... | |
| John Ward (of Chester.) - Mathematics - 1747 - 516 pages
...fo many Quantities are in -ff ¡t will be, as any one of the Antecedents js to it's Confequents ; fp is the Sum of all the Antecedents, to the Sum of all the Confequents. , fa . ae . aee.aeee.aeeee. aeíí &c. increafmg, ^fSln\ aaa '* a г , r thcfe. I a . — . — . -... | |
| Isaac Dalby - Mathematics - 1806 - 526 pages
...If there be any number of proportional quantities, Then either antecedent, is to its consequent, as the sum of all the antecedents, to the sum of all the consequents. Let a : b :: c : d : :f:g : Tiien a : b : : c : d, hence ad = be a- * •••fg "g =... | |
| Isaac Dalby - Mathematics - 1807 - 476 pages
...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 9 : 15) : ;3 + 9... | |
| Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...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. Because A: B:: C: D, AD=BC ; and since... | |
| John Gough - Arithmetic - 1813 - 358 pages
...Proposition f. In r.ny geometrical progression, as any one of the antecedents is to its consequent/so is the sum of all the antecedents to the sum of all the consequents, 2, 4 S, 16, 32, 6*, &c. 2 : 4 : : 2+4-f-8-fl6-( 32(62] !-f 8+16+32-f 64(124) Problem II.... | |
| Bewick Bridge - Algebra - 1818 - 254 pages
...quantities, "•' a : b :• с : d : : e • /:: g. h &c. &c., then will the ßrst be •" to the second as the sum of all the antecedents to the sum of " all the consequents." And so on for any number of these proportions. Тн. 15. " If there be a set of quantities,... | |
| Robert Patterson - Arithmetic - 1819 - 174 pages
...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. 1. And from the above... | |
| Bewick Bridge - Algebra - 1821 - 648 pages
...proportional quantities, " a:b::c:d :: e :f :: g : h &c.&c., then will thejfrj/ be " to the second as the sum of all the antecedents to the sum of " all the consequents." And so on for any number of these proportions. TH. 15. " If there be a set of quantities,... | |
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