 | John Parsons - 1705 - 284 sider
...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,... | |
 | John Ward - 1724 - 242 sider
...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... | |
 | Ignace Gaston Pardies - 1734 - 192 sider
...never fo many Quantities are thus proportional : It will be as any one Antecedent to its Confequent: : So is the Sum of all the Antecedents to the Sum of all the Confequents. v. gr. If 4 : la :: a : 5, : : 3 : 9 : : 5 : 15 : then fhall 14 141:: 4:11. I4< If a :... | |
 | John Ward (of Chester.) - 1747 - 516 sider
...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 .... | |
 | Sir John Leslie - 1809 - 542 sider
...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...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 : : C : D, AD=BC ; and since A... | |
 | John Gough - 1813 - 358 sider
...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. To continue... | |
 | Sir John Leslie - 1817 - 456 sider
...inverse, or perturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of...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,... | |
 | Bewick Bridge - 1818 - 254 sider
...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, a, b, c,... | |
 | Robert Patterson - 1819 - 174 sider
...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. 1. And from the above r series it... | |
 | Sir John Leslie - 1820 - 488 sider
...inverse, or perturbate, equality. PROP. XIX. THEOR. If there be atiy number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the snm of all the consequents. Let A : B :: C : D: t E : F :: G : H ; then A : B :: A+C+E+G: B+D+F+H.... | |
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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. 
