 | John Parsons - 1705 - 284 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 522 σελίδες
...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 A : B:: E: F,... | |
 | John Gough - 1813 - 358 σελίδες
...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 σελίδες
...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, (V.... | |
 | Bewick Bridge - 1818 - 254 σελίδες
...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 σελίδες
...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... | |
 | Bewick Bridge - 1821 - 648 σελίδες
...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, a, b, c,... | |
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If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. 
