 | John Parsons - 1705 - 284 σελίδες
...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 - 1724 - 242 σελίδες
...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... | |
 | Ignace Gaston Pardies - 1734 - 192 σελίδες
...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 : b : : c : d.... | |
 | Isaac Dalby - 1806 - 526 σελίδες
...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 - 1807 - 476 σελίδες
...are proportional, BR : BS :: RD : SP :: DA : PC ; then, as any antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. For BA is the sum of the antecedents, and BC that of the consequents, and the corresponding... | |
 | Sir John Leslie - 1809 - 542 σελίδες
...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 : : C : D, AD=BC ;... | |
 | 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.... | |
 | Sir John Leslie - 1817 - 456 σελίδες
...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 :... | |
 | 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,... | |
 | Robert Patterson - 1819 - 174 σελίδες
...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... | |
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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. 
