 | John Parsons - 1705 - 284 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 - 1806 - 526 pagina’s
...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 = bf Therefore ad + ag = be + bf... | |
 | Isaac Dalby - 1807 - 476 pagina’s
...PC. And if any number of right lines are proportional, BR : BS :: RD : SP :: DA : PC ; then, as any antecedent is to its consequent, so is the sum of...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 segments... | |
 | Sir John Leslie - 1809 - 542 pagina’s
...named inverse, or ptrturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is 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 : B... | |
 | John Gough - 1813 - 358 pagina’s
...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... | |
 | Isaac Dalby - 1813 - 538 pagina’s
...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, &c. then a : a :•• b •• b whence ab = ab a:b::e:d, ad=.cb a:b::f\g ag =fb, &c.... | |
 | Sir John Leslie - 1817 - 456 pagina’s
...named inverse, or perturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is the...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. 6.) AD = BC; and, since A... | |
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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. 
