 | 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 .... | |
 | Isaac Dalby - 1806 - 526 sider
...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 +... | |
 | Isaac Dalby - 1807 - 476 sider
...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 sider
...of this and the preceding Proposition, is named inverse, or ptrturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent...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 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... | |
 | Isaac Dalby - 1813 - 538 sider
...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 sider
...terms, and may, therefore, be more generally expressed thus : A : B : : Cor. 2. Hence, in continued proportionals, as one antecedent is to its consequent, so is the sum or difference of the several antecedents to the corresponding sum or difference of the consequents.... | |
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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. 
