| John Parsons - Algebra - 1705 - 284 pages
...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 - Algebra - 1724 - 242 pages
...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 - Geometry - 1734 - 192 pages
...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.) - Mathematics - 1747 - 516 pages
...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 - Mathematics - 1806 - 526 pages
...-. d — c. (87.) 91. If there be any number of proportional quantities, Then either antecedent, is **to its consequent, as the sum of all the antecedents,...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 - Mathematics - 1807 - 476 pages
...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 segments... | |
| Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...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,... | |
| Isaac Dalby - Mathematics - 1813 - 538 pages
...: d — c. (87.) 91. 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.... | |
| John Gough - Arithmetic - 1813 - 358 pages
...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 - Geometry - 1817 - 456 pages
...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. 6.) AD = BC; and, since A... | |
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