 | John Ward - Algebra - 1724 - 242 pages
...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 - Geometry - 1734 - 192 pages
...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 :... | |
 | Charles Butler - 1814 - 582 pages
...c+d : c — d, therefore ini-ertendo a—b : a + b : : c—d : c + d. 72. If several quantities be proportionals, as any one of the antecedents is to its consequent, so is the sum of any number of the antecedents, to the sum of their respective consequents. Let a : b : : c : d : :... | |
 | Sir John Leslie - Geometry, Modern - 1820 - 488 pages
...perturbate, equality. PROP. XIX. THEOR. If there be atiy number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the snm of all the consequents. Let A : B :: C : D: t E : F :: G : H ; then A : B :: A+C+E+G: B+D+F+H.... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...number of proportionals, of which all the ratios are equal, it will be, as the antecedent of any ratio is to its consequent, so is the sum of all the antecedents of the other ratios to the sum of all the consequents. For, let S = 5, $=;, }=l then will |= £-) =f... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...: : E : F (V. Def. 10). PROPOSITION XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so is the sum of all the antecedents to that of the consequents. If A:B::C:D,andC:D::E:F;A:B:':A + C + E: B + D + F. nB + wD + «F ; and if... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...is, (Sup. 2. schol. 2.) A : B : : E : F. Therefore, ratios, &c. PROP. VIII. THEOR. OF numbers which are proportionals, as any one of the antecedents is to its consequent, so are all the antecedents taken together, to all the consequents. IfA:B::C:D::E:F;;thenA:B::A + C + E:... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...2, schol. 2) A : B :: E : F. Therefore, ratios, &c. PROP. VIII. THEOR. (V. l2).— Of numbers which are proportionals, as any one of the antecedents is to its consequent, so are all the antecedents taken together, to all the consequents. If A : B :: C : D :: E : F; then A... | |
 | Isaac Todhunter - Algebra - 1858 - 530 pages
...а— b :: c + d : c- d. 397. ÏTAeи 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 tlie consequents. Let a : b :: с : d :: e : f; then, a : b :: a + c + e : b +d+f. For ad=bc, and af=... | |
 | Euclides - 1860 - 288 pages
...: : E : F (V. Def. 10). PROPOSITION XII. THEOREM. If any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so is the sum of all the antecedents to that of the consequents. Given A : B : : C : D, and C : D : : E : F ; to prove that A:B::A+C + E:B... | |
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CF as EB is to FD. [V. 16. And as one of the antecedents is to its consequent, so is the sum of the antecedents to the sum of the consequents; [V. 
