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" Prove that if any number of quantities be in continued proportion, as one of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents. "
Elementary algebra, with brief notices of its history - Page 56
by Robert Potts - 1879
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 1

Isaac Dalby - Mathematics - 1807 - 476 pages
...15 9 5 3 13<5. In a rank of proportionals standing in order, two and two. — As any antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. Let the proportionals be 3 : 5 : : 9 : 15 : : 36 : 60. Then 3 : 5 (or...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry ...

John Leslie - Geometry, Analytic - 1809 - 542 pages
...ptrturbate, equality. 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...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 454 pages
...perturbate, equality. 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....
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A Treatise of Practical Arithmetic

Robert Patterson - Arithmetic - 1819 - 156 pages
...antecedents will = — g, 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....
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The Complete Practical Arithmetician: Containing Several New and Useful ...

Thomas Keith - Arithmetic - 1822 - 332 pages
...: A — B :: c : C — D. , IB. If several quantities be proportional, as one of the antecedents is to its consequent ; so is the sum of all the antecedents, to the sum of all the consequents. Thus, if A : B :: C : D :: E : F :: G : H, &c. Then A : B :: A+C+E+G...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 pages
...— ,b::c+d: c — d. 117. WJien any number of quantities are proportionals, i 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, &c. Then shall a:b:: +c+c+&c. : b+d+f+&c....
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The Practical Analyst: Or, A Treatise on Algebra, Containing the Most Useful ...

Enoch Lewis - Algebra - 1826 - 166 pages
...a+b : as-b : : c+d : c*rd. 65. 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. Let a : b : : c :'d : : e :f : : g : h, &c., then (art. 62.) ad=bc,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...division, conversion, and mixing. If several quantities be proportional, as one of the antecedents is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. If four quantities be proportional, and if the first and second be...
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A Treatise on the Elements of Algebra

James Bryce - Algebra - 1837 - 322 pages
...dc, and ba:b::dc:d. 178. V. 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. Let there be any number of proportionals, a:b::c:d::e:f; then ad=bc,...
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The Elements of Algebra: Designed for the Use of Students in the University

John Hind - Algebra - 1837 - 539 pages
...b(a + c + e + &c.): , , aa + c + e + &c. whence, - = : b 6 + d+/+&c. that is, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. Similarly, if a : b = b : c = c : d = &c., we shall have aa + b + c...
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