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" In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art. "
An Introduction to Geometry and the Science of Form: Prepared from the Most ... - Page 154
by Anna Cabot Lowell - 1846 - 161 pages
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The Complete Algebra: Embracing Simple and Quadratic Equations, Proportion ...

Edward Olney - Algebra - 1878 - 516 pages
...: (6 + d+/+ ^ + fc+,ete.) : : a : b, or c : d, or e : f, etc. That is, in a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents, as any antecedent is to its consequent SOLUTION. =- = r or a& = ba, oo ac , , — = -j or ad = be, bd...
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New Practical Algebra: Adapted to the Improved Methods of Instruction in ...

James Bates Thomson - Algebra - 1878 - 322 pages
...THEOREM X. Wlien any number of quantities are proportional, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a : b :: c : d :: e : f, etc. Then a : b :: a + c + e : b + d+f, etc. For (Th. i), ad = be And,...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...Theorem. — If any number of quantities be in proportion, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. If A : B : : C : D : : E . F, etc., then A : B :: A+C+E,etc. : B+D + F,etc. Let A = mB, then (IV. 6)...
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University Algebra

Webster Wells - Algebra - 1879 - 468 pages
...Therefore, - = od 351. If any number of quantities are proportional, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Thus, if a : b = c: d = e :f then (Art. 343), ad = bc and af=be also, ab = ab Adding, a (b + d +/)...
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New Elementary Algebra: Designed for the Use of High Schools and Academies

Benjamin Greenleaf - Algebra - 1879 - 350 pages
...THEOREM X. 321. If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b : : c : d : : e : f; then a : b :: a -\-c-\- e :b -\-d-\- f. For, by Theo. I., ad=bc, and...
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A University Algebra

Edward Olney - Algebra - 1880 - 354 pages
...: c + d :: a— e : Ъ—dl У£. СОЕ. — If there be a series of equal ratios in the form of a continued proportion, the sum of all the antecedents is to the sum of all the consequents, as any one antecedent is to its consequent. DEM. — If a : b : : e : d : : e :f: : g : A, etc., a + c...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...THEOREM IX. 23i If any number of quantities are proportional, any antecedent. is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a :b = c : d =e :f Now ab — ab (A) and by (12) ad = bc (B) and also af = be (C) Adding (A), (B),...
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The Complete Algebra ...

Edward Olney - Algebra - 1881 - 504 pages
...,eíc.) : (b + d+f+h + k + ,etc.) ::a:ö,or с : d, or e : f, etc. That is, in a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents, as any antecedent is to its consequent. _ aa -, -, а с , , Solution, v — т or ab = ba, - = ^01 ad...
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The student's algebra

James Mackean - 1881 - 510 pages
...several quantities are in continued proportion, any one of the antecedents is to its consequent as the sum of all the antecedents is to the sum of all the consequents. a ma + ne + pe Theorem IX., l=mb + nd+pf, and if mnp-1, a a+c+e . . then т = f,i _r~?; ... a:o::a...
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A University Algebra: Comprising a Compendious, Yet Complete and Thorough ...

Edward Olney - Algebra - 1882 - 358 pages
...b : e+d : : а— с :b—d1 72. Сок. — If there be a series of equal ratios in the form of a continued proportion, the sum of all the antecedents is to the sum of all the consequents, as any one antecedent is to its consequent. DEM. — If a : b : : с : d : : e :/: : g : h, etc., a +...
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