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" 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 (1) and by Theorem I. "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 52
by Benjamin Greenleaf - 1862 - 490 pages
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New Elementary Algebra: In which the First Principles of Analysis are ...

Benjamin Greenleaf - Algebra - 1864 - 336 pages
...Therefore, by Art. 38, Ax. 7, | — ^ or, a : b : : c : d. THEOREM X. 324 1 If any number of quantities are proportional, any antecedent is to its consequent...the consequents. Let a : b : : c : d : : e : f; then a : b : : a-\-c-\-e : b -\-d-\- f. For, by Theo. I., od = bc, and af= be ; also, ab = ba. Adding, a...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - Algebra - 1864 - 420 pages
...= -; , and - = — ; therefore r = -7 ; whence, a : i : : c : e?. 319. -Jf any number of quantities are proportional, any antecedent is to its consequent...antecedents is to the sum of all the consequents. If a : b : : c : d : : e :/, then a : b : : a-\-c-\-e : b-\-d-\-f. For, by Art. 311, ad = be, and af...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...tliere be a proportion, consisting of three or more equal ratios, then either antécédent will be to its consequent, as the sum of all the antecedents is to the sum of all the coimequmUs. Suppose a : b = с : d = e : _/°— g : h =, etc. Then by comparing the ratio, a : b,...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...: Q. THEOREM VII. If any number of magnitudes are proportional, any one of the antecedents will be to its consequent as the sum of all the antecedents...the sum of all the consequents. Let A, B, C, D, E, etc., represent the several magnitudes which give the proportions A : B :: C : D A : B :: E : F A :...
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Algebra: Adapted to the Course of Instruction Usually Pursued in the ...

Paul Allen Towne - Algebra - 1865 - 314 pages
...mq = np; whence am X dy = bn X cp, or am : bn :: cp : dq. (14) PROP. IX. In 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. (Vide § SS16, def. ,7.) For, since a : b : : c : d, we...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1866 - 328 pages
...proportions have the two antecedents or the two consequeiits the same in both, the remaining terms will be iu proportion. PROPOSITION XI. — THEOREM. 147. If any...+ E:B + D + F. For, from the given proportion, we hare AxD = BxC, and AXF = BX E. By adding AXB to the sum of the corresponding sides of these equations,...
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New Elementary Algebra

Benjamin Greenleaf - 1866 - 336 pages
...by Art. 38, Ах. Т, •£ = ¿, or, a : 6 : : с : d. THEOREM X. 324. If any number of quantities are proportional, any antecedent is to its consequent...antecedents is to the sum of all the consequents. Let a : b : : с : d : : e : f; then a : b : : a -\-c-\- e :b -\-d-\- f. For, by Theo. I., ad = bc, and af= be;...
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Ray's Algebra, First Book: Primary Elements of Algebra, for Common ..., Book 1

Joseph Ray - Algebra - 1866 - 252 pages
...— In any continued proportion, tlmt is, any number of proportions having the same ratio, any one antecedent is to its consequent, as the sum of all...the sum of all the consequents. Let a : b : : c : d : : m :n, etc. Then will a : b : : a+c+wi : 6+d+n. Since a : b : : c : d, And a : b : : m : n, We have...
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Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - Algebra - 1866 - 250 pages
...— In any continued proportion, that is, any number of proportions having the same ratio, any one antecedent is to its consequent, as the sum of all...the sum of all the consequents. Let a :b : : c :d : :m-.n, etc. Then will a : 6 : : a+c+m : b-\-d-\-n. Since a : b : : c : d, And a :b: :m:n, We have...
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Elements of Algebra: For Colleges, Schools, and Private Students, Book 2

Joseph Ray - Algebra - 1866 - 420 pages
...15 : 135 : : 8 : 72. 27$. Proposition XII. — In any number of proportions having the same ratio, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the contequents. Let ...... a : b : : c : d : : m ; n, etc. Then, ..... a : b : : a+C+W : 6+d+ n. Since...
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