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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. "
An Elementary Geometry - Page 30
by William Frothingham Bradbury - 1872 - 110 pages
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...remaining terms will be in proportion. PROPOSITION XI. — THEOREM. 147. If any number of magnitudes are proportional, any antecedent is to its consequent...all the consequents. Let A : B : : C : D : : E : F ; then will A:B::A+C + E:B + D + F. For, from the given proportion, we hate AXD = BXC, and AXF = BX...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...remaining terms will be in proportion. PROPOSITION XI. — THEOREM. 147. If any number of magnitudes are proportional, any antecedent is to its consequent...all the consequents. Let A : B : : C : D : : E : F ; then will A:B::A + C + E:B + D + F. For, from the given proportion, we have AXD = BXC, and AXF =...
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Elements of Geometry and Trigonometry;: With Practical Applications

Benjamin Greenleaf - Geometry - 1863 - 502 pages
...remaining terms will be in proportion. PROPOSITION XI. — THEOREM. 147. If any number of magnitudes are proportional, any antecedent is to its consequent...all the consequents. Let A : B : : C : D : : E : F; then will A : B : : A + C + E : B + D + F. For, from the given proportion, we have AXD = BXC, and AXF...
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New Elementary Algebra: in which the First Principles of Analysis are ...

Benjamin Greenleaf - 1863 - 338 pages
...: : с : d. THEOREM X. 324 1 If any number of quantities are proportional, any antecedent is to ils consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b : : с : d : : e : f; then a : b : : a -|- с -f- e : b -f- d -J- f. For, by Theo. I., , ad = bc, and...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...If there be a proportion, consisting of three or more equal ratios, then either antecedent will be to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Suppose a : Ь = с : d — e : f= g : h =, etc. Then by comparing the ratio, a : b, first with itself,...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...: B : : . : R. 2 2 7. By composition, implies that if any number of magnitudes are proportionals, the sum of all the antecedents is to the sum of all the consequents as . any one antecedent is to its consequent. Thus, If A : B : : C : D : : E : F, Then A+C+E : B+D+F...
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New Elementary Algebra: In which the First Principles of Analysis are ...

Benjamin Greenleaf - Algebra - 1864 - 336 pages
...ratios, ^ = e-, , ce and -d=-f. Therefore, by Art. 38, Ax. 7, | — ^ or, a : b : : c : d. THEOREM X. 324 1 If any number of quantities are proportional, any...all 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,...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - Algebra - 1864 - 420 pages
...d. _ae , ce .. ac For, - = -; , and - = — ; therefore r = -7 ; whence, a : i : : c : e?. 319. -Jf any number of quantities are proportional, any antecedent...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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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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