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" If any number of magnitudes 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 will A : B : : A + C + E : B + D + F. "
Elements of Geometry and Trigonometry: With Practical Applications - Page 50
by Benjamin Greenleaf - 1862 - 490 pages
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...two consequents the same in both, the remaining terms will be in proportion. THEOREM X. 115. If atiy number of magnitudes are proportional, any antecedent...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 = BX E. By adding AXB...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1873 - 132 pages
...Hence -,- = -=a n c n 6 n rf" that is a" : 6" = c" : d n THEOREM IX. 23. 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 = e : d=.e :f Now ab = ab (A) and by (12) ad —be (B) and also af=be (C) Adding (A), (B), (C) a (b...
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A Treatise on Algebra

Elias Loomis - Algebra - 1873 - 396 pages
...ma _mc nb ~ nd1 or ma : nb : : me : nd. 309. If any number of quantities are proportional, any one antecedent is to its consequent as the sum of all...antecedents is to the sum of all the consequents. Let a:b::c:d::e:f; then, since a:b::c:d, ad=bc; (1.) and, since a : b : : e : ft af=be; (2.) also ab =...
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A University Algebra ...

Edward Olney - Algebra - 1873 - 354 pages
...: b—dl У 2. COR. — 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 : h, etc., a...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1873 - 288 pages
...= 3 bd a" cn Hence -6- = Jn that is an : 6n = c" : dn THEOREM IX. 23« If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedentt is to the sum of all the consequents. Let a : 6 = c : d = e :f Now ab = a 6 (A) and by...
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...115. If any number of magnitiides are proportional, any antecedent is to its consequent as the sitm of all the antecedents is to the sum of 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 = BX E....
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New Elementary Algebra: Containing the Rudiments of the Science for Schools ...

Horatio Nelson Robinson - Algebra - 1874 - 340 pages
...PROPOSITION Xin. 275. If any number of proportionals have the same ratio, any one of the antecedents will be to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = a : b (A) Also, a : b = с : d (B) a : b =m : n (С) &c. = &c. We are to prove that a : b = (a +...
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New Elementary Geometry, with Practical Applications

Benjamin Greenleaf - Geometry - 1875 - 204 pages
...remaining terms will be in proportion. THEOREM X. 115. If any number of magnitudes are proportional, awy antecedent is to its consequent as the sum of all...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 By adding AXB to the sum of the corresponding...
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New Elementary Algebra: In which the First Principles of Analysis are ...

Benjamin Greenleaf - Algebra - 1875 - 338 pages
...Therefore, by Art. 38, Ax. 1, | = ^, or, a : b : : c : d, THEOREM X. 324. -//'' any number of quantities are proportional, any antecedent is to its consequent...antecedents is to the sum of all the consequents. Let a:b::c:d::e:f; then a : b : : a -f- c -|- e : b -\- d -|- f. For, by Theo. I., ad = bc, and af=be;...
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New Elementary Algebra: Containing the Rudiments of the Science for Schools ...

Horatio Nelson Robinson - Algebra - 1875 - 340 pages
...Х1П. 275. If any number of proportionals have the same ratio, any one of the antecedents will be to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a:b=a:b.... (A), a:f=c:d.... (B), / a : b = m: n. . . . (C), &c. = &c. We are to prove that a: b= (a...
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