Books Books 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. Elements of Plane Geometry: For the Use of Schools - Page 54
by Nicholas Tillinghast - 1844 - 96 pages ## Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1869 - 276 pages
...D :: P : Q. THEOREM VII. X If any number of magnitudes are proportional, 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, (7, D, E, etc., represent the several magnitudes which give the proportions To which we may... ## Elements of Algebra: For Colleges, Schools and Private Students

Joseph Ray - Algebra - 1866 - 420 pages
...72. 278. 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 : 6 : : c : d : : m : n, etc. Then, ..... a : b : : a+c+m : 6+d+n. Since... ## An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...a" : b" = c" : dn THEOREM IX. 23 1 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),... ## An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 268 pages
...proved. 23. If any number of quantities are proportional, any antecedent is to its consequent as tl;e 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),... ## New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...be in proportion. THEOREM X. 115. If atiy 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. For, from the given proportion, we have... ## A Treatise on Algebra

Elias Loomis - Algebra - 1873 - 396 pages
...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 the 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... ## 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... ## New Elementary Algebra: Containing the Rudiments of the Science for Schools ...

Horatio Nelson Robinson - Algebra - 1874 - 338 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 :... ## 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,... 