 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.  Complete Secondary Algebra - Page 317by George Egbert Fisher - 1901Full view - About this book
 | Horatio Nelson Robinson - 1869 - 276 pages
...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 annex... | |
 | Benjamin Greenleaf - 1870 - 334 pages
...Ax. 7, ^ = ¿, or, a : b : : с : d. THEOREM X. 324. If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedent» is to the sum of all the consequents. Let a : b : : с : d : : e : f; then a : b : : a... | |
 | Benjamin Greenleaf - Algebra - 1871 - 412 pages
...r = -. ; " J Л J о а whence, a : b : : c : d. 319i If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents M to the sum of all the consequents. If a : b : : c : d : : e : f, then a : b : : a-\-c-\-e : b-\-d-\-f.... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...= -76" dn that is 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...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), (C)... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 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), (C)... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...remaining terms will be in proportion. THEOREM X. 115. If atiy number of magnitudes are proportional, any antecedent is to its consequent as the sum of...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... | |
 | 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 =... | |
 | 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... | |
 | William Frothingham Bradbury - Geometry - 1873 - 288 pages
...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... | |
 | 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 =... | |
| |
