| William Frothingham Bradbury - Algebra - 1868 - 264 pages
...: b'='c : d ac l=d Hence, ? = 5 ie a" : 5" = c" : cf THEOREM XII. 213. If any number of quantities are proportional, any antecedent is to its consequent...sum of all the consequents. Let a : b=; c : d = e if Now ab = ab (1) and by Theorem I. ad = bc (2) and also a/=6« (3) Adding (1), (2), (3), g(b+.d+f)... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...ma me nb ~- nd 1 or ma: nb :: me: nd. n 309. If any number of quantities are proportional, any one antecedent is to its consequent as the sum of all...all the consequents. Let a: b:: c : d :: e: f; then, since a: b:: c: d, ad — be; A (1.) and, since a: b :: e: /, «/=fe; (2.) also ab ~ ba. (3.) Adding... | |
| Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...proportional, any one of the antecedents will be to its consequent as the sum of all thf tnlfcedents is to the sum of all the consequents. Let A, B, C, D, 13, etc., represent the several magm tudes whi ih give the proportions A : B :: C : J) A : B :: E :... | |
| Benjamin Greenleaf - 1869 - 516 pages
...be in proportion. sequents the same in both, the remaining terms will be in proportion. PROPOSITTON XI. — THEOREM. 147. If any number of magnitudes...antecedents is to the sum of all the consequents. feet A:B::C:D::E:F; then will A:B::A + C + E:B + D + F. For, from the given proportion, we have AXD... | |
| 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 the... | |
| Benjamin Greenleaf - 1870 - 334 pages
...Therefore, by Art. 38, 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
...= -j. ; therefore 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
...is 7=3 bd Hence -,- = -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...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) a (b -fd +/) = b (a... | |
| William Frothingham Bradbury - Algebra - 1872 - 268 pages
...7 = -, I d T-, a" c» Hence, = ie a" : bn = c" : ef THEOREM XII. 21 3. 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 = c:d = e:f Now ab — ab (1) and by Theorem I. ad = bc (2) and also af=be (3) Adding (1), (2),... | |
| 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) a (b + d +/) = b (a +... | |
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