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 as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d... Bradbury's Elementary Algebra - Page 212by William Frothingham Bradbury - 1877 - 291 pagesFull view - About this book
| 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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...: 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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...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 +... | |
| Benjamin Greenleaf - Geometry - 1874 - 208 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... | |
| Benjamin Greenleaf - Algebra - 1875 - 338 pages
...= -f, , ce and 5=?. Therefore, by Art. 38, Ax. 1, | = ^, or, a : b : : c : d, THEOREM X. 324. -//'' **any number of quantities are proportional, any antecedent...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;... | |
| 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...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 By adding AXB to the sum... | |
| 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... | |
| William Frothingham Bradbury - 1875 - 280 pages
...5" = c" : <f THEOREM XII. 213. If any number of quantities are proportional, any antecedent is to us **consequent as the sum of all the antecedents is to the sum of all the consequents. Let a** : 6 = с : d=e : f Now ab = ab (1) and by Theorem I. ad = be (2) and also af=be (3) Adding(l),(2),(3),... | |
| Horatio Nelson Robinson - Algebra - 1875 - 430 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:b=c:d — e:f = g:h=, etc. Then by comparing the ratio, a : b, first with itself, and afterward... | |
| William Guy Peck - Algebra - 1875 - 348 pages
...: b + d+f+h + &c. :: a:b; (11) hence, the following principle : 10°. In any continued proportion, **the sum of all the antecedents is to the sum of all the consequents,** as any antecedent is to the corresponding consequent. ь d " bc = ad. a — c' b a = ê' " be = «/•... | |
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