 | Benjamin Greenleaf - 1868 - Liczba stron: 340
...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 AXD = BXC, and AXF = BX E.... | |
 | William Frothingham Bradbury - 1868 - Liczba stron: 270
...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 (1) and by Theorem I. ad = bc (2) and also af=be (3) Adding (1), (2), (3), Hence, by Theorem... | |
 | Elias Loomis - 1868 - Liczba stron: 386
...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 — be; A (1.) and, since a: b :: e: /, «/=fe; (2.) also ab ~ ba. (3.)... | |
 | William Frothingham Bradbury - 1868 - Liczba stron: 264
...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 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)... | |
 | Horatio Nelson Robinson - 1868 - Liczba stron: 276
...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 :... | |
 | Isaac Todhunter - 1870 - Liczba stron: 818
...ab cd or a + b : a — b :: c + d : c — d. 397. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the...antecedents to the sum of all the consequents. Let a : b :: с : d :: e : f; then a : b :: a+c + e : For ad=bc, and o/= be, (Art. 386), also ab = ba ; hence... | |
 | Elias Loomis - 1871 - Liczba stron: 302
...proportional, any one, ante (fjert is to its consequent, as the sum of all the anlecedetts. a to the sum cf all the consequents. Let A : B : : C : D : : E : F, &c. ; then will AB : : A+C+E : B+D+F For, since A : B : : C : D, we have AxD = BxC. And, since A : B : : E : F,... | |
 | William Frothingham Bradbury - 1872 - Liczba stron: 124
...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), (C) a (b -fd +/) = b (a... | |
 | William Frothingham Bradbury - 1872 - Liczba stron: 262
...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 +... | |
 | James Bryce - 1872 - Liczba stron: 386
...: :d :d± c, and b ± a : b : : d ± с : d. 184. When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of аи the antecedents to the sum of all the consequents. Let there he any number of proportionals, a... | |
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When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. 
