 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...  An Elementary Geometry and Trigonometry - Page 30by William Frothingham Bradbury - 1872 - 238 pagesFull view - About this book
 | Paul Allen Towne - Algebra - 1865 - 314 pages
...np; whence am X dy = bn X cp, or am : bn :: cp : dq. (14) PROP. IX. In 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. (Vide § SS16, def. ,7.) For, since a : b : : c : d, we... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...is, any number of proportions having the same ratio, 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 : :m-.n, etc. Then will a : 6 : : a+c+m : b-\-d-\-n. Since a : b : : c : d, And a :b: :m:n, We have... | |
 | Joseph Ray - Algebra - 1866 - 252 pages
...is, any number of proportions having the same ratio, 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 : : m :n, etc. Then will a : b : : a+c+wi : 6+d+n. Since a : b : : c : d, And a : b : : m : n, We have... | |
 | Isaac Todhunter - Algebra - 1866 - 580 pages
...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. Let a : b :: c : d :: e : f; then a : b :: a + c +e : b + d +f. For ad=bc, and af= be, (Art. 386), also ab = ba ; hence ab + ad... | |
 | Horatio Nelson Robinson - Algebra - 1866 - 328 pages
...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. t Let a : b = a : b (A) -Also, a : b = с : d (в) a : b =m : n (С) &c. = &c. We are to prove that... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...— 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 consequent*Let a :b : :c: d : :m :n, die. Then a:b:\ a-\-c+m : b-\-d-\-n. Since a : b : : c : d, we... | |
 | Benjamin Greenleaf - 1867 - 336 pages
...any number of quantities are proportional, any antecedent is to its consequent as the sum of all tJie antecedents is to the sum of all the consequents. Let a : b : : c : d : : e : f; then a : b : : a -\-c-\-e : b-\-d-\- f. For, by Theo. I., ad=bc, and af=be; also, ab = b a. Adding,... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...number of quantities be proportional, then 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::mA:»nB::nA:nB, &c. ; then will A: B:: A : B+mB+»B, &c. ^ B+mB+nB (l+»»+n)BB , For -T— !... | |
 | William Frothingham Bradbury - Algebra - 1868 - 270 pages
...XII. 213. 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 (1) and by Theorem I. ad = bc (2) and also af=be (3) Adding (1), (2), (3), Hence, by Theorem II. a:... | |
 | Elias Loomis - Algebra - 1868 - 386 pages
...n 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 — be; A (1.) and, since a: b :: e: /, «/=fe; (2.) also ab ~ ba. (3.)... | |
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