 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...: B : : .£ : R. 2 2 7. By composition, implies that if any number of magnitudes are proportionals, the sum of all the antecedents is to the sum of all the consequents as . any one antecedent is to its consequent. Thus, If A : B : : C : D : : E : F, Then A+C+E : B+D+F... | |
 | Benjamin Greenleaf - Algebra - 1864 - 336 pages
...Therefore, by Art. 38, Ax. 7, | — ^ or, a : b : : c : d. THEOREM X. 324 1 If any number of quantities are proportional, any antecedent is to its consequent...the consequents. Let a : b : : c : d : : e : f; then a : b : : a-\-c-\-e : b -\-d-\- f. For, by Theo. I., od = bc, and af= be ; also, ab = ba. Adding, a... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...= -; , and - = — ; therefore r = -7 ; whence, a : i : : c : e?. 319. -Jf any number of quantities are proportional, any antecedent is to its consequent...antecedents is to the sum of all the consequents. If a : b : : c : d : : e :/, then a : b : : a-\-c-\-e : b-\-d-\-f. For, by Art. 311, ad = be, and af... | |
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...tliere be a proportion, consisting of three or more equal ratios, then either antécédent will be to its consequent, as the sum of all the antecedents is to the sum of all the coimequmUs. Suppose a : b = с : d = e : _/°— g : h =, etc. Then by comparing the ratio, a : b,... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...: Q. THEOREM VII. If any number of magnitudes are proportional, any one of the antecedents will be to its consequent as the sum of all the antecedents...the sum of all the consequents. Let A, B, C, D, E, etc., represent the several magnitudes which give the proportions A : B :: C : D A : B :: E : F A :... | |
 | Paul Allen Towne - Algebra - 1865 - 314 pages
...mq = 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... | |
 | Benjamin Greenleaf - 1866 - 336 pages
...by Art. 38, Ах. Т, •£ = ¿, or, a : 6 : : с : d. THEOREM X. 324. 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 : : с : d : : e : f; then a : b : : a -\-c-\- e :b -\-d-\- f. For, by Theo. I., ad = bc, and af= be;... | |
 | Joseph Ray - Algebra - 1866 - 252 pages
...— In any continued proportion, tlmt is, any number of proportions having the same ratio, any one antecedent is to its consequent, as the sum of all...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... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...— In any continued proportion, that is, any number of proportions having the same ratio, any one antecedent is to its consequent, as the sum of all...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 - 420 pages
...15 : 135 : : 8 : 72. 27$. Proposition XII. — 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 contequents. Let ...... a : b : : c : d : : m ; n, etc. Then, ..... a : b : : a+C+W : 6+d+ n. Since... | |
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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. 
