 | Theodore Strong - Algebra - 1859 - 570 pages
...+ H + etc. BDP Hence, when (numbers or) quantities of the same kind are proportionals, we say that the sum, of all the antecedents is to the sum of all the consequents, as any antécédent is to it» consequent. (as.) If we have ^ = =: , and т> = т=ч> t^611 by adding... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...c—d Q. K D. PROPOSITION (394.) 13. In a continued proportion, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. DEMONSTRATION. Let a : b : : с : d : : e :f::y: h : : &c. We are to prove that a : 6 ;:a + c+e+g,... | |
 | Mathematics - 1860 - 294 pages
...aa -f- 5 -I- e t ions = — . I Since these ratios are equal, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents ; therefore either fraction equals the sum of all the numerators divided by the mm of all the denominators,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...THEOREM. 147. If any number of 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... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...THEOREM. 147. If any number of 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... | |
 | 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 - 1863 - 338 pages
...THEOREM X. 324 1 If any number of quantities are proportional, any antecedent is to ils consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b : : с : d : : e : f; then a : b : : a -|- с -f- e : b -f- d -J- f. For, by Theo. I., ,... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...THEOREM. 147. If any number of 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,... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...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 : Ь = с : d — e : f= g : h =, etc. Then by comparing the ratio, a : b, first with itself,... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...c : e?. 319. -Jf 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. If a : b : : c : d : : e :/, then a : b : : a-\-c-\-e : b-\-d-\-f. For, by Art. 311, ad = be, and af... | |
| |
In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art. 
