 | Charles Hutton - Mathematics - 1831 - 632 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 conse^uents. Let A : в : : тл : тв : : пл : кн, &с. ; then will ... 'А : в : : А + "»•»•... | |
 | William Scott - Algebra - 1844 - 568 pages
..... ._ a_a+c_a + c+e_ •'• b+d+f+h. . .~?~6~6+3~4+</+/~' ScWhence in every series of equal ratios the sum of all the antecedents is to the sum of all the consequents as one antecedent, a, is to its consequent A, or as a sum of antecedents, a+c, a+c+e, &c., is to a like sum of corresponding... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...10. Prop. 6. If several numbers are in proportion, any one antecedent will be to its consequent, as the sum of all the antecedents is to the sum of all the consequents. If 2:4::3:6::5:10: : 7 : 14, then is 2:4:: (2+3+5+7) : (4+6+10+14), or- 2 : 4 : : 17 : 34. Prop. 7.... | |
 | Charles William Hackley - Geometry - 1847 - 248 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 : mB : : wA : nB, &c. ; then will A : B : ; A + mA + nA : B + mB + nB, &c. B + mB... | |
 | George Clinton Whitlock - Mathematics - 1848 - 338 pages
...a' : с : : a" : c" : : &.C., .'. PROPOSITION V. If any number of couplets have the same ratio: (41) The sum of all the antecedents is to the sum of all the consequents, as any one antecedent to its consequent. We should also have ± a =fc a ± a" ± ... : ± с ± c' i с"... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...that 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, &c. Then will a : b : : a+c+m : b+d+n ; Since a : 6 : : c : d, we have... | |
 | Stephen Chase - Algebra - 1849 - 348 pages
...by ; al= bL .-. (§ 233) a+e+g-\-k : b+f+h+l—a :b = e:f, &c. Hence, In any number of equal ratios, the sum of all the antecedents is to the sum of all the consequents as any one of the antecedents is to its consequent. Thus, if 1:2 = 3:6 = 4:8 = 5: 10, then 1+3+4+5 : 2+6+8+10... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...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 consequents. Let a :b : :c : d : :m :n, &c. Then a : b : : a-\-c-\-m : b-\-d-\-n. Since a : b : : c : d, we have... | |
 | G. Ainsworth - 1854 - 216 pages
...b"= a"> : 6'*>, then a+a, + a"+ .... + o<"> :6 + 6, + 6"+ +bw=a:b. That is, if any quantities be in continued proportion, the sum of all the antecedents is to the sum of all the consequents as one of the antecedents is to its consequent. By the last proposition, a+o, : 6 + 6,=a, : b,=a" : b", a... | |
 | James Cornwell - 1855 - 380 pages
...original ratio. Hence they are equal to one another. 329. III. — If there be any number of equal ratios, the sum of all the antecedents is to the sum of all the consequents, as either of the antecedents is to its consequent* 3 : 5 : : 9 : 16 : : is : 30 : : 330 : 550. . 3 + 9... | |
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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. 
