 | Benjamin Greenleaf - 1861 - Liczba stron: 638
...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 hare AXD = BXC, and " AXF... | |
 | Benjamin Greenleaf - 1862 - Liczba stron: 518
...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... | |
 | Benjamin Greenleaf - 1863 - Liczba stron: 504
...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 =... | |
 | Benjamin Greenleaf - 1863 - Liczba stron: 502
...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... | |
 | Benjamin Greenleaf - 1864 - Liczba stron: 336
...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; then a : b : : a-\-c-\-e : b -\-d-\- f. For, by Theo. I., od = bc, and af= be ; also, ab = ba. Adding,... | |
 | Horatio Nelson Robinson - 1865 - Liczba stron: 474
...proportional, 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, C, D, E, etc., represent the several magnitudes which give the proportions A : B :: C : D A : B :: E : F A :... | |
 | Isaac Todhunter - 1866 - Liczba stron: 580
...— d' 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...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... | |
 | Isaac Todhunter - 1866 - Liczba stron: 618
...a—bc — d or a+b : a— b :: с + 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 + с +e : b + d +f. For ad=bc, and af= be, (Art. 386), also ab... | |
 | Joseph Ray - 1866 - Liczba stron: 250
...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... | |
 | James Pryde - 1867 - Liczba stron: 506
...a c—da — b c—d 42. THEOREM. — If there be any number of quantities which are proportional, as one antecedent is to its consequent, so is the...the antecedents to the sum of all the consequents. _,. ace , a a+ с +е Given ъ = -d=j; to prove that y = T . a ce Then since -r = r, .'. a = rb; and... | |
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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. 
