| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...Q±w (Prop. II.). PROPOSITION X. THEOREM. ••• If any number of quantities are proportionals, **any one antecedent will be to its consequent, as the sum of all the antecedents** to the sum of the consequents. Let M : N : : P : Q : : R : S, &c. then will M : N : : M + P + R : N... | |
| Adrien Marie Legendre - Geometry - 1838 - 386 pages
...N±»» : Q±ra (Prop. II.). PROPOSITION X. THEOREM. If any number of quantities are proportionals, **any one antecedent will be to its consequent, as the sum of all the** antecedent* to the sum of the consequents. Let M : N : : P ; Q : : R jj^ dcc^then will M : N : : M... | |
| Adrien Marie Legendre - Geometry - 1838 - 384 pages
...N±m : Q±w (Prop. II.). PROPOSITION X. THEOREM. If any number of quantities are proportionals, anyone **antecedent will be to its consequent, as the sum of all the antecedents** to the sum of the consequents. Let M M M N N N N F : Q R fcclhen will : : M + P + lt : N + Q+S : :... | |
| 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... | |
| Anna Cabot Lowell - Geometry - 1846 - 216 pages
...This is called a continued proportion, being a series of equal ratios. In every continued proportion **the sum of all the antecedents is to the sum of all the consequents** as one antecedent is to its consequent. Therefore AB + BC + CD+DE + EA : ab+bc + cd -f- de-\-ea= AB... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...— . mA. A THEOREM L. If any 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... | |
| Joseph Ray - Algebra - 1848 - 250 pages
...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 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... | |
| George Clinton Whitlock - Mathematics - 1848 - 324 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'... | |
| Charles Davies - Trigonometry - 1849 - 384 pages
...or, M x (Q±n) =P x (N±m): PROPOSITION X. THEOREM. If any number of quantities are proportionals, **any one antecedent will be to its consequent, as the sum of all the antecedents** to the sum of the consequents. Let M : N : : P : Q : : R jj^ &c^then will M : N : : M + P + R : N +... | |
| Stephen Chase - Algebra - 1849 - 350 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... | |
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