| Joseph Ray - Algebra - 1852 - 410 pages
...ART. 278. 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 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... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...m, or Mx ( Q±n) =Px (N±m) : PROPOSITION X. THEOEEM. If any number of magnitudes 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 :: B : S, £c. Then since, M : N :: P : Q, we have... | |
| Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...proportionals. THEOREM 7. 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=C:D' And ... And ... &c.=&c. Then we are to show that A : B= C+H+ G &c. : D+F+H, &c. If... | |
| Charles Davies - Geometry - 1854 - 436 pages
...: : N±m : Q±n. BOOK II. 55 PROPOSITION X. THEOREM. If any number of magnitudes are proportionals, **any one antecedent will be to its consequent, as the sum of all the antecedents** to the sum of tl1e consequents. Let M : N : : P : Q : : R : S, &c. Then since, M : N : : P : Q, we... | |
| G. Ainsworth - 1854 - 216 pages
...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" :... | |
| James Cornwell - 1855 - 382 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... | |
| John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...+ b :ab : : c+d : 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,... | |
| 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... | |
| Mathematics - 1860 - 294 pages
...a — bb — cc — 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,... | |
| Charles Hutton - Mathematics - 1860 - 1022 pages
...THEOREM I.XXIl. If any number of quantities be proportional, then any one of tne antecedent* "¡/I **be to its consequent, as the sum of all the antecedents, is to the** aim of ¡ли the consfqnents. Let А:В::тА:тпВ::пЛ:пВ, &С.; then will Л : JÎ : : Л -f... | |
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