| Algebra - 1907 - 436 pages
...integral or fractional, *! = -£!. b3 dn XI. In a series of equal ratios the sum of the antecedents t« **to the sum of the consequents as any antecedent is to its** own consequent. If ? = !=-=-' d) о any let fr, 5-r, 5-r, ж-r, (2) bdn у clearing of fractions in... | |
| John Charles Stone, James Franklin Millis - Algebra - 1911 - 702 pages
...SUGGESTION. — Raise both members of - = - to the same power. & d (8) If two or more ratios are equal, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** That is, if 5 = 1 = 1= etc., then bdfb + d+f+ etc. b For, since - = - =•- = etc., let each ratio... | |
| Webster Wells, Walter Wilson Hart - Algebra - 1912 - 504 pages
...EXAMPLE. Since — = — , then, 1±±JE. should equal HL+J* . Does it ? 2 3 10 — 2 15 — 3 314. **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** If « = £ = !, etc., prove « + etc. , ., bdf 6 + d+/+etc. b PROOF. 1. Let v = the common value of... | |
| William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Modern - 1912 - 360 pages
...d = a : c. 3. d : b = c : a. 1. c : a = d : b. 4. d : c = b : a. 8. c : d = a : b. 361. Theorem IV. **In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.** Proof. If T = -7 = !.—•?, kt x represent the value of each bdfh of the ratios. Then a = bx, c =... | |
| Webster Wells, Walter Wilson Hart - Algebra - 1912 - 344 pages
...с — d EXAMPLE. Since — = — , then, 10 + 2 should equal 15_+-? . Does it ? 2 3 10-2 15-3 224. **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** If 5=0 = 1, etc., prove a + c + e + etc' =°. bdf b+d+f+ete. b PROOF. 1. Let v = the common value of... | |
| William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...b : d = a : c. B. d:b = c : a. 7. c: a = d:b. 4. d : c = b : a. 8. c : d = a : b. 361. Theorem IV. **In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.** Proof. If - = - = - = 7, let a; represent the value of each bdf li of the ratios. Then a = bx, c =... | |
| Webster Wells, Walter Wilson Hart - Algebra - 1912 - 344 pages
...— d EXAMPLE. Since — = — , then, 10 + 2 should equal 15 + 3 • Does it ? 2 3 10-2 15-3 224. **In a series of equal ratios, the, sum of the antecedents...the sum of the. consequents as any antecedent is to** UK consequent. If ?=«-!, etc, prove a + с + e + etc. = a. bd f' - & + d+/+ete. 6 PROOF. 1. Let v... | |
| John William Hopkins, Patrick Healy Underwood - Algebra - 1912 - 362 pages
...Y) 7. If»a :Ъ= c: d= e:f, then a + с + e : b + d+f— a: b. If a number of ratios are equal, then **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let** - = - = - = r, then a = br, c= dr, e =fr. oaf e br drr= .. b+d+f b+d+f •'• 1а + л + ! = Г' ora... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1912 - 300 pages
...bk + dk+fk= (b + d+f)k, and a + c + e=fc=g = £ = g. b+d+fbdf That is, If several ratios are equal, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** EXERCISES 1. If ad = bc, show that - = - • Hint. Divide by bd. bd Z If ad=bc, show that- = -• 3.... | |
| Frederick Howland Somerville - Algebra - 1913 - 458 pages
...c + eH =(6 + d +/+ -")r. And, £Or, (a + c + e + •••): (6 + d +/+•••) = a:6. That is : **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** 382. Given a:b = b:c. Then a : c = a2 : b2. Proof: Since - = -, 6 c 4t follows that, °x^ = ?x2. 6... | |
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