 | 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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In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. 
