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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. "
A Text-book of Geometry - Page 135
by George Albert Wentworth - 1888 - 386 pages
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Elementary Algebra

Algebra - 1907 - 446 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...
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Elementary Algebra: First Course

John Charles Stone, James Franklin Millis - Algebra - 1911 - 698 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...
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First Year Algebra

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...
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New High School Algebra

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...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...sides a and a'. To prove that p:p' — a: a'. ab a' b' c' a + b + c -\ _ a Proof. 1. 2. Why ? §361 (In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.) 3. That is, p :p' = « : a'. EXERCISES 1. Two building lots have the same shape. It takes 400 ft. of...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...and the homologous sides a and a'. To prove that p : p' = a : a'. Proof. 1. -( = i = -,etc. Why? " (In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent.) 3. That is, p:p' = a:a'. EXERCISES 1. Two building lots have the same shape. It takes 400 ft. of fence...
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First Year Algebra

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...
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Elementary Algebra

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...
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First Principles of Algebra: Elementary Course

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....
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First Course in Algebra

William Benjamin Fite - Algebra - 1913 - 368 pages
...last equation. A similar result holds for any number of equal ratios, and may be stated as follows : In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. CHAPTER XV QUADRATIC EQUATIONS 156. In § 108 the student learned how to solve certain quadratic equations,...
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