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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. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 17
por International Correspondence Schools - 1906
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A Text-book on Advanced Algebra and Trigonometry, with Tables

William Charles Brenke - 1910 - 343 páginas
...r = 3' TJ = ~TI' Г77 = 377 ' ' ' i then , , „ ,, =,,,,„ I bdbdbd bo о . . . dd d . . . / 10. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent, ie, = d + 61 + ci + • • • : a2 + i>2 + сз + • • • . For if — ' = jî =—=•••=...
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First Course in Algebra

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - 1910 - 334 páginas
...(3), " + ' ^ c = ? = f = f . (10) &+rf+/ bdf This result may be expressed verbally : /и a series o/ equal ratios the sum of the antecedents is to the...consequents as any antecedent is to its consequent. EXERCISES Test the truth of the preceding result in Exercises 1-4 : 1. i = § = TV 3. 3 : 4 = 6 : 8...
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Second-year Mathematics for Secondary Schools, Volumen2

George William Myers - 1910 - 282 páginas
...Using Fig. 105, follow the proof of Proposition VII. PROPOSITION VIII 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. Hypothesis: a/b=c/d=e/f=g/h=. . . . ; Conclusion: Proof: a/b=a/b c/d=a/b(?) e/fa/6(?) g/h=a/b(?) ........
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Elementary Algebra

1907 - 395 páginas
...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 - 1911 - 311 páginas
...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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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 332 páginas
...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 =...
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New High School Algebra

Webster Wells, Walter Wilson Hart - 1912 - 424 páginas
...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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First Year Algebra

Webster Wells, Walter Wilson Hart - 1912 - 327 páginas
...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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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 332 páginas
...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 =...
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First Year Algebra

Webster Wells, Walter Wilson Hart - 1912 - 327 páginas
...— 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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