 | William Charles Brenke - 1910 - 374 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 is to the sum of the consequents as any antecedent is to its consequent, ie, = d + 61 + ci + • • • : a2 + i>2 + сз + • • • .... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - 1910 - 374 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 sum of the consequents as any antecedent is to its consequent. EXERCISES Test the truth of the preceding result in Exercises 1-4... | |
 | George William Myers - 1910 - 304 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(?)... | |
 | John Charles Stone, James Franklin Millis - 1911 - 698 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 -... | |
 | William Betz, Harrison Emmett Webb - 1912 - 368 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 is to the sum of the consequents as any antecedent is to its consequent. Proof. If - = - = - = 7, let a; represent the value of each bdf li... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 360 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 is to the sum of the consequents as any antecedent is to its consequent. Proof. If T = -7 = !.—•?, kt x represent the value of each bdfh... | |
 | Webster Wells, Walter Wilson Hart - 1912 - 504 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 is to the sum of the consequents as any antecedent is to its consequent. If « = £ = !, etc., prove « + etc. , ., bdf 6 + d+/+etc. b PROOF.... | |
 | Webster Wells, Walter Wilson Hart - 1912 - 344 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 is to 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... | |
 | John William Hopkins, Patrick Healy Underwood - 1912 - 362 páginas
...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... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - 1912 - 300 páginas
...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... | |
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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. 
