Books Books
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.
Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages

## Elementary Algebra

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...

## Elementary Algebra: first course

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...

## 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...

## Plane Geometry

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 =...

## 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...

## Plane Geometry

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 =...

## 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...

## 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...