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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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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...c/d, to prove that (a + 6)/(« - 6) = (c+d)/(c- d). Proof. We have = . = . bdbd Th E' p Theorem H. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. Given a/6 = c/d = e/f= —, to prove that ace Proof. Let k be the value of any one of the equal ratios...
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Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 184 pages
...If four quantities are in proportion, they are in proportion by composition and division. Theorem H. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. PART II. PROPORTIONAL LINE-SEGMENTS 145. Theorem I. A line parallel to the base of a triangle divides...
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Plane Geometry

Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...that (a + b)/(a — 6) = (c+d)/(c— d). Proof. We have a±b = c_ + d> mda^b = ed. Th. E,F Theorem H. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. Given a/6 = c/d = e/f= —, to prove that . ace b+d+f+- bdf Proof. Let A; be the value of any one of...
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First Course in Algebra

William Benjamin Fite - Algebra - 1913 - 304 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 149. In § 108 the student learned how to solve certain quadratic equations,...
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Elementary Algebra Revised

Frederick Howland Somerville - Algebra - 1913 - 458 pages
...b = c: d = e:f= •••. Then (a + c + e + •••)• rb -=--e= b~d~f ' Proof: Since 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 = 6 : c. Then a : c=a2: b*. Proof: Since 2 = * 6 c 1t follows that, - x - = - x -...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...257. QED In a similar manner it may be shown that o — b:a = c — die. PROPOSITION VI. THEOREM 269. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Given a: b=c:d=e:f=g : h. To prove that a + c + e + g:b + d +/+ h==a:b. r, <• T iaoeg Proof. Let...
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Second Course in Algebra

Webster Wells, Walter Wilson Hart - Algebra - 1913 - 360 pages
...d EXAMPLE. Since — = Щ- , then, ™±1. should equal ^JJ . Does it ? 2 3 10 — 2 15 — 3 196. In a series of equal ratios, the sum of the antecedents is to ¡he sum of the consequents as any antecedent is to its consequent. If «=« = !, etc, prove « + c...
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Solid Geometry

Sophia Foster Richardson - Geometry, Solid - 1914 - 246 pages
...ratio of similitude of Fl and F2. Then m^_ _ m2 _ m3 _ ..._£» m/ m2' m3' (In a continued proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.) That is, area of surface of Fl ^ 3g area of surface of F2 477. THEOREM. The ratio of the volumes of...
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A Review of Algebra

Romeyn Henry Rivenburg - Algebra - 1914 - 92 pages
...(c) Alternation. (e) Composition. (d) Inversion. (/) Division. (¡7) Composition and division. (A) In a series of equal ratios, the sum of the antecedents is to the sum of the consequents etc. (i) Like powers or like roots of the terms of a proportion etc. 6. If x : m : : 13 : 7, write...
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Plane Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...proportions from each of the following equations: (1) a*-V=cd. (3) ax+bx+cx=nd+nh+nk. 403. Theorem. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. _,. acea Given ---.--I. bdfh _ l - I To prove b+d+f+hbdfh Proof. Let - = r. Then - = r, -=r, g- = r....
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