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

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...word division is here used in a sense entirely different from its usual meaning. 206. Theorem VII. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. Given the equal ratios : -?•=-=-; = oaf To Proof. be r. Then Or Adding: Therefore that a 4- c -\-...
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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...proportion when written in any order that makes one pair the extremes and the other pair the means. 361. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. 362. If four numbers are in proportion, they are in proportion by alternation ; that is, the first...
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Solid Geometry

John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...or like roots of the terms of a proportion are in proportion. (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. 123. If DE is parallel to side AB of triangle ABC and meets AC at D and BC at E, then AC=BO dAC=BC...
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...first, and take the nth root of each member to prove the second. (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, .* ace , , ia + c + e + etc. a if - = - = - = etc., then . , . - = T = etc. bdfb + d+f+etc.....
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Elementary Algebra

Elmer Adelbert Lyman, Albertus Darnell - Algebra - 1917 - 520 pages
...12 21 3+9 + 12 + 21 45 of these fractions. This property of equal fractions may be stated thus : IX. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. ._ т а с ex PEOOF. Let r = - = - = - • bdf у Also let each ratio equal Jc. -=k, from which a...
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Advanced Algebra

William Charles Brenke - Algebra - 1917 - 212 pages
...d", then aa'a" : ЪЪ'Ъ" = cc'c" : dd'd". ., a_c a'_c' a"_c" lori1 ~' ~" *~'" 1hen _ _ b~d' V~d" 10. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Thus: a! : 02 = bi : 62 = Ci : C2 = ai + bi + Ci : 02 + 62 + Cj. For ]i— = — = -=••• =r,...
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Complete Algebra

Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1917 - 674 pages
...; then a = bk, с = dk, c. =fk. bdf Hence a + с + к = bk + dk +fk =(b + d +f)k, b+d+fbdf That is, The sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Mean Proportional. If a : b : : b : x, then b is called a mean proportional between a and x. l I FURTHER...
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Elementary Algebra

George Hervey Hallett, Robert Franklin Anderson - Algebra - 1917 - 432 pages
...; that is, This identity may be expressed in words as follows : In a number of equal ratios the gum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. ace b~T' d ~ Г' } .= r. Then, a = br, c = dr, e=fr. Adding, a + c + e=(b\-d+J Dividing, a + c+ e b+d+f...
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Plane and Solid Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...equations: (1) a? - b2 = cd. (3) ax+bx+cx-rad+rih+rik. 403. Theorem. In a series of equal ratios, the aum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. _. acea Given I=^=7=l' To prove a+c+e+g =a^=e = g_ b+d+f+hbdfh Proof. Let - = r. Then -=r, -=r, -=r....
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...A'B' B'C' C'D' D'E' E'A'' . AB+BC+CD+DE+EA __ AB - 31g A'B' + B'C' + C'D' + D'E' + E'A' A'B' ' * ' ' ' (In a series of equal ratios the sum of the antecedents is to the sum of, etc.) QED That is. P-= AB . p' A'B' SIGHT WORK 1. If in the above figure AB = 6 inches and A'B' = 4...
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