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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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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - 1916 - 467 páginas
...E'B'D'. A BCD ~ A B'C'D'. Why? Why? Why? Why? Why? Why? Why? 296. Fundamental Theorem about Equal Ratios. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. If " = _ = - = ? bdf h' then a + c + e + ga c_ = e^ b+d+f+hbd Proof. 1. Let r = - and hence br = a....
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Plane Geometry

Edith Long, William Charles Brenke - 1916 - 276 páginas
..."division"; a + b _ c + d is called " composition and divia — b ~ c — d sion." 205. Theorem VII. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. _. ,. ...ace Given the equal ratios: r = -j = 7 = . oaf ' „ , a + c 4- e. . . . ace To prove that...
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SOLID GEOMETRY

WILLIAM BETZ, HARRISON E. WEBB - 1916
...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 H. Williams, Kenneth P. Williams - 1916 - 162 páginas
...first two terms is to the second term as the difference of the last two terms is to the fourth. 277. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. 279. Like powers of the terms of a proportion are in proportion. 285. A line drawn through two sides...
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Solid Geometry

John Charles Stone, James Franklin Millis - 1916 - 174 páginas
...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 - 1916 - 278 páginas
...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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First Course in Algebra

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - 1917 - 309 páginas
...c:d, show that (a + 2 6) : b = (e + 2 d) : d. 125. A series of equal ratios. We now proceed to prove that in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent; ., . , .„ а с e , a + c + e а с e that is, if - = - = -, then - = - = - = — . bdf b+-d+fbdf...
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Advanced Algebra

William Charles Brenke - 1917 - 196 páginas
...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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Elementary Algebra

Elmer Adelbert Lyman, Albertus Darnell - 1917 - 503 páginas
...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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Complete Algebra

Herbert Ellsworth Slaught, Nels Johann Lennes - 1917 - 624 páginas
...; 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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