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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 and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...two terms is to their difference. Let a : b = c : d. , 333 Q, ED. PROPOSITION IX. THEOREM. 335. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Let a:b = c:d = e:f = g:h. To prove that a + c + e + yb + d -\-f + h = a : b. _ acea Let r=y = - = - =...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 404 pages
...of any antecedent to its consequent? 2. Transform similarly and investigate other series. Theorem. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Data : Any series of equal ratios, as a: b = c:d = e:f=g:li. To prove a + c + e + g:b + d +/+ A = a...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...two terms is to the second term as the difference of the last two terms is to the fourth term. 335. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. 338. Like powers of the terms of a proportion are in proportion. 342. If a line is drawn through two...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 276 pages
...A'B' = DC : B'C' = CD : C'D', etc. 351 .'. AB + BC + etc. : A'B' + B'C' + etc. = AB : A'B', 335 (in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). That is, P:P' = AB:A'B'. QED Ex. 252. If the line joining the middle points of the hases of a trapezoid...
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...of any antecedent to its consequent? 2. Transform similarly and investigate other series. Theorem. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Data : Any series of equal ratios, as a:b = c:d = e :/= g : h. To prove a + c + e + g:b + d +/+ ft...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...A'B' = BC : B'C' = CD: C'D', etc. 351 .-. AB + BC + etc. : A'B' + B'C' + etc. = AB : A'B', 335 (in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). That is, P:P' = AB:A'B'. QED Ex. 252. If the line joining the middle points of the bases of a trapezoid...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...AB: A'B' = BC: B'C' = CD: C'D', etc. 351 .'. AB + BC + etc.: A'B' + B'C' + etc. = AB: A'B', 335 (in a series of equal ratios the sum of the antecedents...the sum of the consequents as any antecedent is to Us consequent). That is, P:P' = AB: A'B'. Q . ED Ex. 252. If the line joining the middle points of...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...+ d:c — d. QED PROPOSITION IX. THEOREM. _ 335. In a series of equal ratios, the sum of the ients is to the sum of the consequents as any antecedent is to its consequent. Let a:b = c:d = e:f = g:h. To prove that a + c + e + g : b + d + f + h = a : b. aceq Then a — br,- c...
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Elements of Algebra

James Morford Taylor - Algebra - 1900 - 508 pages
...Proof. By 128 aud 186, from (1) we obtain (2). By 221 and 225, from (1) we obtain (3). 331. In a series of equal ratios the sum of the antecedents is to the sum of the consequents as any one antecedent is to its consequent. That is, if a:b = c:d=e:f=—, (1) then a + c + e + — :b + d...
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Grammar School Algebra

George Edward Atwood - 1900 - 264 pages
...= e:f=g: h ba = ab bc = ad be = af bg = ah K)a NOTE. — Students should also be able to show that the sum of the antecedents is to the sum of the consequents as c : d, as :/, and as g-.h. 435. The product of the corresponding terms of two or more proportions...
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