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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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Solid Geometry, Volúmenes6-9

George Albert Wentworth - 1899 - 218 páginas
...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 and Solid Geometry

William James Milne - 1899 - 384 páginas
...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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Plane Geometry

George Albert Wentworth - 1899 - 256 páginas
...- - = - -• a — bc — a Or a + b : a — b = c + d : c — d. QED 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 + y:b + d+f+k = a:b. Then a = br, c = dr, e =fr,...
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Plane Geometry

George Albert Wentworth - 1899 - 256 páginas
...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 - 1899 - 473 páginas
...+ 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,-...
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Elements of Algebra

James Morford Taylor - 1900 - 461 páginas
...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 - 253 páginas
...= 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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Academic Algebra

William James Milne - 1901 - 444 páginas
...? with the ratio of any antecedent to its consequent ? PRINCIPLE 13. — In any multiple proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Principle 13 may be established as follows : Let a :b = с : d = e :/= g : h. It is to be proved that...
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Elements of Plane Geometry

Alan Sanders - 1901 - 247 páginas
...Example: ci c e _ g — — — — — —. GLC* PROPOSITION X. THEOREM 443. In a continued proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let b~d''f~h' « + c + e + g_e b+d+f+h~f a c e _ g To Prove Proof ? = 4 <2> § = ^ ( 3 ) 7=7 w 1=7...
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Solid Geometry, Volúmenes6-9

George Albert Wentworth - 1902 - 218 páginas
...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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