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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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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1874 - 455 páginas
...±2,0 : D ±^D -t qy T f which was to be proved. PEOPOSITION XI. THEOREM. In any continued proportion, the sum of the antecedents is to the sum of the consequents, as any antecedent to its corresponding consequent. From the definition of a continued proportion (D. 3), Adding and factoring,...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 páginas
...2 _ ! = 1 _ i bld L' that is, _, bd or. a — b : b : : с — d : d. a. ED PROPOSITION VIII. 266. 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. We are to prove a + e+e + ¿r:6 + Denote each ratio by r. [-~,',...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 páginas
...Then 2 _ ! = f _ lf that is, _, bd or, a — 6 : 6 : : с — d : d. QED PROPOSITION VIII. 266. 1n a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Let a : b = с : d ! = e : f = g : h. We are to prove a + с + e + g : b + d + f+ h : : a : b. Denote...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 páginas
...of similar polygons are proportional). .-. AB + BC, etc. : A'B' + B'C', etc. : : AB : A'B', § 266 (in a series of equal ratios the sum of the antecedents...the sum of the consequents as any antecedent is to it That is P : P' A П : A' B'. GEOMETRY. BOOK III. PROPOSITION XVII. THEOREM. 296. The homologous...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 páginas
...of similar polygons are proportional). .-.A£ + BC, etc. : A'B' + B'C', etc. : : AB : A'B', § 266 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents ns any antecedent, is to its consequent). That is P : P' : : A£ : A'B'. GEOMETRY. BOOK III. PROPOSITION...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 páginas
...proportional). .-.AB+ BC, etc. : A'B' + B'C', etc. : : AB : A'B', § 266 (in a series of equal ratins the sum of the antecedents is to the sum of the consequents an any an1ecedent is to its consequent). That is P : P' : : A Б : A'В'. GЕOMETRY. BOOK III. PROPOSITION...
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The Collegiate Algebra: Adapted to Colleges and Universities

James Bates Thomson, Elihu Thayer Quimby - 1880 - 346 páginas
...their difference as the sum of the third and fourth is to their difference. COR. 3. — In any number of equal ratios, the sum of the antecedents is to the sum of the consequents as any one antecedent is to its consequent. riH a + e + e + &c. a „ . . , , 5 -2 — - — = r = r = &c....
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The Register, Cornell University

Cornell University - 1880
...circumscribed circle as the conjugate semi-axis is to the transverse semi-axis. VIII. HIGHER ALGEBRA. 1. Prove that in a series of equal ratios, the sum of the antecedents is to the sums of the consequents as any one antecedent is to its consequent. 2. Insert three arithmetical, three...
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Elements of Algebra

George Albert Wentworth - 1881 - 384 páginas
...obtained by: VI. Composition. a + c: c : : b -\- d : d. VII. Division. a — c:c::b — d:d. ' 350. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. r may be put for each of these ratios. Then " = r, l=r, l=r, ?-=r, oa / ft /. a = 6r, c = dr, e =/>•,...
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Elements of Geometry

George Albert Wentworth - 1881
...the equation. Then thatis, bd a~bc~d bd or, a — b : b : : с — d : d. QED PROPOSITION VIII. 266. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Let a : b = с : d = e :/=<7 : h. We are to prove a + c+e + g: b + d+f-\-h: :a:b. Denote each ratio...
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