 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...±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,... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...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 is to...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. [-~,',... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...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 is to 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... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...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... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...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... | |
 | James Bates Thomson, Elihu Thayer Quimby - Algebra - 1880 - 360 pages
...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.... | |
 | George Albert Wentworth - Algebra - 1881 - 400 pages
...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 is to...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 =/>•,... | |
 | George Albert Wentworth - 1881 - 266 pages
...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 is to...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... | |
 | George Albert Wentworth - Geometry - 1882 - 442 pages
...polygons arc proportional). ••• AB + 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...consequents as any antecedent is to its consequent). That is P : P' : : AB : A'B'. QED 158 GEOMETEY. — BOOK Ш. PROPOSITION XVII. THEOREM. 296. The homologous... | |
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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. 
