 | Aaron Schuyler - Navigation - 1873 - 536 pages
...give the continued proportions: AB : AE : : BC : BF :: CD : CG. AB : EB :: BC : FC :: CD : GD. Since the sum of the antecedents is to the sum of the consequents as one antecedent is to its consequent, we have, AD : AE+BF + CG : : AB : AE. NAVIGATION. Now let a right... | |
 | 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... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...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 is to the sum of the consequents as any antecedent is to its consequent. Let a : b = с : d ! = e : f = g : h. We are to prove a + с + e +... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...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... | |
 | 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. (Art.... | |
 | Cornell University - 1880 - 868 pages
...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... | |
 | George Albert Wentworth - 1881 - 266 pages
...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 is to the sum of the consequents as any antecedent is to its consequent). That is P : P' : : AB : A' B'. QED GEOMETRY. — BOOK Ш. PROPOSITION... | |
 | George Albert Wentworth - Algebra - 1881 - 400 pages
...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 is to the sum of the consequents as any antecedent is to its consequent. r may be put for each of these ratios. Then " = r, l=r, l=r, ?-=r,... | |
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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. 
