| 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,... | |
| 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.... | |
| Cornell University - 1880 - 868 pages
...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... | |
| George Albert Wentworth - 1881 - 266 pages
...sides 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...consequents as any antecedent is to its consequent).** That is P : P' : : AB : A' B'. QED GEOMETRY. — BOOK Ш. PROPOSITION XVII. THEOREM. 296. The homologous... | |
| 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...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 - Geometry, Modern - 1879 - 262 pages
...QED PROPOSITION VIII. 266. In a series of equal ratios, of which all the terms are of the same kind, **the sum of the antecedents is to the sum of the consequents...a :6 = c : d — e : f = g : h. We are to prove -a** + c+e + g: b + d+f+h: : a: b. Denote each ratio*by r. Then .r=\ = ^=^=|. Whence, a = br, c = dr, e=fr,... | |
| Franklin Ibach - Geometry - 1882 - 208 pages
...on \ Then or a ± £- a : b ± £- b :: a : b. QED THEOREM XIII. 168. In any continued proportion, **the sum of the antecedents 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 -\- y : b -{- d -\- f -\- h :: a : b. Denote... | |
| George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...Then £ _ i = 1 _ i b ' ' d l> that is, -, bd or, a — b : b : : c — d : d. QED PROPOSITION VIIL **266. In a series of equal ratios, the sum of the antecedents is to the sum of** tlie consequents as any antecedent is to its consequent. Let a : b = c : d = e :f — g : h. We are... | |
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...-\- nc : d + nd. 4. State ' 2' and " 3' in general terms. r THEOREM XII. In a continued proportion, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its** corresponding consequent. Let a : b :: c : d :: e : f :: g : h ; then will a + c + e + g + etc. : b... | |
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