 | Adrien Marie Legendre - Geometry - 1874 - 512 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, Plane - 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... | |
| |
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. 
