 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.  Elementary Algebra - Page 190by Herbert Ellsworth Slaught, Nels Johann Lennes - 1915 - 373 pagesFull view - About this book
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...— 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 + g : b + d + f+ h : : a : b. Denote... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...C'D' + A' D' E' + A' E' F' ~ A A' B' 6" ' (in a series of equal ratios the sum of the antecedents ¿9 to the sum of the consequents as any antecedent is to its consequent). AABC AT? = ' (similar A are to each other as thc squares on their homologous sides) ; . the polygon... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...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 - Algebra - 1881 - 406 pages
...::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. For if a - c - e - ff ' 5 2~/T r may be put for each of these ratios. Then ..rJr-.r.jf.r, .'. a = br,... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...- &A'B'C' + A'C'D' + A' D' E' Л- A' Е' F' Д A' B' C' (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). But АABC -А*-, §342 Л A' B' C' Ä1-Bß (similar A are to each other as the squares on their homologous... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...± £- 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... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...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... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...(a + c + e + g): b + d + f + h = a: b; that is, in a set of continued proportionals, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Cor.—If any number of fractions are equal each to each, the sum of the numerators divided by the... | |
 | George Albert Wentworth - Algebra - 1886 - 284 pages
...d: d. VII. Division. a — с : с : :b — d: d. 295. 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. î-i-7-f г may be put for each of these ratios. Then fr.Sr.ir.fr. oafn .'. a — br, с = dr, e =fr,... | |
 | George Albert Wentworth - Algebra - 1888 - 514 pages
...^ = *£, с ос cd o-» с d .'. a: с — b : d. 193. 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. For, if ? = - = - = 3-, bdfh r may be put for each of these ratios. rru a с e (7 1 hen - = r — =... | |
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