 | William Benjamin Fite - Algebra - 1913 - 368 pages
...last equation. A similar result holds for any number of equal ratios, and may be stated as follows : In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. CHAPTER XV QUADRATIC EQUATIONS 156. In § 108 the student learned how to solve certain quadratic equations,... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...c/d, to prove that (a + 6)/(« - 6) = (c+d)/(c- d). Proof. We have = . = . bdbd Th E' p Theorem H. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. Given a/6 = c/d = e/f= —, to prove that ace Proof. Let k be the value of any one of the equal ratios... | |
 | William Benjamin Fite - Algebra - 1913 - 304 pages
...last equation. A similar result holds for any number of equal ratios, and may be stated as follows : In a series of equal ratios the sum, of the antecedents...consequents as any antecedent is to its consequent. CHAPTER XV QUADRATIC EQUATIONS 149. In § 108 the student learned how to solve certain quadratic equations,... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...If four quantities are in proportion, they are in proportion by composition and division. Theorem H. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. PART II. PROPORTIONAL LINE-SEGMENTS 145. Theorem I. A line parallel to the base of a triangle divides... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...257. QED In a similar manner it may be shown that o — b:a = c — die. PROPOSITION VI. THEOREM 269. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Given a: b=c:d=e:f=g : h. To prove that a + c + e + g:b + d +/+ h==a:b. r, <• T iaoeg Proof. Let... | |
 | Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...that (a + b)/(a — 6) = (c+d)/(c— d). Proof. We have a±b = c_ + d> mda^b = ed. Th. E,F Theorem H. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. Given a/6 = c/d = e/f= —, to prove that . ace b+d+f+- bdf Proof. Let A; be the value of any one of... | |
 | Webster Wells, Walter Wilson Hart - Algebra - 1913 - 360 pages
...d EXAMPLE. Since — = Щ- , then, ™±1. should equal ^JJ . Does it ? 2 3 10 — 2 15 — 3 196. In a series of equal ratios, the sum of the antecedents is to ¡he sum of the consequents as any antecedent is to its consequent. If «=« = !, etc, prove « + c... | |
 | Romeyn Henry Rivenburg - Algebra - 1914 - 92 pages
...pair, etc. 3. Alternation. 4. Inversion. 5. Composition. 6. Division. 7. Composition and division. 8. In a series of equal ratios, the sum of the antecedents...is to the sum of the consequents as any antecedent, etc. Special method .of proving four quantities in proportion. Let - = x, a = bx, etc. Development... | |
 | Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...ratio of similitude of Fl and F2. Then m^_ _ m2 _ m3 _ ..._£» m/ m2' m3' (In a continued proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.) That is, area of surface of Fl ^ 3g area of surface of F2 477. THEOREM. The ratio of the volumes of... | |
 | Romeyn Henry Rivenburg - Algebra - 1914 - 92 pages
...etc. (c) Alternation. (e) Composition. (d) Inversion. (/) Division, (gr) Composition and division. (A) In a series of equal ratios, the sum of the antecedents is to the sum of the consequents etc. (г) Like powers or like roots of the terms of a proportion etc. 6. If x : m : : 13 : 7, write... | |
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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. 
