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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. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 17
por International Correspondence Schools - 1906
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Elementary Algebra

John William Hopkins, Patrick Healy Underwood - 1912 - 341 páginas
...Y) 7. If»a :Ъ= c: d= e:f, then a + с + e : b + d+f— a: b. If a number of ratios are equal, then the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let - = - = - = r, then a = br, c= dr, e =fr. oaf e br drr= .. b+d+f b+d+f •'• 1а + л + ! = Г'...
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First Principles of Algebra: Elementary Course

Herbert Ellsworth Slaught, Nels Johann Lennes - 1912 - 280 páginas
...bk + dk+fk= (b + d+f)k, and a + c + e=fc=g = £ = g. b+d+fbdf That is, If several ratios are equal, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. EXERCISES 1. If ad = bc, show that - = - • Hint. Divide by bd. bd Z If ad=bc, show that- = -• 3....
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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - 1913 - 321 páginas
...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...
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Plane Geometry

Walter Burton Ford, Earle Raymond Hedrick - 1913 - 213 páginas
...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...
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First Course in Algebra

William Benjamin Fite - 1913 - 334 páginas
...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,...
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First Course in Algebra

William Benjamin Fite - 1913 - 285 páginas
...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,...
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Solid Geometry

Walter Burton Ford, Charles Ammerman - 1913 - 107 páginas
...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...
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Elementary Algebra Revised

Frederick Howland Somerville - 1913 - 447 páginas
...c + eH =(6 + d +/+ -")r. And, £Or, (a + c + e + •••): (6 + d +/+•••) = a:6. That is : In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. 382. Given a:b = b:c. Then a : c = a2 : b2. Proof: Since - = -, 6 c 4t follows that, °x^ = ?x2. 6...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - 1913 - 470 páginas
...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...
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Second Course in Algebra

Webster Wells, Walter Wilson Hart - 1913 - 285 páginas
...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...
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