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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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Essentials of Algebra: Complete Course (an Adequate Preparation for the ...

John Charles Stone, James Franklin Millis - 1905 - 506 páginas
...And O2 = «c. §195. Hence, ¿>=j/ac. Thus, in the proportion 9: 18=18: 36, we have 18=1/8 x 36. 205. In a, series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. ampx Suppose that _=_=£.=_== onqy Ti a Let Ъ=г' mpx . . Then — =r. -=r. -—r, etc. Axiom 7. n...
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Elementary Algebra

Walter Randall Marsh - 1905 - 395 páginas
...(1) bd raising each member of (1) to the nth power, whether n is integral or fractional, 6"~d"' XI. In a series of equal ratios the sum of the antecedents...sum of the consequents as any antecedent is to its own consequent. If a_c._m_x si*. , . a с mx /г,-. let - = r, - = r, - = r, -=r, (2) bdny clearing...
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Elementary Algebra

Walter Randall Marsh - 1905 - 395 páginas
...each member of (1) to the nth power, whether n is integral or fractional, an _ cn b'1 ~ cF XI. _Zn д series of equal ratios the sum of the antecedents...sum of the consequents as any antecedent is to its own consequent. К а с т х ,л^ T=J=— = -•> t1) о dn у let f.* «-,,»_,, S.,, (2) о а...
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The Elements of Geometry

Walter Nelson Bush, John Bernard Clarke - 1905 - 355 páginas
...is said to be derived from the given proportion by compositivn and division.) XI. 2. In any number of equal ratios, the sum of the antecedents is to...consequents as any antecedent is to its consequent. Hyp. If a: 6 : : c : e : :/: g : : etc., Cone.: then a + c+/+ ...: b + e + g+ ... : : a: 6 : : c: e...
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Elementary Algebra

George Albert Wentworth - 1906 - 421 páginas
...this in any particular case, it will be found sufficient to substitute ra for b and re for d. 388. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. For, if ? = £ = ! = £=..., bdfh we may put r for each of these ratios. • Then ? = r, C = r, l =...
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High School Algebra: Embracing a Complete Course for High Schools and Academies

William James Milne - 1906 - 391 páginas
...to b + d +f+ h ? Compare this ratio with the ratio a : b ; with the other ratios. PRINCIPLE 13. — In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Thus, when a:6 = C:d = g: ft and so on, a + с + e + g + - : Ь + d +f+ Л + ••• : : a : Ь....
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The First Steps in Algebra

George Albert Wentworth - 1894 - 184 páginas
...composition 7:2 = 21:0; by division, 3:2 = 0:0; and by composition and division 7 :3 = 21 : 9. 216. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. aceg For, let - = j = - = f • bd / h Denote the value of each of these ratios by r. acea Then - =...
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Plane Geometry

Edward Rutledge Robbins - 1906 - 254 páginas
...±b:a = x±y: x; (2) a±b: b= x±y:y; (3) a ± b : x ± y = a : x, etc. NOTE II. In any proportion the sum of the antecedents is to the sum of the consequents as either antecedent is to its consequent. (Explain.) Also, in any proportion the difference of the antecedents...
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College Algebra

Charles Hamilton Ashton, Walter Randall Marsh - 1907 - 279 páginas
...roots of four quantities, a, b, c, d, which are in proportion, are in proportion ; or — =—• XI. In a series of equal ratios the sum of the antecedents...sum of the consequents as any antecedent is to its own consequent. If |=Л = ™ = *, (i) bdn у т : acmx УОЧ let - = r, - = r, - = r, - = r, (2)...
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High School Algebra: Elementary Course

Herbert Ellsworth Slaught, Nels Johann Lennes - 1907 - 297 páginas
...Hence, a + c + e = bk + dk +fk =(b + d +/) k, a+c+e , ace "" 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 2. If ad = bc, show that- = -•...
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