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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. "
Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages
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Elementary Algebra

George Albert Wentworth - Algebra - 1906 - 440 pages
...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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The First Steps in Algebra

George Albert Wentworth - 1894 - 218 pages
...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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High School Algebra: Embracing a Complete Course for High Schools and Academies

William James Milne - Algebra - 1906 - 444 pages
...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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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...b:a = xy: x; (2) ab: b= xy: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 - Algebra - 1907 - 304 pages
...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 - Algebra - 1907 - 328 pages
...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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High School Algebra: Elementary Course

Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1907 - 328 pages
...c + e = bk + dk +fk =(b + d +/) k, a+c+e . ace " --- That is, If several ratios are equal, the s?<m 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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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...(1) a b:a = xy: x; (2) ab:b = xy: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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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...first two terms is to their difference as the sum of the last two terms is to their difference. 334. In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. 336. A straight line parallel to the base of a triangle divides the other two sides proportionally....
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First Course in Algebra: With Eight Thousand Examples Including Three ...

Albert Harry Wheeler - Algebra - 1908 - 698 pages
...applying (vi.) to (1) by the corresponding ratios obtained by applying (vii.) to (1). (ix.) In a seres of equal ratios the sum of the antecedents is to the...consequents as any antecedent is to its consequent. That is, if a : Ъ — с : d = e : f — = m : n, then (a + с + e + + m) : (Ь + d + f + + n) = a...
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