 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.  Solid Geometry - Page 254by John H. Williams, Kenneth P. Williams - 1916 - 162 pagesFull view - About this book
 | 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 - =... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...±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... | |
 | 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)... | |
 | 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- = -•... | |
 | 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 - = -•... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...(1) a ±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... | |
 | 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.... | |
 | Albert Harry Wheeler - Algebra - 1908 - 700 pages
...applying (vi.) to (1) by the corresponding ratios obtained by applying (vii.) to (1). (ix.) In a seríes 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... | |
 | Michigan. Department of Public Instruction - Education - 1908 - 324 pages
...in proportion, they are in proportion by inversion, alternation, composition, and division; (b) that in a series of equal ratios the sum of the antecedents is to the sum , of the consequents as any one antecedent is to its consequent. 6. If y varies inversely as x, and y = 7 when x == 3; what is... | |
 | Frederick Howland Somerville - Algebra - 1908 - 428 pages
...etc. Adding, а Whence, a + c + eH ---- =(b + d+/H ---- )r. And, a Or, That is : JTI a series o/ egwaZ ratios, the sum of the antecedents is to the sum of...consequents as any antecedent is to its consequent. 382. Given a:b = b:c. Then a : c=a2 : b2. Proof: Since ^ = -, Ь с it follows that, ?x6=?x2b с b... | |
| |
