 | William James Milne - 1906 - 444 σελίδες
...ratio with the ratio a : b ; with the other ratios. PRINCIPLE 13. — 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. Thus, when a:6 = C:d = g: ft and so on, a + с + e + g + - : Ь + d +f+ Л + ••• : : a : Ь.... | |
 | George Albert Wentworth - 1894 - 218 σελίδες
...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 is to the sum of the 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 - 1906 - 268 σελίδες
...±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... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - 1907 - 328 σελίδες
...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- = -•... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - 1907 - 304 σελίδες
...b, c, d, which are in proportion, are in proportion ; or — =—• XI. In a series of equal ratios the sum of the antecedents is to the 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 - 1907 - 328 σελίδες
...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 - 1907 - 428 σελίδες
...(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... | |
 | Albert Harry Wheeler - 1908 - 700 σελίδες
...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 sum of 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... | |
 | Elmer Adelbert Lyman - 1908 - 364 σελίδες
...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 is to the sum of the 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.... | |
 | Frederick Howland Somerville - 1908 - 428 σελίδες
...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 the 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... | |
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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. Let a: b = c: d — e :/= g: h. 
