 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.  A College Algebra - Page 110by James Morford Taylor - 1889 - 363 pagesFull view - About this book
 | 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... | |
 | 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... | |
 | 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... | |
 | Michigan. Department of Public Instruction - Education - 1908 - 324 pages
...proportion, they are in proportion by inversion, alternation, composition, and division; (b) that in a series of equal ratios the sum of the antecedents...consequents as any one antecedent is to its consequent. 6. If y varies inversely as x, and y = 7 when x == 3; what is y when s> = 2</, ? 7. Develop the Binomial... | |
 | 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 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... | |
 | 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 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 +... | |
 | 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 the consequents as any antecedent is to its consequent. 382. Given a:b = b:c. Then a : c=a2 : b2. Proof: Since ^ = -, Ь с... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1908 - 520 pages
...dk,e=fk. oaf Hence, a+c + e = bk + dk +fk =(b + d +/) k, , 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 5 = i. Hint. Divide by M. bd 2.... | |
 | Joseph Victor Collins - Algebra - 1908 - 442 pages
...these terms are in proportion. If " = ~, then 7- = °-, or ^r=V (Power and Root Axs.) bd !>" d IJ 4. In a series of equal ratios, the sum of the antecedents is to the .s«m of the consequents as any antecedent is to its consequent. If = =, =. bdf b+d+fb Let - = - =... | |
 | James William Nicholson - Algebra - 1909 - 332 pages
...sides, we have, respectively, an cn л/а л/с ... a" : b" = cn : d", Va : VB = л/с : Vd. 308. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents us any antecedent is to its consequent. i , а с е r/ Let l = d=fh Place each of these ratios equal... | |
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