 | Frederick Howland Somerville - Algebra - 1908 - 428 pages
...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... | |
 | 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. If ad = be, show that - = - •... | |
 | Albert Harry Wheeler - Algebra - 1908 - 700 pages
...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 - Geometry - 1908 - 364 pages
...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.... | |
 | Michigan. Department of Public Instruction - Education - 1908 - 324 pages
...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... | |
 | James William Nicholson - Algebra - 1909 - 332 pages
...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... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...may be shown that a — 6 : a = c — d:c. PROPOSITION' VI. THEOREM 269. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents...any antecedent is to its consequent. Given a: b = c: d=e:f=g: h. To prove that a + c + e + ff'-b + d +f+ h = a:b. Proof. Let r = T = - = - = f,, r T t ace... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Algebra - 1910 - 374 pages
...= ? = f = f . (10) &+rf+/ bdf This result may be expressed verbally : /и a series o/ equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. EXERCISES Test the truth of the preceding result in Exercises 1-4 : 1. i = § = TV 3. 3 : 4 = 6 : 8... | |
 | George William Myers - Mathematics - 1910 - 304 pages
...Using Fig. 105, follow the proof of Proposition VII. PROPOSITION VIII If two or more ratios are equal, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Hypothesis: a/b=c/d=e/f=g/h=. . . . ; Conclusion: Proof: a/b=a/b c/d=a/b(?) e/fa/6(?) g/h=a/b(?) ........ | |
 | William Charles Brenke - Algebra - 1910 - 374 pages
...' ' ' i then , , „ ,, =,,,,„ I bdbdbd bo о . . . dd d . . . / 10. 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, ie, = d + 61 + ci + • • • : a2 + i>2 + сз + • • • . For if — ' = jî =—=•••=... | |
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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. 
