 | 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... | |
 | 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... | |
 | 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 - = - •... | |
 | 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
...both 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... | |
 | William Charles Brenke - Algebra - 1910 - 376 pages
...r = 3' TJ = ~TI' Г77 = 377 ' ' ' i then , , „ ,, =,,,,„ I bdbdbd bo о . . . dd d . . . / 10. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent, ie, = d + 61 + ci + • • • : a2 + i>2 + сз + • • • . For if — ' = jî =—=•••=... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...QED In a similar manner it 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...consequents as 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 = - =... | |
 | Herbert Edwin Hawkes, Frank Charles Touton, William Arthur Luby - Algebra - 1910 - 368 pages
...a + с + e = (b + d + f)r. (8) Therefore ±±£±i = ,. (9) This result may be expressed verbally : In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent. EXERCISES Test the truth of the preceding result in Exercises 1-4 : 1. ^ = | = T^. 3. 3 : 4 = 6 : 8... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Algebra - 1910 - 374 pages
...(3), " + ' ^ c = ? = 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...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(?) ........ | |
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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. 
