| 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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