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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. "
Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages
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Elementary Algebra

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...
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Report of the Superintendent of Public Instruction

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...
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High School Algebra: Complete Course

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 - = - •...
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Practical Elementary Algebra

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 .sm of the consequents as any antecedent is to its consequent. If = =, =. bdf b+d+fb Let - = - =...
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School Algebra

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...
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A Text-book on Advanced Algebra and Trigonometry, with Tables

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 — ' = j =—=•••=...
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Wentworth's Plane Geometry

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 = - =...
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First Course in Algebra

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...
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First Course in Algebra

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...
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Second-year Mathematics for Secondary Schools, Volume 2

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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