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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. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 17
por International Correspondence Schools - 1906
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High School Algebra: Elementary Course

Herbert Ellsworth Slaught, Nels Johann Lennes - 1907 - 297 páginas
...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 2. If ad = bc, show that - = -•...
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Plane and Solid Geometry

Edward Rutledge Robbins - 1907 - 412 páginas
...(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...
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Plane and Solid Geometry

Elmer Adelbert Lyman - 1908 - 340 páginas
...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...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....
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First Course in Algebra: With Eight Thousand Examples Including Three ...

Albert Harry Wheeler - 1908 - 664 páginas
...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...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...
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Report of the Superintendent of Public Instruction

Michigan. Department of Public Instruction - 1908
...a * + 2 ab + b * as the square of (a + b). (b) a * — b * as equal to (a 4- b) (a — b). 4. Show 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. 5. (a) Prove that (ab) n = a'' b". (b) Discuss the Binomial Theorem....
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Elementary Algebra

Frederick Howland Somerville - 1908 - 407 páginas
...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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High School Algebra: Complete Course

Herbert Ellsworth Slaught, Nels Johann Lennes - 1908 - 494 páginas
...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 - 1908 - 420 páginas
...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 - = - =...
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School Algebra

James William Nicholson - 1909 - 316 páginas
...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 - 1910 - 343 páginas
...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 =—=•••=...
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