 | Elmer Adelbert Lyman - 1908 - 364 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 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... | |
 | Albert Harry Wheeler - 1908 - 700 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 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 +... | |
 | Frederick Howland Somerville - 1908 - 428 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 the consequents as any antecedent is to its consequent. 382. Given a:b = b:c. Then a : c=a2 : b2. Proof: Since ^ = -, Ь с... | |
 | Joseph Victor Collins - 1908 - 442 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 - = - =... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - 1908 - 520 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.... | |
 | James William Nicholson - 1909 - 332 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... | |
 | Herbert Edwin Hawkes, Frank Charles Touton, William Arthur Luby - 1910 - 368 páginas
...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 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... | |
 | William Charles Brenke - 1910 - 374 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 is to the sum of the consequents as any antecedent is to its consequent, ie, = d + 61 + ci + • • • : a2 + i>2 + сз + • • • .... | |
 | George Albert Wentworth, David Eugene Smith - 1910 - 287 páginas
...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 is to the sum of the 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+... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - 1910 - 374 páginas
...(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 sum of the consequents as any antecedent is to its consequent. EXERCISES Test the truth of the preceding result in Exercises 1-4... | |
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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. 
