Why do people interpret "Lucifer" as being Satan in Isaiah 14? In almost every case I've heard Isaiah 14:12-15 quoted or preached about, I'm told that these are the words of Satan in his rebellion against God.

Isaiah 14:12-15 (KJV):


  12How art thou fallen from heaven, O Lucifer, son of the
  morning! how art thou cut down to the ground, which didst weaken the
  nations! 13For thou hast said in thine heart, I will ascend into
  heaven, I will exalt my throne above the stars of God: I will sit also
  upon the mount of the congregation, in the sides of the north: 14I
  will ascend above the heights of the clouds; I will be like the most
  High. 15Yet thou shalt be brought down to hell, to the sides of the
  pit.


For example, here.

Yet if you jump up to verse 4, it says 


  That thou shalt take up this proverb against the king of Babylon, and
  say, How hath the oppressor ceased! the golden city ceased!


and continues on through the previously cited verses.  So to me, a clear reading indicates that this it the Kind of Babylon saying in his heart,"I will ascend..."

I understand that the prophetical books are often open to interpretation, but I believe I'm missing something.  Why are these quotes attributed to Satan, when it appears that they're meant to be attributed to the king of Babylon?
It is commonly believed to be Satan.  &quot;Lucifer&quot;, however, is a transliteration of the word in the Latin Vulgate.  So, basically, it's a transliteration of a translation.  Many more modern translations render the original word rather than following the traditional transliteration.

How you are fallen from heaven,    O Day Star, son of Dawn! How you
are cut down to the ground,    you who laid the nations low! (Isaiah 14:12, ESV)
quomodo cecidisti de caelo lucifer qui mane oriebaris corruisti in terram qui vulnerabas gentes (Isaiah 14:12, Biblia Sacra Vulgata).