3 Answers

Shakespeare wrote in English. "Prevent" meant the same to him as it does to any other English speaker, to stop something from happening. An example is in Hamlet Act 3 Scene 1 in which King Claudius says, "the hatch and disclose will be some danger; which for to prevent . . ." In other words, he foresees danger which he hopes to prevent by sending Hamlet to England.

You will find prevent in the P section of a dictionary.

http://wiki.answers.com/Q/What_did_Shakespeare_mean_by_the_word_prevent

In the 1600s, "prevent" could also mean "come before," as in this excerpt from the KJV Bible (published in 1611, five years before Shakespeare died).

"...we which are alive and remain unto the coming of the Lord shall not prevent them which are asleep. For....the dead in Christ shall rise first."
1 Thes. 4:15

The "come before" sense of "prevent" is also mentioned here:
http://www.etymonline.com/index.php?term=prevent

shakespeare lived in the 1600's and could have meant   "prevent" as in   anticipate.     like my eyes anticipate the morning since i cant sleep anway.  or my i anticipate the time that i get to leave work so i can go eat dinner.