I did a quick search on ancestry.com using Smith as a surname and 1500 as the birth date.
http://awt.ancestry.com/cgi-bin/igm.cgi?surname=Smith&byear=1500&start=1
As you can see, none of the first 6 or so pages of matches have middle names. I would say it's very rare for someone in the 1500's or post 1500s to have a middle name.
Hope that helped.
Melina