One central ideal common to all of the above is that of personal responsibility to the society one lives in. Personal duty to your society, that duty being to act in ways which positively impact your society, goes hand in hand with the concepts of personal liberty.
Judaism emphasized the obligation of moral behavior toward your neighbors, and Christianity added more emphasis on personal freeedom and responsibility toward individuals as well as society as a whole. The Rennaissance saw the rise of political philosophies again emphasizing duty to one's society and culture, and individual morality. The Reformation brought even more emphasis on the individual's personal freedom and responsibilities as the two sides of a societal coin.
Think of the priveleges you have as an independant, free person in a free society. The other side of that coin is the responsibility to use that freedom and those priveleges for the good of your neighbor as well as yourself. That is the democratic principle in a nutshell, and also the central thrust of the philosphies that have come down to us through the four influences you mention.