Puree the ricotta, one container at a time, in a blender or food processor. Combine all the ricotta with the milk in a large nonreactive pan. Heat, stirring over low heat, to about 170 degrees. Add the vinegar and continue stirring until the curds begin to separate and the whey begins to drain away.
Line a large stainless steel strainer or colander with the cheesecloth, napkin or towel,