Sagging floors are a common problem in turn of the century homes. The wood then was massive, but, more often than not, it was installed in an over-spanned condition (the distance between support points being greater than needed to properly maintain flatness for long periods of time). The result: very slow sagging that is most apparent at the midpoint of the over-spanned configuration.
Solution: One method of repair is to attach a large beam to the underside of - and perpendicular to - the sag in the floor framing members. Use a pair of house jacks near each end of the new beam to raise it and the sagging section of floor, and then install solid wood posts under each end of the beam down to the existing foundation (or a new one if necessary).