They did this in colonial times, in the 1600s and 1700s. Lots of houses from those days have floors of oak or some other relatively hard wood, but there are rectangles of pine where it was assumed there would be an area rug. A 113 year old house, that would be turn of the century, I wouldn't think they would do that, but I suppose it's possible.

It's also possible that a section of the floor was removed due to damage (such as water damage). Since a previous owner was covering the floor with carpeting, perhaps she/he didn't want to pay the extra costs to restore the floor with a more expensive wood that would have matched the other planks.

If you like, you can still have these "unfinished" spots replaced with a wood that matches the rest of the flooring better. You may want to look at lumber from a reclaimed wood dealer so that you can have an older, more weathered look that might match your older flooring better than new flooring would.

Parts of the floor have not been removed the finish literally ends mid board.

When we went to remove the carpets we discovered in 2 rooms that there is an unfinished rectangle on the floors. It looks almost like there was a large rug in each room and they only finished the floor not covered by the rug???? Any ideas of what/why this is?