Etymology of "Quarters"

Speculation based on the first chapter of  the Lyndal Roper book: "Martin Luther: Renegade and Prophet".  My logic:

• towns tend to be located at the intersection of trails/paths/roads.
• most such intersections are of two roads
• most such intersections divide the town into "quarters"
• hence "quarter" originally referred to one of four areas of the town in which one lived.

Posting this here because this website wouldn't allow me to contribute my 2 cents.

The book promises to be good, BTW.