1) Half 2) Moiety 3) One-half 1) Middle 2) Moiety 
• (n.) The middle part; half; moiety.
Me·di'e·ty noun [ Latin medietas .] The middle part; half; moiety. [ Obsolete] Sir T. Browne. 
The strict meaning of the word is equal parts, sometimes referred to as a Moiety. An ecclesiastical parish required the appointment of a rector. Some parishes supported more than one rector and in that case the the parish would be divided to suit the number of medieties both in the collection of tithes and the rectorial responsibilities.
archaic or obsolete terms > General: Middle of