A module (Latin modulus, a measure) is a term that was in use among Roman architects, corresponding to the semidiameter of the column at its base.
The term was first set forth by Vitruvius (book iv.3), and was employed by architects in the Italian Renaissance to determine the relative proportions of the various parts of the Classical orders.
[1] When illustrating Palladio, the British architect Isaac Ware (The Four Books of Andrea Palladio's Architecture, London 1738; illustration, right) laid out the Doric order as an exercise in modular construction.
The tendency in Beaux-Arts architectural training was similarly to adopt the whole columnar diameter as the module when determining the height of the column or entablature or any of their subdivisions.
Thus module can be extended to mean more generally a unitary part that gives the measuring unit for the whole.