'compositeness' originates from Latin, specifically the past participle 'compositus' of 'componere', where 'com-' meant 'together' and 'ponere' (root 'posit-') meant 'to place'.

'compositeness' was formed in English from the adjective 'composite' (from Latin 'compositus' via Old French/Medieval Latin) by adding the noun-forming suffix '-ness', eventually becoming the modern English noun 'compositeness'.

Initially related to the literal idea of 'having been put together' (from Latin), it evolved to mean the general 'state or quality of being composed of parts' and, in mathematical contexts, 'the property of being composite (not prime)'.