'arbitrarily-composed' originates from the combination of 'arbitrary' and 'compose', where 'arbitrary' comes from Latin 'arbitrarius', meaning 'dependent on the will', and 'compose' from Latin 'componere', meaning 'to put together'.

'arbitrarily-composed' changed from the combination of 'arbitrary' and 'compose' in English, eventually becoming the modern English term 'arbitrarily-composed'.

Initially, it meant 'put together without a specific plan', and this meaning has largely remained the same in modern usage.