'assertorily' originates from Latin, specifically from the Medieval Latin adjective 'assertorius', where the root 'asser-' (from 'asserere'/'asserĕre') meant 'to affirm, claim, or assert'.

'assertorily' developed in English by formation from the adjective 'assertory' / 'assertorius' in Medieval Latin; the modern adverb was formed by adding the English adverbial suffix '-ly' to the adjective, yielding 'assertorily'.

Initially it meant 'in a manner of asserting or affirming'; over time it has retained that sense and is used to mean 'in an assertive or declarative manner'.