to ask/beg
epaiteo describes seeking alms, whether as an action contemplated or as a roadside activity.
The two occurrences show the verb in the sphere of seeking alms: a manager says he is ashamed to undertake it in Luke 16:3, while a blind man is described as doing it beside the road in Luke 18:35.
Senses in use
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Seeking alms · dominant
In Luke 16:3, the present active infinitive occurs in the manager's statement that he is ashamed to do what the APB renders "to beg." In Luke 18:35, the present active nominative singular masculine participle describes the blind man sitting beside the road; the APB renders the activity "begging."
In the Anselm Project Bible: The APB presents the activity as "to beg" in Luke 16:3 and "begging" in Luke 18:35. These renderings confirm the clauses' presentation rather than establish a finer distinction.