For the first synonym/gloss given here, qera/peuein, cf. alpha 845, alpha 847.
The headword verb itself, a)kei=sqai, when used in the sense of healing or remedying, may originally derive from a relationship between a surgeon's craft and its other common use for the cutting and needle-stitching practised in trades such tailoring and shoe-making, and would undoubtedly in later times have comic overtones if used of a doctor's work (alpha 842). In Homer (see alpha 848) and early literature, however, it is a common word for healing, perhaps originally of mending a wound but certainly often in a more general sense, including the healing of grief. The words for 'doctor' may derive from this verb of stitching and its associated noun a)kestri/a 'seamstress' in Phrygian and Attic Greek (scholion to Homer, Iliad 22.2; cf. alpha 851), but this was vigorously denied by Eustathius (1647.56), citing Aelius Dionysius. See alpha 851 for the important distinction between the masculine nouns for 'doctor' and 'tailor'. This verb has no active form, and is thus unrelated to a)ke/wn (alpha 831). The one active use is a learned Alexandrian back-formation by Apollonius Rhodius, Argonautica 1.765; cf. alpha 841.
[1] From the scholia to Plato, Republic 364C, where the headword occurs. See also Photius s.v.