Desolate
late Middle English: from Latin desolatus ‘abandoned’, past participle of desolare, from de- ‘thoroughly’ + solus ‘alone’.
wiktionary
From Middle English desolate, from Latin dēsōlātus, past participle of dēsōlāre(“to leave alone, make lonely, lay waste, desolate”), from sōlus(“alone”).
etymonline
desolate (adj.)
mid-14c., of persons, "disconsolate, miserable, overwhelmed with grief, deprived of comfort;" late 14c., of persons, "without companions, solitary, lonely;" also, of places, "uninhabited, abandoned," from Latin desolatus, past participle of desolare "leave alone, desert," from de- "completely" (see de-) + solare "make lonely," from solus "alone" (see sole (adj.)). Related: Desolately; desolateness.
desolate (v.)
late 14c., "render (a region or place) lonely by depopulation or devastation; lay waste, ruin," from desolate (adj.) or Latin desolatus. Meaning "overwhelm with grief, make sorry or weary by affliction" is from 1520s. Related: Desolated; desolating.