1560s, probably from Italian maneggiare "to handle," especially "to control a horse," ultimately from Latin noun manus "hand" (see manual (adj.)). Influenced by French manège "horsemanship" (earliest English sense was of handling horses), which also was from Italian. Extended to other objects or business from 1570s. Slang sense of "get by" first recorded 1650s. Related: Managed; managing. Managed economy was used by 1933.
To cope satisfactorily; survive; get by: It's a lot to pay, but we'll manage (1655+)