mid-14c., "to reach, grope, feel around," possibly a metathesis of grapsen, from Old English *græpsan "to touch, feel," from Proto-Germanic *grap-, *grab- (source also of East Frisian grapsen "to grasp," Middle Dutch grapen "to seize, grasp," Old English grapian "to touch, feel, grope"), from PIE root *ghrebh- (1) "to seize, reach" (see grab (v.)). With verb-formative -s- as in cleanse. Sense of "seize" first recorded mid-16c. Transitive use by 17c. Figurative use from c. 1600; of intellectual matters from 1680s. Related: Grasped; grasping.
1560s, "a handle," from grasp (v.). As "act of grasping" from c. 1600; also "power of grasping." Meaning "power of intellect" is from 1680s.
Ah, but a man's reach should exceed his grasp,
Or what's a heaven for?
[Browning, "Andrea del Sarto"]