reachyoudaoicibaDictYouDict
reach: [OE] Reach goes back ultimately to a prehistoric West Germanic *raikjan, a word of uncertain origin which also produced German reichen and Dutch reiken. It originally meant ‘stretch out the hand’, and ‘attain’ and ‘arrive at’ are secondary semantic developments.
reach (v.)youdaoicibaDictYouDict
Old English ræcan, reccan "reach out, stretch out, extend, hold forth," also "succeed in touching, succeed in striking; address, speak to," also "offer, present, give, grant," from West Germanic *raikjan "stretch out the hand" (cognates: Old Frisian reka, Middle Dutch reiken, Dutch reiken, Old High German and German reichen), from Proto-Germanic *raikijanau, perhaps from PIE root *reig- "to stretch out" (cognates: Sanskrit rjyati "he stretches himself," riag "torture" (by racking); Greek oregein "to reach, extend;" Lithuanian raižius "to stretch oneself;" Old Irish rigim "I stretch").

Shakespeare uses the now-obsolete past tense form raught (Old English ræhte). Meaning "arrive at" is early 14c.; that of "succeed in influencing" is from 1660s. Related: Reached; reaching. Reach-me-down "ready-made" (of clothes) is recorded from 1862, from notion of being on the rack in a finished state.
reach (n.)youdaoicibaDictYouDict
1520s, from reach (v.); earliest use is of stretches of water. Meaning "extent of reaching" is from 1540s; that of "act of reaching" is from 1560s.
Ah, but a man's reach should exceed his grasp,
Or what's a heaven for?

[Browning, "Andrea del Sarto"]