c. 1200, recenen, from Old English gerecenian "to explain, relate, recount, arrange in order," from Proto-Germanic *(ga)rakinaz "ready, straightforward" (source also of Old Frisian rekenia, Middle Dutch and Dutch rekenen, Old High German rehhanon, German rechnen, Gothic rahnjan "to count, reckon"), from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule."
Intransitive sense "make a computation" is from c. 1300. In I reckon, the sense is "hold an impression or opinion," and the expression, used parenthetically, dates from c. 1600 and formerly was in literary use (Richardson, etc.), but came to be associated with U.S. Southern dialect and was regarded as provincial or vulgar. Related: Reckoned; reckoning.
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