late 14c., coten , "to mark (a book) with chapter numbers or marginal references," from Old French coter , from Medieval Latin quotare "distinguish by numbers, number chapters," from Latin quotus "which in order? what number (in sequence)?," from quot "how many," from PIE *kwo-ti- , from pronomial root *kwo- (see who ).
The sense development is via "to give as a reference, to cite as an authority" (1570s) to "to copy out or repeat exact words" (1670s). Modern spelling with qu- is from early 15c. The business sense of "to state the price of a commodity" (1866) revives the etymological meaning. Related: Quoted ; quoting .