late 14c., "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, what number (in sequence)," from quot "how many," related to quis "who" (see who).
The sense development is via "to give as a reference, to cite as an authority" to "to copy out exact words" (1670s). The business sense of "to state the price of a commodity" (1866) revives the etymological meaning. Related: Quoted; quoting.