quoteyoudaoicibaDictYouDict[quote 词源字典]
quote: [14] Latin quot meant ‘how many’. From it was derived the adjective quotus ‘of what number’, whose feminine form quota was used in post-classical times as a noun, denoting literally ‘how great a part’ – whence English quota [17]. Quotus also formed the basis of the medieval Latin verb quotāre ‘number’, which was used specifically for the practice of marking sections of text in manuscripts with numbers, as reference points.

English took the verb over as quote, and by the 16th century was using it for ‘cite’ or ‘refer to’. The derived unquote is first recorded in a letter by e e cummings, dated 1935. Also based on quot was Latin quotiēns ‘how many times’, which has given English quotient [15]; and quotidian ‘daily’ [14] goes back ultimately to a Latin compound formed from quotus and diēs ‘day’.

But the archaic quoth [OE], despite a certain similarity in form and sense, is not related; it comes from cwæth, the past tense of Old English cwethan ‘say’.
=> quota, quotient[quote etymology, quote origin, 英语词源]
quote (v.)youdaoicibaDictYouDict
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 pronominal 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.
quote (n.)youdaoicibaDictYouDict
"a quotation," 1885, from quote (v.). From c. 1600 as "a marginal reference." Quotes for "quotation marks" is from 1869.