Where does ‘cliché’ come from?

"How They Met Themselves" (1860-64) by Dante Gabriel Rossetti

Umberto Eco once wrote, 'Two clichés make us laugh but a hundred clichés move us, because we sense dimly that the clichés are talking among themselves, celebrating a reunion.' But where does 'cliché' come from?

Robert Macfarlane in Original Copy: Plagiarism and Originality in Nineteenth-Century Literature (2007) answers:

It comes from the early nineteenth-century French term for a stereotype block, presumably due to the noise the blocks made whilst printing (clicher is a variant of the verb cliquer, to click). It existed in this literal meaning until the 1890s: the OED offers Andrew Lang, writing in Longwood’s Magazine in 1892, as providing the first usage of cliché as a metaphor meaning ‘A stereotyped expression, a commonplace phrase’. The coinage stuck, and the word cliché itself became a cliché, reproduced many times over to designate something reproduced many times over. (p. 160)

In a footnote, Macfarlane also explains the origin of 'stereotype':

It began as an eighteenth-century noun meaning 'A method of replicating a relief printing surface', but by 1850 had been abstracted to signify 'A thing continued or constantly repeated without change, esp. a phrase or formula, etc.; stereotyped diction or usage' (OED). (p. 160) 

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