{quoting} is about environments like quote and quotation which set text blocks off by indenting them. Popular packages are {quoting} and {csquotes}. For questions about quotation marks, choose {punctuation} instead.

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using section types inside of blockquote

I'm still new to latex, but can someone explain to me why this one works: \begin{document} \begin{quote} \subsubsection{Just some Text} \end{quote} \end{document} but this one does not: ...
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rows and columns in quotes

I am trying to reproduce the text from the footnote of page 96 (76 in document) of Hadamard's essay: An Essay on the Psychology of Invention in the Mathematical Field As is evident, the quote has to ...