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\documentclass[a4paper]{report}

\usepackage{epigraph}
    \setlength\epigraphwidth{0.93\textwidth}
    \setlength{\epigraphrule}{0pt}

\begin{document}

Consequently, under application of the aforementioned criterion of physical reality:
\epigraph{(I) Only one of the corresponding properties can be 'real' at any time.}
Subsequently, the focus is shifted onto an entangled state of two particles that have seized to interact and are far removed from another.

\end{document}

produces the following output: enter image description here Amending the code by \noindent, i.e.:

\documentclass[a4paper]{report}

\usepackage{epigraph}
    \setlength\epigraphwidth{0.93\textwidth}
    \setlength{\epigraphrule}{0pt}

\begin{document}

Consequently, under application of the aforementioned criterion of physical reality:
\epigraph{(I) Only one of the corresponding properties can be 'real' at any time.}
\noindent Subsequently, the focus is shifted onto an entangled state of two particles that have seized to interact and are far removed from another.

\end{document}

improves the output to: enter image description here A) Why is this necessary and B) How can I get rid of the remaining indentation on the paragraph starting with "Subsequently"?

1
  • 1
    I'm afraid you're confusing an epigraph and a cross-reference or a quote. An epigraph is not designed to be found mid document.
    – Bernard
    May 29 '20 at 16:18
1

The epigraph package was never designed for putting an epigraph in the middle of a paragraph. An epigraph essentially forms its own kind of displayed "paragraph".

I have modified your MWE to show how \paragraph is normally used.

% epigraphprob.tex SE 546919

\documentclass[a4paper]{report}

\usepackage{epigraph}
    \setlength\epigraphwidth{0.93\textwidth}
    \setlength{\epigraphrule}{0pt}
\epigraphnoindent

\begin{document}

Consequently, under application of the aforementioned criterion of 
physical reality:

\chapter{One}
\epigraph{(I) Only one of the corresponding properties can be 'real' 
at any time.}{}

Subsequently, the focus is shifted onto an entangled state of two particles 
that have seized to interact and are far removed from another.

\end{document}

Two comments: the \epigraphnoindent in the preamble stops the indentation of text that follows a paragraph that follows a divisional heading (\chapter in the above); \paragraph takes two argument, namely the text and the source --- you provided only the text.

I think that you would be better off using something like the quote environment.

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