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I want to align

\begin{quote}
  Text
  Author (\cite{Source})
\end{quote}

to the right side of the paper. How can I do this?

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1  
What exactly do you want? You want the right margin of the quote environment to be the same as the right margin of the surrounding text? –  Seamus Oct 20 '11 at 9:55
5  
look for "epigraph" on ctan. also, this has been addressed a few times in [tug.org/tugboat](tugboat); again, search for "epigraph". (i'm not where i can easily do the search effectively at the moment.) –  barbara beeton Oct 20 '11 at 11:00
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3 Answers

redefine the quote environment

\renewenvironment{quote}
  {\begin{trivlist} \setlength\leftskip{2cm} \setlength\rightskip{0pt}
   \item\relax}
  {\end{trivlist}}

or define a new Quote environment with the same code

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Staying close to the definition of the quote environment (in the article class file), I'd recommend the following redefinition in order to achieve what (I think) you're looking for:

\makeatletter
\renewenvironment{quote}
     {\list{}{
        \if@twocolumn
           \leftmargin {3em} 
               \else
                \leftmargin {5em}
               \fi
               \rightmargin 0pt}%
            \item\relax}
    {\endlist}
\makeatother

Remark: If you're sure you're only going to use this code in a single-column environment, you can simplify the code considerably (note, in particular, that you no longer need the \makeatletter and \makeatother commands):

\newenvironment{quote}
     {\list{}{\leftmargin {5em}
              \rightmargin{0pt}}%
       \item\relax}
     {\endlist}

Of course, depending on your preferences, you may prefer to increase or decrease the amount of left-hand indentation; the 5em amount is simply an example (obtained by doubling the amount set in the article.cls file).

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Add to your preamble:

    \makeatletter{}
\g@addto@macro\quote\flushright
\makeatother

And quotes will be printed flushright.

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Is this a (correct) solution for the OP's problem? The way I understand the question, the OP wants to have the whole quote environment shifted to the right, while preserving full justification rather than getting right-justification)of the text inside the quote. I agree with @barbarabeeton's comment that he should use the epigraph environment for this job. –  Mico Oct 20 '11 at 13:50
    
@Mico: Maybe you are right, maybe me. Let's hope OP will specify his question. –  Keks Dose Oct 20 '11 at 15:13
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