How Can I Query a Specific Page From a MultiPage paginated Post

WordPress uses the PHP explode function to split the content into a
array of ‘pages’. Happens in the setup_postdata function with this
code:

$pages = explode(”, $content);

source

So you could do something like :

function wpse_103026( $content, $pagenum ) {
  if ( strpos( $content, '<!--nextpage-->' ) ) {
    $pages = explode('<!--nextpage-->', $content); 
    return isset ( $pages[$pagenum-1] ) ? trim( $pages[$pagenum-1] ) : $content;
    } else {
    return false;
  }
}

And then you can retrieve content of page 4 with :

echo apply_filters( 'the_content', wpse_103026( $post->post_content, 4 ) );