my $lines_per_page = 50;  # print 50 lines per page
my $y_init  = 600;        # initial top line pos

my ( @pages, $page, $y );       # declare and scope these vars

foreach my $line ( 0 .. $#textstrings ) {

    # get line from array using index
    my $text = $textstrings[$line];

    # remove all control characters using tr with /d(elete)
    # option. these are specified in octal notation
    $text =~ tr/\000-\037//d;
    
    # we will have removed the traling newline from each line.
    # I doubt that it is required but if it is...
    $text .= "\n";

    # use modulus operator % to make a new page whenever
    # the current line number divided by the lines per 
    # page has a remainder of zero. this will get us a new
    # $page object when $line == 0, 50, 100 ...
    # we push each completed page into the @pages array
    if ( $line % $lines_per_page == 0 ) {
        push @pages, $page;
        $page = $root->newpage;
        $y = $y_init;    # reset the $y value to page top
    }

    # add the text to the current page
    $page->string( $f1, 10, 20, $y,  $text );

    # move y position down 10 pixels
    $y = $y - 10;
}

# now summate the pages in @pages (if that's what you need)
$page = join'', @pages;