\documentclass[a4paper]{book}
\usepackage[polutonikogreek,american]{babel}
\usepackage{calc,ifthen}
\pagenumbering{alph}
\begin{document}
\selectlanguage{polutonikogreek}
\title{E>~inai >'omorfa ed~w p'anw to \greeknumeral{12345}}
\author{M~ak~hs Maram'enos}
\maketitle
\tableofcontents
\chapter{Par'arthma m~as} 
\greeknumeral{1834} \expandafter\uppercase\expandafter{\today}
s'hmera e'inai s'abbato.  ``Nai?''\&\textsc{``Nai?''} \texttt{``Nai''}
\textsf{p'ws eisai?}\\
\={a} \u{o} \Greeknumeral{999999} \texttt{\textit{Areske'ias}}
\Grtoday e'inai? \textsf{p'ws e'isai?}\newline
%%%%*****************************************************************
%%% The following symbols are no longer supported.
%%%\tao\space \Qoppa\space \varqoppa\space \Sampi\space \vardigamma
%%%%*****************************************************************
A>~inos
\selectlanguage{american} 
a~b
\fbox{\selectlanguage{polutonikogreek} ~a}
\selectlanguage{polutonikogreek}
\begin{enumerate}
\item 1
\item \begin{enumerate}
\item a \item b \item g \item d \item e \item z \item j
\begin{enumerate} \item a \item b \item g \item d \item e \item z \item j
\begin{enumerate} \item q \item q \item q \end{enumerate}
\end{enumerate}
\end{enumerate}
\end{enumerate}
\greeknumeral{100}
\newcounter{bullshit}
\setcounter{bullshit}{1997}
\Greeknumeral{\value{bullshit}}
\begin{enumerate}
\item lolo \begin{enumerate}
\item 1 \item 2 \item 3 
\begin{enumerate} \item a \item b \item g \end{enumerate}
\end{enumerate}
\end{enumerate}
\footnote{~a ~h ~i}
\begin{center}
\begin{minipage}[t]{150pt}
Gei'a sas\footnote{ap'o ton 'Ar~h!} kala\footnote{e'iste?} 
\end{minipage}
\end{center}
\newpage
\appendix
\chapter{Q'aq'a} 
\newcounter{num}
\setcounter{num}{1}
\whiledo{\value{num}<101}{\greeknumeral{\value{num}}
\newline\addtocounter{num}{1}}
\chapter{Q'oq'o}
\textit{\textbf{italiko'i 'entonoi}}
\chapter{Q'iq'i}
\end{document}