[Tex/LaTex] How to type an old style greek phrase in text mode

font-encodingsgreek

I need to type an greek phrase: Let no one untrained in geometry enter. Jusk like

I hope it looks like the old style as much as possible.

enter image description here

I have tried 

\documentclass{article}
\usepackage[LGR,T1]{fontenc}
\newcommand{\textgreek}[1]{\begingroup\fontencoding{LGR}\selectfont#1\endgroup}

\begin{document}
\textgreek{'agewm`etrhtos mhde`is e'is'itw}
\end{document}

The result is not satisfying.

enter image description here

The main problems are

  • I need \epsilon, but get a \varepsilon
  • There are symbols with comma above it, how to type that?
  • There are differences between the fonts, e.g. \mu

UPDATE

Thanks to @Sverre, omma problem is solved. Except \epsilon problem, I still think there are font problems. My latex result is a little slim, and some detail is different, e.g. the tail of the \mu.

\documentclass{article}
\usepackage[LGR,T1]{fontenc}
\newcommand{\textgreek}[1]{\begingroup\fontencoding{LGR}\selectfont#1\endgroup}

\begin{document}
\textgreek{>agewm`etrhtos mhde`is e>is'itw}
\end{document}

enter image description here

UPDATE

The first picture missed a letter $\tau$, and the actual sculpture looks like this

enter image description here

with all letters captialized. So I need not bother to persuit any effect. Anyway, this question is fruitful, leading to LGR and GFS Philostratos solutions.

Best Answer

This is less an answer than a response to requests in the comments. If the point is to make the Greek appear to be on the old side, there are many possibilities opened up by lualatex and xetex, which can use any unicode-encoded TrueType or OpenType font. Here are four specimens:

\documentclass[12pt]{article}
\usepackage{fontspec}
\setmainfont{GFS Philostratos}% a 19th-century antiqua
\newfontface\milan{Avdira}[% http://users.teilar.gr/~g1951d/
  Ligatures=Rare]
\newfontface\compl{GFS Complutum}% 16th century
\newfontface\ign{GFS Ignacio}% because there were no minuscules in Plato’s day
\begin{document}
\centering
% GFS Philostratos; I’d reduce the linespread
ἀγεωμέτρητος\\
μηδεὶς εἰσίτω

\bigskip

\linespread{1.10344}
% Avdira
\milan ἀγεωμέτρητος\\
μηδεὶς εἰσίτω

\bigskip

% GFS Complutum
\compl ἀγεωμέτρητος\\
μηδεὶς εἰσίτω

\bigskip

% GFS Ignacio
\ign ΑΓΕΩΜΕΤΡΗΤΟΣ\\
ΜΗΔΕΙΣ ΕΙΣΙΤΩ
\end{document}

output of the source above

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