Mixing greek and latin text in LaTeX Ubuntu

Don't use the math mode $\alpha$, etc for ordinary greek words.

$ sudo apt-get install texlive-lang-greek

Add to preamble:
/usepackage[greek, english]{babel}
% makes latin/english the default

In the document, switch in and out of greek with
\greektext .... \latintext ...

This allows you to type greek on your keyboard.

An alternative is the switch with
\begin{greek} .... \end{greek}
I haven't used this. It's possibly better for extended greek text.
I've just been interested in putting in occasional words and
short phrases.

Example:

These grounds are quite sufficient for deeming
mathematical training an indispensible basis of real
scientific education, and regarding, with Plato,
one who is \greektext `agewm'etrhtoc%
\footnote{\latintext -- {\it ageometretos }, i.e. ignorant of geometry
(or, perhaps, unskilled in geometry, or indifferent to geometry).
The motto said to have been
carved above the entrance to Plato's
Academy was: \greektext O`udeic `agewm'etrhtoc e`is'itw --
\latintext {\it Let no-one
ignorant of geometry enter.}}
\latintext as wanting in one of the
most essential qualifications for the successful cultivation
of the highest branches of philosophy.
}