The English reading of the  very ancient Greek,
word for word (separated by hyphens) is as follows:

SIDE A: Foreseen (are) - as given - standing straight lines (perpendiculars)
- to be constructed (drawn). - To the side - of either such line segment
- extend - a partner line - running - alongside. - The Problem (LEMMA):
- Consider - whether these - Parallel Lines - extended - stay - Parallels.
Consider - whether these - Parallels - extended converge (diverge).
- The synthetic - added line - would foresee - a medial (uncertain) - termination.
- Extended (beyond bounds) - a fixed (converging) - termination.
 

SIDE B: Next to - the categorized - just constructed lines - and flat to
- the side walls' - diameter - inscribe - a closed arc - and make it so that
- the new line - curve -  in its course - the side walls - diagonally - joins.
- Tie together - yoked - the branched lines. - Connect - the standing
straight lines - and branched lines. - Run a line so that - the newly created
- geodetic lines - are met - and the branched lines - pair is yoked.
- The promised - solution - is given.