> "Sir Thomas Little Heath's translations ... let us down when it
> comes to certain subtleties. See David Lachterman's ETHICS OF GEOMETRY.
> I'll give just one example:
>
> In the very first proposition: Heath writes
>
> With centre A and distance AB let the circle BCD be described.
>
> Lachterman: let the circle BCD have been described [gegraphthO].
>
>Lachterman's comment:
>
> The phrases inite us, perhaps, to recollect or imagine someone's
> describing the circles; they do not oblige us to imitate these
> recollected actions *in status nascendi".
>...
To be fair to Heath, we should observe that at the first appearance
of this usage (precisely in this proposition) his comments include
...to be noted (1) the elegant and practically universal
use of the perfect passive imperative in constructions,
meaning of course "let it _have_ been described" or
"suppose it described"...
Thus he has (properly, I think) used the ordinary English phraseology
in the text but supplied the extra information for those who might
want to know about it.
I wouldn't want to comment for sure about Lachterman's interpretation
without knowing more of its context, but the Smith-Messing Greek Grammar
(Section 1864) says simply that this verb form "is used of a fixed
decision concerning what is to be done or has been done."
William C. Waterhouse
Penn State