I agree that Heath is not confused. He knows that Euclid is saying
something like
Let it have been described.
However, the too trusting reader will not get that from the translation
alone. Those who use the Encyclopaedia Britannica text have all thirteen
books of Euclid in a single volume, but they have no notes at all.
Best wishes,
Sam Kutler
>Samuel S. Kutler wrote that
>
>> "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