Re: [HM] geometrical algebra in Euclid
William C Waterhouse (wcw@math.psu.edu)
Tue, 1 Sep 1998 14:41:04 -0400 (EDT)
On August 30, John Hannah <J.Hannah@math.canterbury.ac.nz> asked
>...a student ...would like to ask about the following (fine?) point
of translation.
>
> ==============================================================================>...
> (1) How do you handle the phrase
>
> to upo twn A, BC periexomenon orthogwnion
>
> Is it 'the rectangle contained by A, BC'
> or is 'the rectangle contained by A and BC' okay?
>
> I just don't understand whether Euclid means us to think of the two line
> segments as being 'one thing' (I have here rectangle formation in mind) or
> whether they are two seperate things (and hence the latter translation is
> better.
The article form "twn" is plural, so grammatically at least
the language is treating the segments as two things. And
Definition II.1 refers explicitly to "two lines".
William C. Waterhouse
Penn State