[FOM] Standard Language of Euclid
a_mani_sc_gs at yahoo.co.in
Sat Sep 26 19:06:31 EDT 2009
(was Re: [FOM] New Proof of Fundamental Theorem of Arithmetic)
On Friday 25 Sep 2009 11:53:25 pm joeshipman at aol.com wrote:
> 2) On the other hand, there is something meaningless about finding new
> proofs of results which follow infallibly from a general theory.
> Already in high school geometry I had learned that any theorem that
> could be stated in the standard language of Euclid could be proved by
> reducing everything to coordinates and applying analytic geometry,
> since all questions ultimately got reduced to questions about
> equalities and inequalities between real polynomials which were clearly
> answerable by standard calculus techniques. [This was of course
> formally established by Tarski in the 30's but long before then there
> had ceased to be any "open questions" in the subject because everyone
> implicitly understood this.]
You are not being very correct in using "standard language of Euclid".
In the original language of Euclid it is not possible to remove the schematic
figures from the proof. It definitely possess a 'logic of diagrams' component.
It seems nobody has actually formalized it. 'School geometry' like in some of
the older British texts (Hall & Stevans for e.g) is in the language you
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