[FOM] 605: Integer and Real Functions

[william tait]

John Baldwin pointed out to me that Descartes followed Euclid's theory of similarity, which presupposed Archimedes' Axiom. Hilbert eliminated this unnecessary assumption.

Bill

Sent from my iPad

> On Sep 8, 2015, at 6:00 PM, mlink at math.bu.edu wrote:
> 
> 
> Dear Professor Tait,
> 
> Yes, maybe so: in Bos 2001 there appears a construction like this
> due to Descartes.
> 
> 
> Bos, Henk J.M.  2001.  Redefining Geometrical Exactness.
> Descartes' Transformation of the Early Modern Concept of
> Construction.  New York:  Springer.  
> 
> --ml
> 
> 
> 
> 
> On 9/3/2015 9:37 PM, WILLIAM TAIT wrote:
> On Sep 3, 2015, at 8:22 AM, John Baldwin <jbaldwin at uic.edu>
> wrote:\
> 
> Hilbert proved that in any Euclidean field one can define a
> multiplication by similarity of triangle that distributes over
> addition. Thus he defines a field of line segments.
> but it has fallen into disuse, for good reason.)
> 
> Isn't the construction Descartes?
> 
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