[FOM] 605: Integer and Real Functions

[WILLIAM TAIT]

I thought it was through similar triangles. (maybe I just invented some histor---that is the way he should and certainly could have done it!

Bill. 

> On Sep 4, 2015, at 6:22 AM, John Baldwin <jbaldwin at uic.edu> wrote:
> 
> The construction is Euclid's of the 4th proportional. But he doesn't regard it
> as multiplication.  Descartes regards it as multiplication - but bases it as Euclid
> on the what Bolzano calls the atrocious detour: through area.  
> 
> Hilbert reverses the process; defines multiplication by the 4th proportional construction
> and the computes areas by this multiplication.
> 
> John Baldwin
> 
> John T. Baldwin
> Professor Emeritus
> Department of Mathematics, Statistics,
> and Computer Science M/C 249
> jbaldwin at uic.edu
> 851 S. Morgan
> Chicago IL
> 60607
> 
> On Thu, Sep 3, 2015 at 8:37 PM, WILLIAM TAIT <williamtait at mac.com> 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?
> 
> Bill
> 
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