[FOM] 605: Integer and Real Functions

[John Baldwin]

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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