Re: proof by contradiction in Euclid's elements

In article <Pine.BSI.4.58.0504261958020.29630@xxxxxxxxxxxxxxxxx>,
William Elliot <marsh@xxxxxxxxxxxxxxxxxx> wrote:

> On Tue, 26 Apr 2005, ken quirici wrote:
>
> > PROP: If in a triangle two angles equal one another, then the sides
> > opposite the equal angles also equal one another.
> >
> > Let ABC be a triangle having the angle ABC equal to the angle ACB.
> > I say that the side AB also equals the side AC.
> >
> Let AD bisect angle BAC with D on BC. Show ADB and ADC congruent.
> ....



Euclid didn't prove the existence of angle bisectors until I.9, so
he avoided assuming it in proving I.6.

Ken Pledger.
.

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