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Topic: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Replies: 62   Last Post: Feb 22, 2014 12:11 AM

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 thenewcalculus@gmail.com Posts: 1,361 Registered: 11/1/13
Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Posted: Feb 16, 2014 5:42 PM

On Sunday, February 16, 2014 10:09:02 PM UTC+2, Ross A. Finlayson wrote:
> On 2/14/2014 10:24 PM, John Gabriel wrote:
>

> > On Saturday, February 15, 2014 6:04:10 AM UTC+2, Ross A. Finlayson wrote:
>
> >> On 2/14/2014 6:00 PM, Ken Quirici wrote:
>
> >>
>
> >>> According to Wikipedia, Book 1 Proposition 1 (constructing equilateral triangle on given line segment)
>
> >>
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> >>> is missing a premise - that if two different circles share a radius (that is, a line segment connecting
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> >>
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> >>> their centers is a radius for both circles).
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> >>
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> >>>
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> >>
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> >>> Could somebody provide a proof of this premise?
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> >>
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> >>>
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> >>
>
> >>> Regards,
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> >>
>
> >>>
>
> >>
>
> >>> Ken
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> >>
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> >>>
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> >>
>
> >>
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> >>
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> >>
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> >>
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> >>
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> >>
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> >>
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> >>
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> >> (proximal, proximity)
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> >>
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> >>
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> >>
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> >> The circle fills space uniformly with the least perimeter for
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> >>
>
> >> area so they are the same. It is half-way then for the
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> >>
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> >> equilateral, because the angles are equi-angular, in the
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> >>
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> >> evolution of angles, they are equal.
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> >>
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> >>
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> >>
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> >> Sorry, this is a rather poor geometric construction, I'd be
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> >>
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> >> most surprised to hear of something like that in Euclid.
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> >>
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> >>
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> >>
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> >> Then, it would because the radii at a distance from the line
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> >>
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> >> with the parallel line, with the adjustable compass from
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> >>
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> >> drawing the parallel lines, would form the triangles with that
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> >>
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> >> height that form the equilateral triangle (that the side is
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> >>
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> >> equal, to find then the parallel line at the height of the
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> >>
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> >> equilateral triangle. This is finding the center from
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> >>
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> >> shifting that up then finding the mid-point of that, bisecting
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> >>
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> >> the segment with the compass and edge, then halving and
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> >>
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> >> doubling, for the projection of the triangle that is of the
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> >>
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> >> parallel lines, to the orthogonal parallel distance that is of
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> >>
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> >> the third side of the equilateral triangle, through that.
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> >>
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> >>
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> >>
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> >> Or, having three compasses.
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> >
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> > What absolute rubbish. I can tell you don't understand the Elements at all!
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> >
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>
>
> About Euclid, no that actually is a reasonable construction
>
> of the equilateral triangle.
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>
>
> Here, the question is "define the area of a triangle".
>
>
>
> It is a question for Euclid.

Proposition has NOTHING to do with area of a triangle.

Date Subject Author
2/14/14 ken quirici
2/14/14 ross.finlayson@gmail.com
2/15/14 thenewcalculus@gmail.com
2/15/14 bert
2/15/14 thenewcalculus@gmail.com
2/16/14 ross.finlayson@gmail.com
2/16/14 thenewcalculus@gmail.com
2/15/14 thenewcalculus@gmail.com
2/15/14 Brian Q. Hutchings
2/15/14 ken quirici
2/15/14 FredJeffries@gmail.com
2/15/14 ken quirici
2/15/14 thenewcalculus@gmail.com
2/16/14 ken quirici
2/16/14 ken quirici
2/16/14 thenewcalculus@gmail.com
2/17/14 ken quirici
2/17/14 thenewcalculus@gmail.com
2/17/14 ken quirici
2/17/14 thenewcalculus@gmail.com
2/17/14 ken quirici
2/17/14 thenewcalculus@gmail.com
2/17/14 ken quirici
2/17/14 thenewcalculus@gmail.com
2/17/14 YBM
2/18/14 thenewcalculus@gmail.com
2/17/14 David Hartley
2/17/14 thenewcalculus@gmail.com
2/17/14 ken quirici
2/17/14 David Hartley
2/17/14 ken quirici
2/19/14 David Hartley
2/20/14 thenewcalculus@gmail.com
2/17/14 ross.finlayson@gmail.com
2/18/14 thenewcalculus@gmail.com
2/17/14 ken quirici
2/17/14 thenewcalculus@gmail.com
2/17/14 Brian Q. Hutchings
2/17/14 thenewcalculus@gmail.com
2/17/14 Ken.Pledger@vuw.ac.nz
2/17/14 thenewcalculus@gmail.com
2/18/14 David Bernier
2/18/14 thenewcalculus@gmail.com
2/18/14 Ken.Pledger@vuw.ac.nz
2/18/14 thenewcalculus@gmail.com
2/18/14 thenewcalculus@gmail.com
2/18/14 ken quirici
2/18/14 thenewcalculus@gmail.com
2/18/14 Wizard-Of-Oz
2/18/14 thenewcalculus@gmail.com
2/18/14 Wizard-Of-Oz
2/19/14 thenewcalculus@gmail.com
2/19/14 Wizard-Of-Oz
2/19/14 Brian Q. Hutchings
2/18/14 thenewcalculus@gmail.com
2/18/14 thenewcalculus@gmail.com
2/18/14 ken quirici
2/18/14 thenewcalculus@gmail.com
2/18/14 Brian Q. Hutchings
2/18/14 thenewcalculus@gmail.com
2/18/14 Brian Q. Hutchings
2/20/14 Brian Q. Hutchings
2/22/14 thenewcalculus@gmail.com