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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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ross.finlayson@gmail.com

Posts: 1,220
Registered: 2/15/09
Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Posted: Feb 16, 2014 3:09 PM
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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)
>>
>>> is missing a premise - that if two different circles share a radius (that is, a line segment connecting
>>
>>> their centers is a radius for both circles).
>>
>>>
>>
>>> Could somebody provide a proof of this premise?
>>
>>>
>>
>>> Regards,
>>
>>>
>>
>>> Ken
>>
>>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> (proximal, proximity)
>>
>>
>>
>> The circle fills space uniformly with the least perimeter for
>>
>> area so they are the same. It is half-way then for the
>>
>> equilateral, because the angles are equi-angular, in the
>>
>> evolution of angles, they are equal.
>>
>>
>>
>> Sorry, this is a rather poor geometric construction, I'd be
>>
>> most surprised to hear of something like that in Euclid.
>>
>>
>>
>> Then, it would because the radii at a distance from the line
>>
>> with the parallel line, with the adjustable compass from
>>
>> drawing the parallel lines, would form the triangles with that
>>
>> height that form the equilateral triangle (that the side is
>>
>> equal, to find then the parallel line at the height of the
>>
>> equilateral triangle. This is finding the center from
>>
>> shifting that up then finding the mid-point of that, bisecting
>>
>> the segment with the compass and edge, then halving and
>>
>> doubling, for the projection of the triangle that is of the
>>
>> parallel lines, to the orthogonal parallel distance that is of
>>
>> the third side of the equilateral triangle, through that.
>>
>>
>>
>> Or, having three compasses.

>
> What absolute rubbish. I can tell you don't understand the Elements at all!
>


About Euclid, no that actually is a reasonable construction
of the equilateral triangle.

Here, the question is "define the area of a triangle".

It is a question for Euclid.



Date Subject Author
2/14/14
Read Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/14/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ross.finlayson@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
bert
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ross.finlayson@gmail.com
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
FredJeffries@gmail.com
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/15/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/16/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
YBM
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
David Hartley
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
David Hartley
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/19/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
David Hartley
2/20/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ross.finlayson@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read book fourteen is the best (Hypsicles, to start with [ph* the
encyclopedic "curriculum
Brian Q. Hutchings
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Ken.Pledger@vuw.ac.nz
2/17/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
David Bernier
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Ken.Pledger@vuw.ac.nz
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Wizard-Of-Oz
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Wizard-Of-Oz
2/19/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/19/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Wizard-Of-Oz
2/19/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
ken quirici
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
thenewcalculus@gmail.com
2/18/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/20/14
Read Re: Euclid's Elements Book 1 Proposition 1 - something Euclid missed?
Brian Q. Hutchings
2/22/14
Read A discussion about my discussion with Ken Quirici.
thenewcalculus@gmail.com

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