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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 15, 2014 1:23 AM
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On Saturday, February 15, 2014 4:00:41 AM UTC+2, 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


The Greek implies that the circles so drawn are equal, for otherwise the construction such that the sides of the equilateral triangle are equal would not be possible. It follows logically from the context. There is no missing premise. In the construction you must use circles with equal radii for otherwise you cannot construct an equalitareal triangle. This proposition is used to construct angles such as 60 degrees and 30 degrees.


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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