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Topic: A question about straight lines
Replies: 103   Last Post: Feb 8, 2014 8:28 AM

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Domenico Rosa

Posts: 2,091
Registered: 2/16/05
Re: A question about straight lines
Posted: Jan 29, 2014 1:27 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 29 Jan 2014, Neighbor wrote:

> that is to say, initially we have AB and finally
> (after the division being made) we have A(C) C (C)B,
> and A(C) and (C)B are said to be the two equal
> straight-lines in which AB has been divided, for the
> point C cannot be divided between them, having no parts.


One of the notions of Euclidean Geometry is that a point has no length. Therefore all four lines [A,C], [B,C] [A,C) and [B,C) have the same length. The fact that point C "has no parts" has no bearing whatsoever on this.

The gap in Euclid's construction has nothing to due with point C. As pointed out in

Edwin E. Moise and Floyd L. Downs, Jr.
Geometry, Addison-Wesley (1982) 680p.

an additional postulate is required in order to guarantee that the arcs of equal radii, involved in the construction, will in fact intersect. The following are some of the additional postulates listed in the above book, a book that played a key role in the demise of high school Euclidean Geometry and in the subsequent promotion of junk geometry.

CHAPTER Page
2. Sets, real Numbers, and Lines 15
The distance postulate
The ruler postulate
The ruler placement postulate
Betweenness. The point-plotting theorem
The line postulate
3. Lines, Planes, and Separation 49
The plane-space postulate
The flat plane postulate
The plane postulate
Intersection of planes postulate
The plane separation postulate
The space separation postulate
4. Angles and Triangles 77
The angle measurement postulate
The angle construction postulate
The angle addition postulate
The supplement postulate


Date Subject Author
1/26/14
Read A question about straight lines
Neighbor
1/26/14
Read Re: A question about straight lines
kirby urner
1/27/14
Read Re: A question about straight lines
Neighbor
1/27/14
Read Re: A question about straight lines
Robert Hansen
1/27/14
Read Re: A question about straight lines
Bishop, Wayne
1/27/14
Read Re: A question about straight lines
kirby urner
1/27/14
Read Re: A question about straight lines
Neighbor
1/27/14
Read Re: A question about straight lines
Robert Hansen
1/27/14
Read Re: A question about straight lines
Neighbor
1/27/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Gary Tupper
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Louis Talman
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/29/14
Read Re: A question about straight lines
Bishop, Wayne
1/29/14
Read Re: A question about straight lines
GS Chandy
1/29/14
Read Re: A question about straight lines
Domenico Rosa
1/29/14
Read Re: A question about straight lines
Neighbor
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Neighbor
1/29/14
Read Re: A question about straight lines
Domenico Rosa
1/30/14
Read Re: A question about straight lines
Bishop, Wayne
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Neighbor
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/30/14
Read Re: A question about straight lines
Neighbor
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/30/14
Read Re: A question about straight lines
Louis Talman
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/30/14
Read Re: A question about straight lines
Neighbor
1/30/14
Read Re: A question about straight lines
Jonathan Crabtree
1/30/14
Read Re: A question about straight lines
Joe Niederberger
1/30/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
kirby urner
1/30/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Neighbor
1/30/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Neighbor
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Neighbor
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Neighbor
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
GS Chandy
1/31/14
Read Re: A question about straight lines
GS Chandy
1/31/14
Read Re: A question about straight lines
GS Chandy
1/31/14
Read Re: A question about straight lines
Joe Niederberger
2/1/14
Read Re: A question about straight lines
GS Chandy
2/1/14
Read Re: A question about straight lines
Robert Hansen
2/1/14
Read Re: A question about straight lines
kirby urner
2/1/14
Read Re: A question about straight lines
Robert Hansen
2/1/14
Read Re: A question about straight lines
Joe Niederberger
2/1/14
Read Re: A question about straight lines
Robert Hansen
2/1/14
Read Re: A question about straight lines
Joe Niederberger
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
kirby urner
2/1/14
Read Re: A question about straight lines
Joe Niederberger
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
James Elander
2/2/14
Read Re: A question about straight lines
GS Chandy
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
GS Chandy
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
Joe Niederberger
2/2/14
Read Re: A question about straight lines
GS Chandy
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
GS Chandy
2/4/14
Read Re: A question about straight lines
GS Chandy
2/4/14
Read Re: A question about straight lines
GS Chandy
2/4/14
Read Re: A question about straight lines
GS Chandy
2/8/14
Read Re: A question about straight lines
GS Chandy

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