
Re: Euclid's Elements Book 1 Proposition 1  something Euclid missed?
Posted:
Feb 16, 2014 3:09 PM


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 halfway then for the >> >> equilateral, because the angles are equiangular, 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 midpoint 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.

