Talk:Equation of Straight Line in Plane

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What axioms and definitions are supposed to be in play here? This could well be taken as the definition of a line in Cartesian geometry. --Dfeuer (talk) 05:57, 28 May 2013 (UTC)

The original plan was:
a) to take the definition of the cartesian space (n-dimensional) and demonstrate that it is isomorphic to the Euclidean plane / space as "assumed" by Euclid (nowhere does he actually "define" the plane)
b) Somehow demonstrate that the equation as given is equivalent to that given by Euclid (i.e. that it doesn't deviate from itself, or however the wording is)
but I didn't have the mathematical vocabulary when I started it and probably still don't but I know better now what I don't know).
I wonder whether Tarski's Axioms (somewhere on $\mathsf{Pr} \infty \mathsf{fWiki}$, someone else posted them up) may not contain the seeds of what we need here. --prime mover (talk) 06:24, 28 May 2013 (UTC)