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Rewrite the statement "If with any straight line, and at a point on it, two straight lines not lying on the same side make the sum of the adjacent angles equal to two right angles, then the two straight lines are in a straight line with one another."

So that it makes sense in a Hilbert plane, and then give a careful proof of it. most of the time with these questions one can adapt Euclid proof to work with the tools of Hilbert but in this case i can't seem to figure it out

Faust
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  • What does Euclid mean for 2 lines to be ''in a straight line with one another'' ? Did Euclid actually write that or is someone's notion of a translation? – DanielWainfleet Nov 02 '17 at 23:26
  • its just saying that they are a straight line not a bent line.

    Also i am not sure how to answer that Euclid spoke Greek...

     – Faust Nov 03 '17 at 01:49
  • It seems to me from the condition on the angles that it means the 2 lines are parallel. – DanielWainfleet Nov 03 '17 at 02:00

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