The geometric interpretation of the "addition law" on Edward Curves is not the same as for Weierstrass Curves.

The correct interpretation for this kind of curves is "adding their angles".
It works as on a clock.

You can give a look to the [ECCHacks: a gentle introduction to elliptic-curve cryptography][1] (starting at page 6) by Daniel J. Bernstein and Tanja Lange


  [1]: https://fahrplan.events.ccc.de/congress/2014/Fahrplan/system/attachments/2501/original/20141227.pdf