Peel the cucumber, remove the core and grate the flesh. Add salt and keep aside for 15 minutes. Squeeze out the liquid (use this liquid to grind the rice). You must have about 1 cup of grated cucumber now.
Grind the rice with coconut and jaggery, using the cucumber liquid to a smooth batter. Add water if needed to get the consistency of dosa batter. Mix in the cucumber.
Pour a ladle full of batter on a hot dosa pan and spread it like pancake. (slightly thicker than normal dosa). Pour some oil around it. When one side is cooked, turn over and cook the other side. Use all the batter thus. Serve with treacle or honey.