well,
thanks, I can now determine the x-y coordinate in a tile image,
but it is not that precise

I know the left upper corners lat/lon and the right lower lat/lon of the tile image and the positions lat/lon,
but how can i now determine the correct x-y coordinate of a position in that tile image?

Edit:
This Link helped me out: http://www.netzwolf.info/kartografie/osm/tilebrowser?lat=51.157800&lon=6.865500&zoom=14