Marc-Antoine
TreeHouser
For the broken stone, clean the both sides, removing the small stone fragments which impair a tight matching. Warm and dry both sides with a torch (gently) hair dryer or what you want.
Then, epoxy glue on both sides. Not too much to avoid drooling, but enough to do the job. The little warming makes it more fluid, so the broken piece fits well and doesn't slide nor tilt, and it speeds the curing too.
Put the piece "first try" to get a good layer of glue with the smallest amount of bubbles. Hold the piece with no move at all, at least a good hour, more would be better if you can strap it (duct tape, sling ...), and you should be good.
Then, epoxy glue on both sides. Not too much to avoid drooling, but enough to do the job. The little warming makes it more fluid, so the broken piece fits well and doesn't slide nor tilt, and it speeds the curing too.
Put the piece "first try" to get a good layer of glue with the smallest amount of bubbles. Hold the piece with no move at all, at least a good hour, more would be better if you can strap it (duct tape, sling ...), and you should be good.