Hi, Thales! I loved your theorems, when I had geometry
Seriously, to repair this, I'd drill a small hole in the hilt, where the blade broke off, and use CA glue (cyano-acrylate, aka Super Glue) to reattach the blade. There are a couple of ways to prepare the blade piece:
If the blade is cast thick enough, you might be able to drill a hole in the blade, then, too, and use a piece of fine wire to pin it back to the sword hilt.
If the blade is not cast thick enough, you might be able to insert a piec of fine wire into the hole in the hilt, and make a groove in the base of the blade, to fit over the pin.
If the blade is too thin to drill or to make a groove, you could file the bottom of the blade to a thin point, and then fit this into the hole in the hilt.
You might also consider getting a piece of brass strip to replace the cast blade. You can get brass strip at hobby shops. But either way, I'd drill the hole in the base, and fit the blade or a pin into it. That will result in a strong join.
Hope that helps!
Prost!
Brad