I seem to remember seeing, on some swords, a small triangular bit that extended up from the hilt onto the center of the blade. Does anybody know what that bit was called and what it was for? I guessed it was reinforcement to reduce stress on the point where the blade meets the tang.

Perhaps you are thinking about the eccusson that projects form the guard? It is like a small tongue that can be more or less triangular or stem like. It has nothing to do with reinforcing the blade and tang juncture. It is a decorative feature that may have (some times) some practical function in keeping the blade snugly centered in the scabbard.

The meeting of blade and tang is not such a weak point as it is often made out to be.
On many modern low quality blades the lack proper distal taper and bad heat treating procedures, do result in the base of the tang being both weakened and subject to increased stress. On period blades that are shaped so impact and bending stresses are effectively distributed over the length of the blade, there is in reality very little risk for the sword to fail at this point.
I think the idea that the base for the tang is a weak spot is something that carries over from knife making (where it may be true at times?) or possibly from re-enactment fighting where often very cheap swords are favored. When low price is top priority, compromises are made that perhaps should best be avoided.

Historical blades tend to break in the middle of the forte (strong part of the blade) or the middle of the foible (or weak part of the blade: some where in the outer third of the blade). This is perhaps most often a result of nicks in the edges creating breaking points.

Of all the swords I´ve seen from bronze age to nearly modern times, I have seen very, very few , if any, that have failed at the base of the tang. I can remember seeing only one or two roman spathae that had riveted on tangs. This may not even be a result of their tangs breaking in the first place...

Some traditional Indian sword designs do have blade reinforcements, or stiffening plates and/or strips of steel riveted to very thin blades, as a means to mount them to the blade and help increase stiffness in the base of the blade. This is a unique design feature that swords from this part of the world shares. It is intentional and should not be seen as a way to help fix a a weak spot or correct a badly thought out design.

On some later hilts (especially 17th c. "mortuary" types,) there are small langets that appear to serve the function of stability and keeping the blade aligned, and which are created by the piercing of the guard for the tang.

More on the subject here: http://www.myArmoury.com/talk/viewtopic.php?t...s+mortuary