I've seen on this site and in other places various things attributed to Archimedes(e.g. Stewart's Theorem, Broken Chord Theorem, Herron's formula) which do not appear in his complete works. Can someone please explain how people know that he knew these things? Thanks.

Greg

One one hand, no one doubts that the Complete Works of Archimedes are actually incomplete. We know for sure that some of his work have been lost. So this leaves room to making guesses.

On the other hand, his works and theorems have been described, copied and translated over the centuries by authentic authors like Vitruvius and Pappus and by regular scribes. So it is customary to believe that we know pretty well of what Archimedes might have been interested in and certainly of what he was capable of.

To say that when people suggest a possibility of a past event they "know" of the event having taken place is an exaggeration. That they admit a reasonable likelihood that Archimedes did this or that without having a definite supporting reference demonstrates the esteem his abilities and knowledge are usually being held in.

I checked the statements you mention at my site. Never in these instances did I use a language of certainty in making attributions to Archimedes.

(Just in case you have not seen that, your problem involving circular segment altitudes had an interesting development.)