From Plutarch's Life of Aristides (http://ancienthistory.about.com/library/bl/bl_text_plutarch_aristides.htm):

For taking hold of the spears with their bare hands, they broke many of them, and betook themselves not without effect to the sword; and making use of their falchions and scimitars, and wresting the Lacedaemonians' shields from them, and grappling with them, it was a long time that they made resistance.

The Arms and Armour Glossary of Terms defines it thusly:

Falchion: A short, heavy, broad-bladed sword with a single edge, bearing a similarity to a heavy scimitar.

http://www.chronique.com/Library/Glossaries/glossary-AA/arms_f.htm#falchion


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