Hi Billman,
I'd disagree about hedges being an 18th century invention. According to the British historical ecologists I've read, hedges are much older (cf: books by Arthur Rackham).
But let's get to some linguistics? The Dacian implement was termed a falx, and that name comes into French as fauchard, which implements such as bank blades are still called in French. In English, a fauchard is a bill.
To my eye, falx also looks like it gave rise into falchion, and the conventional excuse for the relative dearth of historical falchions relative to swords was that they were used in agriculture when not used in the field.
I'm not going to try to trace the machete from the falchion, but I think they were similar blades doing similar things, and I also think the linguistic evidence suggests that the falx and the falchion are related, at least according to the people who used them.
Best,
F
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