Bracchiati or Brachiati?

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Were the Bracchiati/Brachiati named after their bracchia (armlets) or brachae (trousers?) I'm finding both spellings and both explanations in credible sources on the Late Roman Army. Similarly, I was sure that that Cornuti were named for their horned helmets, but now read in Ferguson that they were known as the "hornblowers."
Thanks for any answers,
Best regards,
Milo