Where does “cross-banded” come from?

cross-banded (English) comes from English banded, from English Band-Aid, from English aid, from Middle English aiden, from Middle French ayder, from Old French aidier, from Latin adiūtō, from Latin -tō — Derives action nouns from verb roots.

Ancestry of “cross-banded”, step by step

StepLanguageWordMeaning
1EnglishbandedMarked with bands of colour; Divided into bands;...
2EnglishBand-AidAn adhesive bandage, a small piece of fabric or plastic that may be stuck to the skin in order to temporarily cover a small wound
3EnglishaidHelp; assistance; succor, relief; A helper; an...
4Middle EnglishaidenTo aid
5Middle Frenchayderto help; to aid
6Old Frenchaidierto help
7Latinadiūtōto help, serve, assist
8Latin-tōForms here
9Latin-tusForms the past participle of verbs; Forms...
10Proto-Italic-tus
11Proto-Indo-European-tusDerives action nouns from verb roots
Every word from Proto-Indo-European -tus