Correct weapons and armor, introduce their real names (long sword I am looking at you), Remove items without historic equivalent (leather/studded leather). Rework the damage of the quarterstaff (it should be 1d6 and two handed use only. Expand the weapons and armor list.
I agree about accurate names.
Now the 5e longsword works well as a versatile "hand-and-half" sword, like historical long sword, claymore, bastard sword, espadon, etcetera.
What is still missing is the "normal" sword, the spatha, viking sword, knightly sword, arming sword, etcetera.
So add to the weapons table a "sword" that can be a finesse weapon.
Call it "sword" or "knightly sword" or "knightsword"
The greatsword corresponds to historical zweihander, bihander, but also serves as a fantasy buster sword.
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greatsword 2d6 slashing: heavy, two-handed, [
reach 10]
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longsword 1d8 slashing, versatile [
1d12] slashing
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sword 1d8 slashing or piercing: finesse
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rapier 1d8 piercing: finesse
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katana 1d6 slashing, versatile 1d10 slashing: finesse
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shortsword 1d6 piercing: finesse, light
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scimitar 1d6 slashing: finesse, light
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seax 1d6 slashing or piercing: finesse, light
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knife 1d4 slashing or piercing: finesse, light, throw 30
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dagger 1d4 piercing: finesse, light, throw [
30]