Medieval weapons were designed as technological advances as war developed.
Just like today we have .50 caliber sniper rifles because of bullet-resistant vests, medieval men-at-arms needed weapons such as warhammers, maces, longswords and broadswords to adapt to the already present chainmail armour and the increasingly popular plate armour as the old Roman style shortswords were becoming obsolete.
As plate armour developed more and more, as well as lower class armours such as brigandine, jacks of plates and part-plate were also coming into play, weapons had to be improved to allow skilled combatants to pierce and dent armour.
Long range weapons such as English longbows, Mongolian recurve bows, corssbows and even "hand-cannons" (the first ever handheld guns) were also being developed. Bows gave the decisive advantage of shooting speed, a skilled archer with a powerful bow could loose 10-12 arrows a minute. Crossbows had the intense power to pierce even plate armour and required much less training to use, but could only shoot 3-4 bolts a minute. Guns were very low powered (despite people falsely claiming they made armour immediately obsolete) and could only shoot 1-2 bullets a minute, but required almost no training to use.
Medieval weapons, armour, skills and tactics were superior to their ancient equivalents. The militarily primitive Aztecs learnt this harsh lesson from Hernan Cortéz and his Spanish army.
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