Reddit reviews Complete Works Fiore Dei Liberi Vol 1 Hb: Historical Overview and the Getty Manuscript (Flowers of Battle Series) (Complete Martial Works of Fiore Dei Liberi, a Master-At-Arms)
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So the book I was referring to is called Flowers of Battle (precisely the one which you have literally in the title....) (https://www.amazon.com/Complete-Works-Fiore-Liberi-Master-At-Arms/dp/1937439186)
That indeed is the exact same book you were talking about and I'm a bamboo head for not checking the title first before making any comments ... it's just that I simply did not put together the books cover with its name.
Also I have (for reasons unknown) assumed Fiore would not put info on polearm and longswords into one manuscript - pair that with absence of knowledge that he wrote just one thing and you have the ressult you've witnessed.