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• Two Taxiarchies, which were ſixteen Files, made a Syntagmatarchy of two hundred fifty ſix men; its Commander Syntagmatarcha was our private Captain. This Company was a ſquare of men, ſixteen in Rank and ſixteen in File, and whatever way you turn’d it, ſtill ſixteen. […¶] Two Syntagmatarchies compos’d a Pentecoſiarchy conſiſting of five hundred and twelve men[.…] By this account we find in every Phalange two Diphalangarchies, four Phalangarchies, eight Myriarchies, ſixteen Chiliarchies, two and thirty Pentecoſiarchies, ſixty four Syntagmatarchies; in all one thouſand twenty four Files, which conſiſted of ſixteen thouſand three hundred eighty four men, at ſixteen in every File. [¶] Here you are to obſerve, that every Syntagmatarchy or private Company, conſiſting of two hundred fifty ſix men, had beſide the Captain and others already ſpoken of, five other Officers, whom Ælian calls ſupernumerary or extraordinary.
• Sixteen of theſe files compoſed what was called a ſyntagmatarchy or a ſquare body of 256 men.
• In the phalanx,…were 64 syntagmatarchies; and it evidently appears that the number of cavalry…assigned to act with the phalanx, was 4096 men; now this number being divided by 64, will exactly furnish a troop consisting of a like number to each syntagmatarchy.
• Two diphalangarchies are a tetraphalangarchy, 1,024 files, 16,384 men, so that in the phalanx as a whole there will be 2 wings, 4 phalangarchies, 8 merarchies, 16 chiliarchies, 32 pentakosiarchies, 64 syntagmatarchies, 128 taxiarchies, 256 tetrarchies, 512 dilochiai, 1,024 files.