[This term][1] is used in a double sense: for [it means] either the place where the phalanx [is] when the number of the men remains the same, or the number itself. Each of these [senses may be distinguished] in two ways, either by files [lochoi] or by ranks [zuga]. [This is] the same as saying by length or by depth. Thus a doubling of men by length occurs whenever we insert [troops] between the already-existing files, or insert others [equal] in number to them, maintaining the length of the phalanx in itself, so that a close order can only arise from the doubling of the men. But [a doubling] by depth [occurs] whenever we insert [troops] between the already-existing ranks or insert others unequal in number, so that a close order can only arise by depth. By length a doubling of the place occurs whenever we change by length the above-mentioned close order into a loose one, or whenever the inserted men counter-march by length; a doubling of the place by depth occurs whenever we change by depth the above-mentioned close order into a loose one, or whenever the inserted men counter-march by depth. Some do not approve of these kinds [of manoeuvres], especially when the enemy is close, but by extending the light-armed infantry and the cavalry on both wings, they obtain the appearance of a doubling without [creating] any confusion in the phalanx.
Search [for information] about this at the end of the book in the [entry] diplasia/sai.[2]