A commentary to Plato’s Charmaides by unknown scholar describes
a clear distinction between ideal natural numbers and numbers
used for mundane everyday counting: Logistic is the science that
treats of numbered objects, not of numbers; it does not consider
number in the true sense, but it works with 1 as unit and the
numbered object as number, e.g. it regards 3 as a triad and 10
as a decad, and applies the theorems of arithmetic to such
cases. It is, then, logistic which treats on the one hand the
problem called by Archimedes the cattle-problem, and on the
other hand melite and phialite numbers, the latter appertaining
to bowls, the former to flocks; in other types of problem too it
has regard to the number of sensible bodies, treating them as
absolute. Its subject-matter is everything that is numbered; its
branches include the so-called Greek and Egyptian methods in
multiplications and divisions, as well as the addition and
splitting up of fractions, whereby it explores the secrets
lurking in the subject-matt