There is a confusing passage in chapter 2 of our Classical Arithmetic text, translated by Thomas Taylor. This confusion is not caused by the subject but by the the history and evolution of the English language.
Taylor says that "One is both impartible and indivisible".
The confusion begins when we look up the word "impartible" in the Oxford English Dictionary, and find it defined as, "indivisible". This, of course, cannot be the meaning, since it is contrasted in our reading with...indivisible!
The second use of "impartible" in the OED must be that of Taylor in our reading, which actually means the opposite! Impartible means "divisible", or "able to divided into parts".
This makes sense of our lesson, which explains that One is both impartible (divisible) and indivisible.
One is impartible in the sense that it is divided, as a body, into parts. One is indivisible, as a number, for there is no number less than one itself. Thus, One is understood to be--in two different senses--divisible an divisible.
No more confusion!
William Michael, Headmaster
Classical Liberal Arts Academy