Pope Sylvester's Abacus

Recently wrote on "This Day in Math"  about the day that Gerbert became Pope Sylvester II .  Then today I just found a really good Post at Math DL that talks about his mathematics, including his mixture of the Abacus and the use of small discs with arabic numerals.   I clipped the page about his abacus. 

 

Gerbert's Abacus

Gerbert devised a new kind of abacus which one could use to calculate with the Hindu numerals, a flat board with columns drawn on it, corresponding to ones, tens, hundreds, and so forth.  (Some scholars believe he may have been the first person to use the Latin term abacus.)  He had a shield-maker construct small pieces of animal horn with the numerals on them; called apices, the pieces could then be placed on the board to represent numbers.  A zero was not necessary; the absence of a marker in the tens’ place, for instance, meant that there were no tens.  An eleventh-century manuscript found in Limoges illustrates the representation of numbers on such an abacus.  (Note that the numerals had changed slightly in the next hundred years.)


Gerbert compiled a list of rules for computing with his abacus, Regula de Abaco Computi, in which he painstakingly explained how to multiply and divide, as well as add and subtract, in the new system.  A companion work, Liber Abaci, by his student Bernelin, is often included in the collected works of Gerbert; it predates the book of the same name by Fibonacci by two hundred years.