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Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.
The Muqaddimah. An Introduction to History.
Gerbert d'Aurillac and the March of Spain: A Convergence of Cultures
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.
To see an example of how to add numbers using Gerbert’s abacus, click here. [This is a power point animation of the process.]
And for an example of subtraction, click here.