Quadrivium Miscellany with Rithmomachia

...the individual denominations, you will multiply them. And from this multiplication, if you have replaced the original pristine? dividends without anything hindering you, you will rejoice that you have acted most correctly.

ON COMPOUND DIVISION WITH DIFFERENCE original: De Composita Divisione cum Differentia. Compound division involves divisors with multiple digits. The "difference method" is a medieval calculation shortcut where one uses the complement of a number relative to ten—for example, the "difference" of 8 is 2—to simplify the movement of counters on the abacus.

Compound division occurs when there are two or more divisors, or one or more dividends. Once the divisors and dividends have been properly placed, place beneath the smallest divisor such a difference so that it can reach the part namely, the divided and the difference at our ten denarius; in this context, the number ten, representing the next vertical column or decimal place on the abacus. For the rest of the divisors—however many there may be except for the greatest one—attach and add differences up to nine nouenarius; the number nine.

And if anywhere an interval of the lines the vertical columns drawn on the abacus board should occur to occur, in that place establish a multiplier for the nine in place of a difference. And if any of the divisors of the should be nine, place no difference for that one. Leave the greatest divisor of all without a difference.

These things having been so placed: if the unit unitas; the number one or a single counter of the greatest divisor has been marked with a character original: caractere; refers to the specific Western Arabic numerals (Apices) used on the Gerbertian abacus, which were still a novelty in the medieval West, for by that same similar? sight another unit comes upon it according to the part of the dividend required for the denomination—whether it be a two or a three...