Quadrivium Miscellany with Rithmomachia

...if you should doubt that you have done [the calculation correctly], you will be able to prove it by multiplying the denominations original: nominationibus. In this context, denominations refers to the digits of the quotient. by the divisor in the same way as before.

ON COMPOSITE DIVISION OR BY DIFFERENCES.

"Composite division" refers to dividing by numbers with multiple digits. "Differences" (differentiis) refers to a specific medieval abacus technique where divisors are rounded up to the nearest power of ten, and the "difference" is handled separately to simplify the math.

You can also perform composite division without difficulty in the following manner. Therefore, when you have correctly placed the dividends and divisors: if the dividend has a character original: caracterem. These are the physical tokens or "apices" marked with numerals used on the abacus board. larger than the greatest divisor, you should place the divisor on the same line original: linea. These are the vertical columns on the abacus board representing decimal places (units, tens, hundreds, etc.). as that dividend.

But if it is equal to it, or if the divisor has a larger character, it is situated one line before the dividend. Once this is placed, however many other divisors there are, let them follow while maintaining their original order.

When this has been done, you will compare the largest divisor to the dividend. Thus, if it is placed on the same line, it is treated as a single unit to a single unit; if [placed one line before], it is as a single unit to a ten.

line

And so, by comparing, you will give whatever [value] is in the dividend as the whole character of the denomination original: nominationis. This is the resulting quotient digit.. Observing only this: that [you leave] some part of that dividend in which the greatest divisor...