Quadrivium Miscellany with Rithmomachia

The Numerous Individual Small Parts Placed Beneath

The Rule of Individual Small Fractions original: minutiarū; in medieval mathematics, this refers to fractions or subdivisions of a whole unit, which were essential for precise calculations on the abacus.

throughthrough. if tenthtenth - thirdthird - sicilicussicilicus original: sicemen; likely a corruption of sicilicus, a Roman fractional unit representing 1/48 of a whole - fourthfourth - together
let them be fifths. And when you have withdrawn original: retracteris; this refers to the physical act of moving or placing counters on the abacus board the dividend, you will multiply the difference of the divisor differentia; the "difference" is a medieval division technique where one divides by the difference between the divisor and the next power of ten (e.g., if dividing by 9, the difference is 1), making calculation easier without a modern notation system. by its own quantity.
And whatever results from that same multiplication,
you withdraw again in a similar manner and multiply by that same difference.
And you shall do the same for as long as you are able to relocate the dividends
through the appropriate lines the vertical columns on the abacus board representing decimal places without any obstruction.
Then, the difference having been removed, you will compare the remaining
number with the divisor; and if it is less than the divisor,
know that it remains in that same place.
If it is equal, that [number] being removed, you add a unit
to the previous denominators denominans; here, this refers to the numbers being "named" or recorded in the quotient/result column. If it happens to be greater,
look carefully how many times cunti? it contains the divisor
within itself, and add just as many units to the denominator.
And if there is any remainder, allow it to stay in that place.
These things having been done in this way, whatever you find in the gathered
denominators, you will know more certainly than certain that the quantity
of the divisor was contained in the dividend that many times.
If, however, you doubt that you have done it correctly, [multiply the result] with the divisor itself...