Quadrivium Miscellany with Rithmomachia

& in the fixed arc of the number I never divide

• in that [arc] itself, for the debt of the ten original: deceni; referring to the decimal carry or the remainder needed to reach the next power of ten must be divided; and still from that [value] in whatever higher arc [it is] drawn, in that [place] the arc must be divided for the debt of the ten.
  Afterward, it is drawn from that place and cannot be taken away by the opponent. From each side, many [pieces] are found suitable for all the limits of the arithmeticians. On the other side, however, they find all these by the power of Gerbert original: areberti; referring to Gerbert of Aurillac (c. 946–1003), the scholar-pope who reintroduced the abacus to Europe and refined the game's mathematical basis and D. I. likely an abbreviation for an authority or a specific rule. Let no one think that these [numbers] were born or placed loosely and without order, if he is mindful of these three precepts in which it is certain that every inequality inequalitas; in Boethian arithmetic, this refers to any ratio other than 1:1, such as 2:1 or 3:2 is born from equality equalitas; the ratio of 1:1, considered the "parent" or source of all other numerical relationships. All this and the monad monadic surface original: monadicam superficiem; a geometric representation of the number one, the fundamental unit of the game is created from three units, if only the [first] precept is neglected. He who desires a binary two-fold surface should double the monadic; if ternary three-fold, triple it; if quaternary four-fold, quadruple it; if quinary five-fold, quintuple it; if senary six-fold, sextuple it.

ON MULTIPLICATION AND DIFFERENCE.

Simple division is spoken of with the difference where there is one divisor and one or more dividends. To this divisor, therefore, you should always apply such a difference In medieval abacus calculation, the "difference" was the amount a divisor lacked to reach the next power of ten (e.g., if dividing by 8, the difference is 2) so that, by filling the void of the decimal number original: denarii numerum; the "number of ten", it makes the sum. And you should always pull back the dividend through the appropriate lines the vertical columns or "arcs" on the abacus board to the denomination of those same terms; in this way, once divided, the dividends themselves are paid out to each...