Quadrivium Miscellany with Rithmomachia

...distinct in [length] of the spaces. Upon which, on the other side, let them be arranged up to a tenfold proportion decupla; a 10:1 ratio in every space according to the aforementioned species. From here, the smaller white pieces indeed have proportions named from even numbers: the double original: dupla, such as 4 to 2; the quadruple original: quadrupla, such as 16 to 4; the sextuple original: sescupla, such as 36 to 6; and the octuple original: octupla, such as 64 to 8. Opposite these, of the same kind, let the smaller black pieces be named from odd numbers, having these proportions: the triple original: tripla, such as 9 to 3; the quintuple original: quintupla, such as 25 to 5; the septuple original: septupla, such as 49 to 7; and the nonuple original: nonupla; ninefold, such as 81 to 9. Behind the white pieces, let there be red ones of the superparticular kind superparticularium; a ratio where the greater number contains the lesser plus one unit, like 3:2 or 9:8. These include the sesquialtera (3:2) sesquialtera; literally "one and a half" so that they are [paired] with the doubles; the sesquiquartan (5:4) with the quadruples; the sesquisextan (7:6) with the sextuples; and the sesquioctavan (9:8) with the octuples. And behind the black [pieces], let there be larger white pieces of the same kind [of ratio] in the third? of the thirds; likewise, let there be [joined] to the triples: the sesquiquintan (6:5) to the quintuples; the s...? septiman (8:7) to the septuples; and the sesquinonan (10:9) to the nonuples. Behind the red pieces, let there be larger black pieces of the superpartient kind superpartient; a ratio where the greater number contains the lesser plus more than one unit, such as 5:3, such as the superbipartients (5:3) with the sesquiquartans; the super-six-partients with the sesquisextans; and the super-eight-partients with the sesquioctavans...

namely the first division