RITHMIMACHIA original: Rythmomachia; the "Battle of Numbers." The bracketed text in the original is likely a scribal shorthand for the game's title.

...not only from the pyramid, [but] from whichever square it may exist A "Pyramid" is a special composite piece in the game made of several stacked numbers; a "square" refers to the shape of the highest-tier pieces. let him take it the pyramid. In the same way, let it be done from the pure numbers? prepared for the camp... from its base. He who strives for victory, which is otherwise [achieved] on either side by all the movements of the modes from the primary positions of the places. If he should strive in the [opponent’s] camp to create proportions medietates; mathematical "means" or sequences of numbers, both harmonic and arithmetic. Both of these consist of three terms placed in relation to one another: the greatest, the middle, and the least the minimum the lowest?. These must be placed with such diligence that no terms from the opponent's side can interfere. But the first from the terms of the pieces? is placed in the territory of the adversary. In either both part of the forces, he should strive to create an arithmetic [mean] with the pieces. For the harmonic [mean], it is necessary to seek one [piece] from the spoils, so that when the harmonic sequence is in the other part, it is as follows: from the other part let there be a 15, a 20, and a 30; or a 25, 45, and [unclear]; or 25, [unclear], and 15; or 45, 90, and 30, [and] 45 The author is listing sets of numbers that form a Harmonic Mean. In a Harmonic Mean, the ratio of the differences between the terms equals the ratio of the outer terms. For example, in 30, 20, 15: (30-20=10) and (20-15=5). The ratio 10:5 is the same as 30:15 (2:1).. And this is the property of them all: that as the greatest term is to the least, so is the difference of the greatest and middle to the difference of the middle and the minimum.

An arithmetic [mean] is easier to find, and I provide one example: such as 60, 75, 90, [or] 6, 16, [unclear]. The property of these is that the difference between the greatest and the middle is the same as the difference between the middle and the minimum In an Arithmetic Mean, the intervals are equal. For 60, 75, and 90, the difference is exactly 15 between each step..