[The mean is] what participates in what is equal.[1]
For the excesses and defects, in being opposite each other, in moral virtues are [ranged] under the vice. By contrast, virtues, in being their means, are [ranged] under another genus, for [they are ranged] under virtue. Or because this happens [sc. to be so] not only to these means, but also to the opposite [states] of each extremity. For [it derives] from what is big and small, the one being in excess, and the other in defect, and what is intermediate to them, the equal, is [ranged] under the same genus. So what is of that sort according to the blending of extremities is a mean in the strict sense; and it must be under the same genus as the extremities. Virtue, however, is not a mean between evils; for 'mean' is said homonymously; for even in the circle the center is called 'mean'; but also a mean is the one underlying the limits and the one which is predicated of it or, in general, the [mean][2] that is assumed twice in the combination of premises.[3] And in such cases it is called 'mean' when both [premises] participate in the extremities; for the mean contains the cause for the thesis, the blending and the mixture of the state in all the cases.
Homer [writes]: "decide in the middle between both of us" It does not imply coming into the middle, but decide impartially, and do not indulge either him or me. This is why he also adds: "do not help [any part]".[4]
"But myself I am held in the mean." Meaning I am defeated. From a metaphor of athletes taking the middle [places].[5]
"A mean and a measure cannot become more and less. But since excess and deficiency go toward an infinite, this is why they used to call them an indefinite dyad."[6]