Virtue, then, is a state involving rational choice, consisting in a mean relative to us and determined by reason — the reason, that is, by reference to which the practically wise person would determine it. It is a mean between two vices, one of excess, the other of deficiency. It is a mean also in that some vices fall short of what is right in feelings and actions, and others exceed it, while virtue both attains and chooses the mean.

[ἔστιν ἄρα ἡ ἀρετὴ ἕξις προαιρετική, ἐν μεσότητι οὖσα τῇ πρὸς ἡμᾶς, ὡρισμένῃ λόγῳ καὶ ᾧ ἂν ὁ φρόνιμος ὁρίσειεν. μεσότης δὲ δύο κακιῶν, τῆς μὲν καθ᾽ ὑπερβολὴν τῆς δὲ κατ᾽ ἔλλειψιν: καὶ ἔτι τῷ τὰς μὲν ἐλλείπειν τὰς δ᾽ ὑπερβάλλειν τοῦ δέοντος ἔν τε τοῖς πάθεσι καὶ ἐν ταῖς πράξεσι, τὴν δ᾽ ἀρετὴν τὸ μέσον καὶ εὑρίσκειν καὶ αἱρεῖσθαι.]

Aristotle (384-322 BC) Greek philosopher

Nicomachean Ethics [Ἠθικὰ Νικομάχεια], Book 2, ch. 5 (2.6.15-16) / 1106b.35 (c. 325 BC) [tr. Crisp (2000)]
    (Source)

(Source (Greek)). Alternate translations:

Virtue then is “a state apt to exercise deliberate choice, being in the relative mean, determined by reason, and as the man of practical wisdom would determine.” It is a middle state between too faulty ones, in the way of excess on one side and of defect on the other: and it is so moreover, because the faulty states on one side fall short of, and those on the other exceed, what is right, both in the case of the feelings and the actions; but Virtue finds, and when found adopts, the mean.
[tr. Chase (1847)]

Moral virtue, then, is a certain formed state, or habit of purpose, which conforms to the relative mean in action, and which is determined to that mean by reason, or as the prudent man would determine it. And it is the mean between two vices, one of which consists in excess, and the other in defect. So that vices sometimes fall short of what is right in our emotions and in our actions, and sometimes exceed it, while virtue fines the mean and chooses it.
[tr. Williams (1869)]

Virtue then is a state of deliberate moral purpose consisting in a mean that is relative to ourselves, the mean being determined by reason, or as a prudent man would determine it. It is a mean state firstly as lying between two vices, the vice of excess on the one hand, and the vice of deficiency on the other, and secondly because, whereas vices either fall short of or go beyond what is proper in the emotions and actions, virtue not only discovers but embraces the mean.
[tr. Welldon (1892)]

Virtue, then, is a habit or trained faculty of choice, the characteristic of which lies in moderation or observance of the mean relatively to the persons concerned, as determined by reason, i.e. by the reason by which the prudent man would determine it. And it is a moderation, firstly, inasmuch as it comes in the middle or mean between two vices, one on the side of excess, the other on the side of defect; and, secondly, inasmuch as, while these vices fall short of or exceed the due measure in feeling and in action, it finds and chooses the mean, middling, or moderate amount.
[tr. Peters (1893)]

Virtue, then, is a state of character concerned with choice, lying in a mean, i.e. the mean relative to us, this being determined by a rational principle, and by that principle by which the man of practical wisdom would determine it. Now it is a mean between two vices, that which depends on excess and that which depends on defect; and again it is a mean because the vices respectively fall short of or exceed what is right in both passions and actions, while virtue both finds and chooses that which is intermediate.
[tr. Ross (1908)]

Virtue then is a settled disposition of the mind determining the choice of actions and emotions, consisting essentially in the observance of the mean relative to us, this being determined by principle, that is, as the prudent man would determine it. And it is a mean state between two vices, one of excess and one of defect. Furthermore, it is a mean state in that whereas the vices either fall short of or exceed what is right in feelings and in actions, virtue ascertains and adopts the mean.
[tr. Rackham (1934)]

Virtue, then, is a deliberately choosing state, which is in a medial condition in relation to us, one defined by a reason and the one by which a practically-wise person would define it. Also, it is a medial condition between two vices, one of excess and the other of deficiency. Further, it is also such a condition because some vices are deficient in relation to what the relevant feelings and actions should be and other are excessive, but virtue both finds the mean and chooses it.
[tr. Reeve (1948)]

[Ethical] virtue, then, is a habit, disposed toward action by deliberate choice, being at the mean relative to us, and defined by reason and as a prudent man would define it. It is a mean between two vices, one by excess and the other by deficiency; and while some of the vices exceed while the others are deficient in what is right in feelings and actions, virtue finds and chooses the mean.
[tr. Apostle (1975)]

So virtue is a purposive disposition, lying in a mean that is relative to us and determined by a rational principle, and by that which a prudent man would use to determine it. It is a mean between two kinds of vice, one of excess and the other of deficiency; and also for this reason, that whereas these vices fall short of or exceed the right measure in both feelings and actions, virtue discovers the mean and chooses it.
[tr. Thomson/Tredennick (1976)]

Virtue, therefore, is a characteristic marked by choice, residing in the mean relative to us, a characteristic defined by reason and as the prudent person would define it. Virtue is also a mean with respect to two vices, the one vice related to excess, the other to deficiency; and further, it is a mean because some vices fall short of and others exceed what should be the case in both passions and actions, whereas virtue discovers and chooses the middle term.
[tr. Bartlett/Collins (2011)]