No. The same active intellect is not in various men because it is impossible that one same power belong to various substances.
Non est idem intellectus agens in diversis hominibus quia non potest esse quod una et eadem virtus numero sit diversarum substantiarum.
If the active intellect is something belonging to the soul, as one of its powers, we are bound to say that there are as many active intellects as there are souls, which are multiplied according to the number of men, as we have said above (Q76, A2).
Si autem intellectus agens sit aliquid animae, ut quaedam virtus ipsius, necesse est dicere quod sint plures intellectus agentes, secundum pluralitatem animarum, quae multiplicantur secundum multiplicationem hominum, ut supra dictum est.
The truth about this question depends on what we have already said (Q79, A4). For if the active intellect were not something belonging to the soul, but were some separate substance, there would be one active intellect for all men. And this is what they mean who hold that there is one active intellect for all.
Veritas huius quaestionis dependet ex praemissis. Si enim intellectus agens non esset aliquid animae, sed esset quaedam substantia separata, unus esset intellectus agens omnium hominum. Et hoc intelligunt qui ponunt unitatem intellectus agentis.
All things which are of one species enjoy in common the action which accompanies the nature of the species, and consequently the power which is the principle of such action; but not so as that power be identical in all. Now to know the first intelligible principles is the action belonging to the human species. Wherefore all men enjoy in common the power which is the principle of this action: and this power is the active intellect.
Omnia quae sunt unius speciei, communicant in actione consequente naturam speciei, et per consequens in virtute, quae est actionis principium, non quod sit eadem numero in omnibus. Cognoscere autem prima intelligibilia est actio consequens speciem humanam. Unde oportet quod omnes homines communicent in virtute quae est principium huius actionis, et haec est virtus intellectus agentis.
But there is no need for it to be identical in all. Yet it must be derived by all from one principle. And thus the possession by all men in common of the first principles proves the unity of the separate intellect, which Plato compares to the sun; but not the unity of the active intellect, which Aristotle compares to light.
Non tamen oportet quod sit eadem numero in omnibus. Oportet tamen quod ab uno principio in omnibus derivetur. Et sic illa communicatio hominum in primis intelligibilibus, demonstrat unitatem intellectus separati, quem Plato comparat soli; non autem unitatem intellectus agentis, quem Aristoteles comparat lumini.
The Philosopher says (De Anima iii, 5) that the active intellect is as a light. But light is not the same in the various things enlightened.
Philosophus dicit, in III de anima, quod intellectus agens est sicut lumen. Non autem est idem lumen in diversis illuminatis.
The active intellect is the cause of the universal, by "abstracting" it from matter. But for this purpose it need not be the same intellect in all intelligent beings; but it must be one in its relationship to all those things from which it "abstracts" the universal, with respect to which things the universal is one. And this befits the active intellect inasmuch as it is immaterial.
Intellectus agens causat universale "abstrahendo" a materia. Ad hoc autem non requiritur quod sit unus in omnibus habentibus intellectum, sed quod sit unus in omnibus secundum habitudinem ad omnia a quibus "abstrahit" universale, respectu quorum universale est unum. Et hoc competit intellectui agenti inquantum est immaterialis.
The Philosopher proves that the active intellect is separate, by the fact that the passive intellect is separate: because, as he says (De Anima iii, 5), "the agent is more noble than the patient."
Philosophus probat intellectum agentem esse separatum, per hoc quod possibilis est separatus; quia, ut ipse dicit, "agens est honorabilius patiente".
Now the passive intellect is said to be separate, because it is not the act of any corporeal organ. And in the same sense the active intellect is also called "separate"; but not as a separate substance.
Intellectus autem possibilis dicitur separatus, quia non est actus alicuius organi corporalis. Et secundum hunc modum etiam intellectus agens dicitur separatus, non quasi sit aliqua substantia separata.