No. Neither actually nor habitually can our intellect know the infinite, but only potentially, because the nature of our mind is to know species abstracted from phantasms.
Nec actu nec habitu intellectus noster potest cognoscere infinita, sed in potentia tantum, quia intellectus noster natus est cognoscere species per abstractionem a phantasmatibus.
Therefore it cannot know actually or habitually species of numbers or figures that are not in the imagination, except in a general way and in their universal principles; and this is to know them potentially and confusedly.
Et ideo illas species numerorum et figurarum quas quis non est imaginatus, non potest cognoscere nec actu nec habitu, nisi forte in genere et in principiis universalibus; quod est cognoscere in potentia et confuse.
As we have said above (Q7, A1), God is called infinite, because He is a form unlimited by matter; whereas in material things, the term 'infinite' is applied to that which is deprived of any formal term. And form being known in itself, whereas matter cannot be known without form, it follows that the material infinite is in itself unknowable.
Sicut supra dictum est, Deus dicitur infinitus sicut forma quae non est terminata per aliquam materiam, in rebus autem materialibus aliquid dicitur infinitum per privationem formalis terminationis. Et quia forma secundum se nota est, materia autem sine forma ignota, inde est quod infinitum materiale est secundum se ignotum.
But the formal infinite, God, is of Himself known; but He is unknown to us by reason of our feeble intellect, which in its present state has a natural aptitude for material objects only. Therefore we cannot know God in our present life except through material effects. In the future life this defect of intellect will be removed by the state of glory, when we shall be able to see the Essence of God Himself, but without being able to comprehend Him.
Infinitum autem formale, quod est Deus, est secundum se notum, ignotum autem quoad nos, propter defectum intellectus nostri, qui secundum statum praesentis vitae habet naturalem aptitudinem ad materialia cognoscenda. Et ideo in praesenti Deum cognoscere non possumus nisi per materiales effectus. In futuro autem tolletur defectus intellectus nostri per gloriam, et tunc ipsum Deum in sua essentia videre poterimus, tamen absque comprehensione.
As our intellect is infinite in power, so does it know the infinite. For its power is indeed infinite inasmuch as it is not terminated by corporeal matter. Moreover it can know the universal, which is abstracted from individual matter, and which consequently is not limited to one individual, but, considered in itself, extends to an infinite number of individuals.
Sicut intellectus noster est infinitus virtute, ita infinitum cognoscit. Est enim virtus eius infinita, secundum quod non terminatur per materiam corporalem. Et est cognoscitivus universalis, quod est abstractum a materia individuali, et per consequens non finitur ad aliquod individuum, sed, quantum est de se, ad infinita individua se extendit.
The intelligible species enter into our intellect successively; since many things cannot be actually understood at the same time: and therefore there must be a definite and not an infinite number of species in our intellect.
Sed species intelligibiles ingrediuntur intellectum nostrum successive, quia non multa simul actu intelliguntur. Et ideo oportet numeratas, et non infinitas species esse in intellectu nostro.
Now in material things the infinite does not exist actually, but only potentially, in the sense of one succeeding another, as is said Phys. iii, 6. Therefore infinity is potentially in our mind through its considering successively one thing after another: because never does our intellect understand so many things, that it cannot understand more.
In rebus autem materialibus non invenitur infinitum in actu, sed solum in potentia, secundum quod unum succedit alteri, ut dicitur in III Physic. Et ideo in intellectu nostro invenitur infinitum in potentia, in accipiendo scilicet unum post aliud, quia nunquam intellectus noster tot intelligit, quin possit plura intelligere.
On the other hand, our intellect cannot understand the infinite either actually or habitually. Not actually, for our intellect cannot know actually at the same time, except what it knows through one species. But the infinite is not represented by one species, for if it were it would be something whole and complete.
Actu autem vel habitu non potest cognoscere infinita intellectus noster. Actu quidem non, quia intellectus noster non potest simul actu cognoscere nisi quod per unam speciem cognoscit. Infinitum autem non habet unam speciem, alioquin haberet rationem totius et perfecti.
Consequently it cannot be understood except by a successive consideration of one part after another, as is clear from its definition (Phys. iii, 6): for the infinite is that "from which, however much we may take, there always remains something to be taken." Thus the infinite could not be known actually, unless all its parts were counted: which is impossible.
Et ideo non potest intelligi nisi accipiendo partem post partem, ut ex eius definitione patet in III Physic., est enim infinitum cuius quantitatem accipientibus semper est aliquid extra accipere, et sic infinitum cognosci non posset actu, nisi omnes partes eius numerarentur, quod est impossibile.
For the same reason we cannot have habitual knowledge of the infinite: because in us habitual knowledge results from actual consideration: since by understanding we acquire knowledge, as is said Ethic. ii, 1.
Et eadem ratione non possumus intelligere infinita in habitu. In nobis enim habitualis cognitio causatur ex actuali consideratione, intelligendo enim efficimur scientes, ut dicitur in II Ethic.
Wherefore it would not be possible for us to have a habit of an infinity of things distinctly known, unless we had already considered the entire infinity thereof, counting them according to the succession of our knowledge: which is impossible.
Unde non possemus habere habitum infinitorum secundum distinctam cognitionem, nisi consideravissemus omnia infinita, numerando ea secundum cognitionis successionem, quod est impossibile.