Okay, I collected quotes from his notebooks. Obviously these are translated from 1400s/1500s era Italian, so they will likely sound a bit odd. I assigned possible functions or combinations thereof that I hypothetically consider apparent in each statement.
No one statement should be taken in isolation to mean anything conclusive about his type. I also realize other types/quadras will share some of these same sentiments expressed by Da Vinci. But the point here is to look at the overall gestalt that emerges from everything he says, from which I think it can be derived that Ni-ENTj is clearly his type.

“Experience does not err; only your judgments err by expecting from her what is not in her power. Men wrongly complain of Experience; with great abuse they accuse her of leading them astray but they set Experience aside, turning from it with complaints as to our ignorance causing us to be carried away by vain and foolish desires to promise ourselves, in her name, things that are not in her power; saying that she is fallacious. Men are unjust in complaining of innocent Experience, constantly accusing her of error and of false evidence.”

“Experience, the interpreter between formative nature and the human race, teaches how that nature acts among mortals; and being constrained by necessity cannot act otherwise than as reason, which is its helm, requires her to act.”

“Although nature commences with reason and ends in experience it is necessary for us to do the opposite, that is to commence with experience and from this to proceed to investigate the reason.”

“The acquisition of any knowledge is always of use to the intellect, because it may thus drive out useless things and retain the good. For nothing can be loved or hated unless it is first known.”

“Weight, force and casual impulse, together with resistance, are the four external powers in which all the visible actions of mortals have their being and their end.”

“There is no certainty in sciences where one of the mathematical sciences cannot be applied, or which are not in relation with these mathematics.”

“Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.”

“Many will think they may reasonably blame me by alleging that my proofs are opposed to the authority of certain men held in the highest reverence by their inexperienced judgments; not considering that my works are the issue of pure and simple experience, who is the one true mistress. These rules are sufficient to enable you to know the true from the false—and this aids men to look only for things that are possible and with due moderation—and not to wrap yourself in ignorance, a thing which can have no good result, so that in despair you would give yourself up to melancholy.”

/

“Necessity is the theme and the inventress, the eternal curb and law of nature.”

/

“Though human ingenuity may make various inventions which, by the help of various machines answering the same end, it will never devise any inventions more beautiful, nor more simple, nor more to the purpose than Nature does; because in her inventions nothing is wanting, and nothing is superfluous, and she needs no counterpoise when she makes limbs proper for motion in the bodies of animals.”

/

“Those who fall in love with practice without theory are like a sailor who enters a ship without a helm or a compass, and who never can be certain whither he is going.”

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“The senses are of the earth; Reason, stands apart in contemplation.”

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“Science is the observation of things possible, whether present or past; prescience is the knowledge of things which may come to pass, though but slowly.”

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“O time, swift robber of all created things, how many kings, how many nations hast thou undone, and how many changes of states and of various events have happened since the wondrous forms of this fish perished here in this cavernous and winding recess. Now destroyed by time thou liest patiently in this confined space with bones stripped and bare; serving as a support and prop for the superimposed mountain.”

“Nature is full of infinite causes that have never occurred in experience.”

“Why does the eye see a thing more clearly in dreams than the imagination when awake?”

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“All our knowledge has its origins in our perceptions.”

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“Beyond a doubt truth bears the same relation to falsehood as light to darkness; and this truth is in itself so excellent that, even when it dwells on humble and lowly matters, it is still infinitely above uncertainty and lies, disguised in high and lofty discourses; because in our minds, even if lying should be their fifth element, this does not prevent that the truth of things is the chief nutriment of superior intellects, though not of wandering wits.”

/

“When the thing taken into union is perfectly adapted to that which receives it, the result is delight and pleasure and satisfaction.”

“Iron rusts from disuse; water loses its purity from stagnation... even so does inaction sap the vigor of the mind.”

“The lion is never afraid, but rather fights with a bold spirit and savage onslaught against a multitude of hunters, always seeking to injure the first that injures him.”

“Obstacles cannot crush me. Every obstacle yields to stern resolve. He who is fixed to a star does not change his mind.”

/

“It's easier to resist at the beginning than at the end.”

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“If any man could have discovered the utmost powers of the cannon, in all its various forms and have given such a secret to the Romans, with what rapidity would they have conquered every country and have vanquished every army, and what reward could have been great enough for such a service! Archimedes indeed, although he had greatly damaged the Romans in the siege of Syracuse, nevertheless did not fail of being offered great rewards from these very Romans; and when Syracuse was taken, diligent search was made for Archimedes; and he being found dead greater lamentation was made for him by the Senate and people of Rome than if they had lost all their army.”

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“Every action needs to be prompted by a motive. To know and to will are two operations of the human mind. Discerning, judging, deliberating are acts of the human mind.”

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“Any one who in discussion relies upon authority uses, not his understanding, but rather his memory. Good culture is born of a good disposition; and since the cause is more to be praised than the effect, I will rather praise a good disposition without culture, than good culture without the disposition.”

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“The greatest deception men suffer is from their own opinions.”

/

“You can have no dominion greater or less than that over yourself.”

“Man has much power of discourse which for the most part is vain and false; animals have but little, but it is useful and true, and a small truth is better than a great lie.”

“Many have made a trade of delusions and false miracles, deceiving the stupid multitude.”

“To lie is so vile, that even if it were in speaking well of godly things it would take off something from God's grace; and Truth is so excellent, that if it praises but small things they become noble.”

“It is ill to praise, and worse to reprimand in matters that you do not understand.”

“The lover is moved by the beloved object as the senses are by sensual objects; and they unite and become one and the same thing. The work is the first thing born of this union; if the thing loved is base the lover becomes base.”

“To speak well of a base man is much the same as speaking ill of a good man.”

“Men out of fear will cling to the thing they most fear.”

“He who offends others, does not secure himself.”

/

“Justice requires power, insight, and will.”

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“He who does not punish evil commands it to be done.”

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“Nothing strengthens authority so much as silence.”

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“It is easier to contend with evil at the first than at the last.”

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“Ask counsel of him who rules himself well.”

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“Where the spirit does not work with the hand, there is no art.”

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“Just as eating against one's will is injurious to health, so study without a liking for it spoils the memory, and it retains nothing it takes in.”

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“Patience serves us against insults precisely as clothes do against the cold. For if you multiply your garments as the cold increases, that cold cannot hurt you; in the same way increase your patience under great offences, and they cannot hurt your feelings.”

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“Our life is made by the death of others.”

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“Though I may not, like them, be able to quote other authors, I shall rely on that which is much greater and more worthy—on experience, the mistress of their Masters. They go about puffed up and pompous, dressed and decorated with [the fruits], not of their own labours, but of those of others. And they will not allow me my own. They will scorn me as an inventor; but how much more might they—who are not inventors but vaunters and declaimers of the works of others—be blamed.”

/

“Oh! human stupidity, do you not perceive that, though you have been with yourself all your life, you are not yet aware of the thing you possess most of, that is of your folly? and then, with the crowd of sophists, you deceive yourselves and others, despising the mathematical sciences, in which truth dwells and the knowledge of the things included in them. And then you occupy yourself with miracles, and write that you possess information of those things of which the human mind is incapable and which cannot be proved by any instance from nature. And you fancy you have wrought miracles when you spoil a work of some speculative mind, and do not perceive that you are falling into the same error as that of a man who strips a tree of the ornament of its branches covered with leaves mingled with the scented blossoms or fruit.”
These passages relate to Da Vinci's views on drawing/painting and geometry.

/

“The smallest natural point is larger than all mathematical points, and this is proved because the natural point has continuity, and any thing that is continuous is infinitely divisible; but the mathematical point is indivisible because it has no size.”

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“The line has in itself neither matter nor substance and may rather be called an imaginary idea than a real object; and this being its nature it occupies no space. Therefore an infinite number of lines may be conceived of as intersecting each other at a point, which has no dimensions and is only of the thickness (if thickness it may be called) of one single line.”

/

“All bodies together, and each by itself, give off to the surrounding air an infinite number of images which are all-pervading and each complete, each conveying the nature, colour and form of the body which produces it.”

“All objects project their whole image and likeness, diffused and mingled in the whole of the atmosphere, opposite to themselves. The image of every point of the bodily surface, exists in every part of the atmosphere. All the images of the objects are in every part of the atmosphere.”

“Shadow is not the absence of light, merely the obstruction of the luminous rays by an opaque body. Shadow is of the nature of darkness. Light is of the nature of a luminous body; one conceals and the other reveals. They are always associated and inseparable from all objects. But shadow is a more powerful agent than light, for it can impede and entirely deprive bodies of their light, while light can never entirely expel shadow from a body, that is from an opaque body.”

? “A shadow may be infinitely dark, and also of infinite degrees of absence of darkness. The beginnings and ends of shadow lie between the light and darkness and may be infinitely diminished and infinitely increased. Shadow is the means by which bodies display their form. The forms of bodies could not be understood in detail but for shadow.”

“Perspective is nothing more than a rational demonstration applied to the consideration of how objects in front of the eye transmit their image to it, by means of a pyramid of lines. The Pyramid is the name I apply to the lines which, starting from the surface and edges of each object, converge from a distance and meet in a single point.”

“Represent your figures in such action as may be fitted to express what purpose is in the mind of each; otherwise your art will not be admirable.”

/

“The motions of men must be such as suggest their dignity or their baseness.”

? “Many are they who have a taste and love for drawing, but no talent; and this will be discernible in boys who are not diligent and never finish their drawings with shading.”

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“The painter who draws merely by practice and by eye, without any reason, is like a mirror which copies every thing placed in front of it without being conscious of their existence.”

“These rules will enable you to have a free and sound judgment; since good judgment is born of clear understanding, and a clear understanding comes of reasons derived from sound rules, and sound rules are the issue of sound experience—the common mother of all the sciences and arts. Hence, bearing in mind the precepts of my rules, you will be able, merely by your amended judgment, to criticise and recognise every thing that is out of proportion in a work, whether in the perspective or in the figures or any thing else.”

/

“The eye, which is called the window of the soul, is the principal means by which the central sense can most completely and abundantly appreciate the infinite works of nature; and the ear is the second, which acquires dignity by hearing of the things the eye has seen. If you, historians, or poets, or mathematicians had not seen things with your eyes you could not report of them in writing. And if you, O poet, tell a story with your pen, the painter with his brush can tell it more easily, with simpler completeness and less tedious to be understood. And if you call painting dumb poetry, the painter may call poetry blind painting. Now which is the worse defect? to be blind or dumb? Though the poet is as free as the painter in the invention of his fictions they are not so satisfactory to men as paintings; for, though poetry is able to describe forms, actions and places in words, the painter deals with the actual similitude of the forms, in order to represent them. Now tell me which is the nearer to the actual man: the name of man or the image of the man. The name of man differs in different countries, but his form is never changed but by death.”

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“O Man, who will discern in this work of mine the wonderful works of Nature, if you think it would be a criminal thing to destroy it, reflect how much more criminal it is to take the life of a man; and if this, his external form, appears to thee marvellously constructed, remember that it is nothing as compared with the soul that dwells in that structure; for that indeed, be it what it may, is a thing divine. Leave it then to dwell in His work at His good will and pleasure, and let not your rage or malice destroy a life—for indeed, he who does not value it, does not himself deserve it.”
“Some of the evil of my tale may have been inherent in our circumstances. For years we lived anyhow with one another in the naked desert, under the indifferent heaven. By day the hot sun fermented us; and we were dizzied by the beating wind. At night we were stained by dew, and shamed into pettiness by the innumerable silences of stars. We were a self-centered army without parade or gesture, devoted to freedom, the second of man's creeds, a purpose so ravenous that it devoured all our strength, a hope so transcendent that our earlier ambitions faded in its glare.” —T.E. Lawrence