"OF VANITY"
This drawing seems to illustrate some lines that Montaigne quotes from Horace (Odes I, 35), describing the recurrent times of civil strife that plagued Rome:
By brothers blows, by brothers' blood
Our souls are gashed and stained.
Alas! What horror have we fled?
What crime not wrought? When hath the dread
Of heaven our youth restrained?
Where is the altar unprofaned
By them? (Jacob Zeitlin translation, p. 162-163)
Montaigne was writing in the midst of France's Wars of Religion, not long after the terrible St. Bartholomew's Day massacre. Likewise Dali had seen--from a distance, to be sure--his own Catalonia plunged into civil war.
Shakespeare's England had of course seen its own civil war in the War of the Roses, described in his history plays. Here is an example of Shakespeare's similar treatment of the theme. One man comes on stage with the body of another whom he has just slain, his face covered by a visor. The King, Henry VI, is looking on in the background, unobserved.
SON. Who's this? O God! it is my father's face,
Whom in this conflict I unwares have kill'd.
O heavy times, begetting such events!
From London by the King was I press'd forth;
My father, being the Earl of Warwick's man,
Came on the part of York, press'd by his master;
And I, who at his hands receiv'd my life,
Have by my hands of life bereaved him.
Pardon me, God, I knew not what I did!
And pardon, father, for I knew not thee!
My tears shall wipe away these bloody marks;
And no more words til they have flow'd their fill.
KING HENRY. O piteous spectacle! O bloody times!
While lions war and battle for their dens,
Poor harmless lambs abide their enmity.
Weep, wretched man, I'll aid thee tear for tear;
And let our hearts and eyes, like civil war,
Be blind with tears, and break o'ercharged with grief. (III Henry VI 2.5.61f.)
Montaigne was not for civil war, but he also did not ignore the underlying issues, in his time, freedom of worship. He was a close adviser to Henry of Navarre, who eventually became Henry IV of France and ruled France through a brief period of religious tolerance.
Later in the same essay we come upon this drawing of Dali's:

Here Dali is depicting the mood of the text that surrounds it, in which Montaigne describes his feelings when visiting Rome:
Finding myself of no use to this age I throw myself back upon that other; and am so enamored of it, that the free, just, and flourishing state of ancient Rome (for neither love it in its birth nor its old age) interests me to a degree of passion; and therefore I cannot so often visit the places of their streets and houses and those ruins profound as the Antipodes, that it does not always put me into the dumps...I ruminate those great names between my teeth, and make them ring in my ears. Of things that are in some part great and admirable, I admire even the common parts; I could wish to see them talk, walk and sup... (p. 369).
Shakespeare obliges him with his Roman plays, where these great figures do indeed “walk, talk, and sup,” and who, as Montaigne concludes, “by their example, give us so many good instructions, knew we how to follow them” (p. 369).
Montaigne emphasizes that almost nothing remained of the ancient city. New palaces were simply built over the rubble of the old. The palace in the background is new; only the headless statue is of the past.
"OF PHYSIOGNOMY"
Montaigne describes his thought in the midst of civil war, subject not only to the two sides but also to those who would take advantage of the general lawlessness. And he was a Catholic in a region dominated by Protestants. Montaigne ponders his situation:
I was already considering to whom, among my friends, I might commit a helpless and decrepit age; and having turned my eyes quite round, I found myself bare. ..At last I saw that it was safest for me to trust to myself in my necessity; and if it should so fall out, that I should be but upon cold terms in fortune's favor, I should so much the more pressingly recommend me to my own, and attach myself and look to myself all the more closely...( p. 384f.)
So it is that Dali illustrates this movement of turning one's eyes "quite round," and finding oneself "bare"--all except for one's virtues or vices, which were conventionally represented by the planets.
In such times as his, when everyone sees himself on the brink of total ruin,” one must “have his courage supplied with the strongest and most vigorous provisions” (p. 385). And more than just this one virtue is required. Montaigne gives examples from his own life.
One time, during the Wars of Religion, a Protestant neighbor asked for refuge in his house, for him and whoever of his men survived, to escape some enemies on the road. Montaigne obliged. Then bit by bit others came, and Montaigne began to wonder if perhaps the whole thing was a ruse. But he decided that since he began by being courteous, he would continue that way, because "I could not disengage myself from them without spoiling all" (p. 400). So he continued in as kind a manner as he had started. The result was that the chief of the men simply had them all ride away. Later the neighbor said that Montaigne's "countenance and frankness had snatched the treachery out of his hands" (p. 400).
Thus it is a combination of virtues, especially an air of innocence and good-will, and not just courage, that saved him.
However, for Montaigne it was not only that. He observes:
I am, moreover, .a man who willingly commit myself to Fortune, and throw myself headlong into her arms, I have hitherto found more reason to applaud than to blame myself for so doing, having ever found her more discreet about, and a greater friend to my affairs, than I am myself. There are some actions in my life whereof the conduct may justly be called difficult or, if you please, prudent; of these, supposing the third part to have been my own, doubtless the other two-thirds were absolutely hers. We make, methinks, a mistake, in that we do not enough trust to heaven with out affairs, and pretend to more from our own conduct than appertains to us; and therefore it is that our designs so often miscarry. Heaven is jealous of the extent that we attribute to the right of human prudence above its own, and cuts it all the shorter by how much the more we amplify it. (p. 400)

And so Dali illustrates these words with a friar bowing to heaven. We have to treat Heaven in the same non-threatening way that we would treat a political superior to whom we are beholden.
This is of course something he has said before, and which Shakespeare had Hamlet notice as well, in his comment that "There's a divinity shapes our ends." But our own humility in relation to this divinity also matters.
Montaigne's image here does capture some of the sense of this passage. But he would probably have disliked the saintly get-up; he has already, in “Of Cannibals,” decried the cruelty justified in the name of religion; And in “On Experience” he comments, “There are two things I have always observed to be in singular accord: supercelestial thoughts and subterranean conduct” (Frame translation, p. 856). Montaigne’s generic image of appropriate behavior is that of the common peasant, who submits to what comes but keeps his common sense.
Montaigne goes on to give another example in the same vein. Again the chief of the pillagers changes his mind, by the courage by which the author conducted himself. For example, he had freely declared his Catholic faith to this Protestant. And in particular it was the way these qualities showed on his face--hence the essay's title, "On Physiognomy." His face and manner showed courage but no haughtiness, which the pillager might have wanted to lay low. Montaigne observes:
If my face did not answer for me, if men did not read in my eyes and in my voice the innocence of my intention, I had not lived so long without quarrels and without giving offense, seeing the indiscreet liberty I take to say, right or wrong, whatsoever comes into my head, and to judge rashly of things. (p. 402)
Rashness, of course, is the excess of courage. As the owner of an isolated chateau, and for a time Mayor of Bordeaux, Montaigne was often required to make snap decisions on insufficient knowledge. Rashness was a necessity.
Perhaps not coincidentally, Hamlet makes a similar endorsement of rashness, recounting to his friend Horatio what occurred on the sea voyage to England that his uncle had forced upon him:
…Rashly--
And praised by rashness for it: let us know
Our indiscretion sometimes serves us well…
--Up from my cabin,
My sea-gown scarf’d about me, in the dark,
Grop’d I to find out them, had my desire… (5.2.6)
Hamlet rashly rifled the pockets of his traveling companions in the night. What he found was a letter from his uncle to the King of England, sealed with the King’s own seal. Hamlet broke the seal and read the letter, written in his uncle’s hand: it was an order to execute him, in lieu of the customary tribute money. If Hamlet had thought about what he was doing, he probably wouldn’t have dared to do it. But “there’s a divinity that shapes our ends.” Hamlet had learned the same "fair" handwriting as his uncle, and even had with him his father's seal, identical to the one his uncle now used. The forgery of a new letter was easily accomplished.
In Montaigne’s case, God protected the innocent. In addition, for Montaigne, the virtues of goodwill, straightforwardness, charitableness, and humility tended to inspire the same in others.
Here Shakespeare might have added qualifiers. It depends upon one's opponents. Do they feel themselves free to honor such qualities? Or do they feel themselves bound to suspect treason and danger even in the kindest of faces? I am thinking of England's Henry VIII beheading Sir Thomas More; or his contemporary, Emperor Charles IV, burning countless Protestants at the stake, regardless of their humility and goodwill. Had Montaigne been an ordinary Protestant in the hands of renegade members of the Catholic League, would his virtues have helped? The same question would arise if he were someone accused of witchcraft by either Protestants or Catholics. People's hearts are often hardened by what seems to them to threaten the basic structure of their society. Hamlet, once set on betraying and killing his king, was in the same predicament.
Montaigne knows full well about such situations. The point is, to the extent one is able, to prevent them from occurring, so that people are not so threatened, even if one has to hide one's fears, suspicions, and even knowledge of others' plots in order to do so. That is what Montaigne does in his first example, hiding his suspicions about his neighbor's true intent and continuing to act with good will. That is what Hamlet learns too late.