Last two pages of the book King Lear with The Tempest:
There is a similar relation, [to that between Romeo and Juliet and A Midsummer Night’s Dream] based on a common pattern, between the British tragedy of Lear and the Italian comedy. These are the two non-historical plays that deal especially with a succession of Royal Rule. The unwise management of the three parts of the British kingdom by Lear is contrasted with the wise management of the Italian succession by Prospero. The tragic relation of Lear to his daughter, and perhaps his error regarding her marriage, is contrasted with the success of Prospero in securing a happy life for Miranda. The storm scenes, on the land in the center of Lear and at sea in the opening of the Tempest, indicate a treatment of the same theme, of the dissolution of the conventional orders.  The Tempest seems to presuppose the center, and hence the whole of Lear. The conventional kingship of Lear, which in the tragedy comes crashing down,is contrasted with the natural royalty or philosophic statesmanship of wisdom. Ironically, this natural royalty proves in certain ways to be what the flattery of custom told Lear he was as king.
As noted above, there is some parallel between Edgar and Prospero. The Tempest raises the theme of a conflict between brothers to the center of focus. The conflict of two brothers in Lear effects the changes of the kingdom in the main plot only as Edmund rises toward the tyranny, until Edgar, in the decisive duel, prevents Edmund from turning the fall of Lear into a tyranny. As in the Tempest, the victory of the royal nature over tyranny depends on the return of the divested but virtuous character to active rule. Like Prospero,  Edgar returns from his divestment to wear the clothing of his true appearance in the end. Edgar develops through the play from a gullible but true son through a series of disguises He takes on the appearance first of a Bedlam beggar, then ascends to the peasant’s clothes in which he leads his father, to the guise of a sailor or seaman who convinces Gloucester that the madman was a fiend. In this guise he slays Oswald, From here he changes clothing again to the knight who appears armed and defeats Edmund. Having completed the recovery of his position as heir to the earldom, he publicly reveals himself as Edgar. From here he ascends again,as he is invited by Albany to share in the ruling of the “gored state” of Britain. He may come to fulfill the royal nature- a perfection of ethical virtue. [Thomas G.] West compares Edgar with King Henry V, in that these two “redeem the time- exercising kingly rule in imitation of the redemption . His foresight and effectiveness indicate that he is, as Berns writes, the paradigm of virtue in the play.” 
The wise rule of Prospero is based on a discovery of the higher nature, especially a political knowledge of the human souls, by which for example, he separates each of the three groups on the island  and orchestrates the marriage of Ferdinand and Miranda.  It is by this higher nature- the same as that revealed in the Socratic turn, that the philosophic Duke knows how each thing would be best, and works with nature to bring this good about. By this knowledge, Prospero sends Ariel to deceive even the King of Naples intpo believing that he has lost his son as punishment for deposing the Duke of Milan It is on the basis of a similar sort of knowledge that Edgar deceives his already penitent father into believing that the gods have acted not in the punishment but in the preservation of his bodily life.
When Lear sees Edgar in the hovel, he takes the disguised appearance of natural virtue, two or three times removed, to be the thing itself. [Lawrence] Berns writes of Edgar:
The same consummate irony that led him, correctly but for the wrong reasons, to be called the “thing itself,” that is, the natural man, by Lear, may be at work also in his being called “philosopher.”
Berns, Gratuitude, Nature and Piety, p. 51
The royal character who is not a philosopher is also an image of the philosopher (Hamlet II,ii, 260-271). This principle allows for the natural prince in the plot of Lear to reflect the action of Prospero, and the highest argument regarding the most fundamental principles, taken up by the playwright himself. He represents the claim of natural merit, although unlike Edmund, Edgar never uses the word “nature.” These two appeals to nature are two fundamental understandings of self interest or the good, one in basic accord with, but the other rejecting, justice. The other rejects natural right not in the sense of the claim to rule by nature- which it has, based on power- but in the sense of the upright character and what is right among human according to nature. The connection of the character of Edgar to the Shakespearean recovery of natural right is veiled in his being the true claimant to all that Edmund attempts to usurp, both in the appeal from custom to natural virtue and in the appeal to Grace, which Goneril made for him. By being in truth what he is by custom, Edgar demonstrates the natural being which is the cause of the reflection in the custom or law. Edgar is not only a knight, but is also the godson of Lear.  His being the godson of Lear seems to suggest that the symbolic meaning of the ceremonial orders of the old monarchy is continued in, and possibly fulfilled by, the natural virtue of Edgar.
Like the character of Prospero in the Tempest, the character of Edgar may be autobiographical. Like Prospero, the work of Edgar is to prevent his evil brother, here the embodiment of the principle acquisition or power, from seizing rule. The response of Edgar to this potentially horrifying circumstance would be like the practical aspect of the thought of Shakespeare toward his own circumstance, or like the position of philosophy regarding the soul and the ruling opinion of the West. Contrary to the assertion of Howard White in his Copp’d Hills Toward Heaven,, the project of Shakespeare seems to aim more to oppose the principle introduced into the soul of the West by Machiavelli, than it aims to affirm a classical teaching in contrast with Christian custom or Christianity.  One might say that the problem of Prospero is more Antonio than Alonso, and the problem of Edgar more Edmund than Gloucester or Lear.
Unlike Prospero, Edgar does not act to effect the arrangement of royal rule, but acts only to prevent the tyranny of his brother. In this limited governance, the statesmanship of the royal nature is distinguished from the philosophic statesmanship of Prospero, which does address the fundamental orders. The work of philosophy or wisdom inn the political world, as distinct from the magic island,is not literal royal rule, but, as in the care of the American founding fathers, the prevention of tyranny.
6. Paul Cantor. Prospero’s Republic p. 241.
7. John Alvis, John Postscript.” In Shakespreare’s understanding of honor, p. 10 (443).
8. West, Thomas G. Institute colloquium on King Lear, 1986.
9 Lawrence Berns, “Gratitude, Nature and Piety in King Lear,” p. 50.
10. Allan Bloom; “Interpretive Essay” on Plato’s Republic. p. 361
11. Jaffa writes: “According to Plato, the arrangement of marriages is the central mystery of philosophic rule. The arrangement of the marriage between Ferdinand and Miranda is the culmination of the exercise by Prospero of that wisdom he has gained by making the liberal arts “all my study” (“An Interpretation of the Shakespearean Universe,” p. 281).
12. De Alvarez, The Clearing, Class 2; Berns, p. 51, note 68.
13. Alulis, “Wisdom and Fortune: The Education of the Prince in King Lear.”p. 389 note 21.
14. White, Copp’d Hills, p. 65. There is admittedly a sense in which Shakespeare as a writer is classical rather than Christian. Because of the separation of Church and state, American public life and public education cannot turn to Jerusalem in the attempt to address the erosion of the ethical foundation of self government. The secular solution consistent with American liberty might be to set American public life and education on the foundation of Athenian ethical and political philosophy. This can include Shakespeare, who, like Plato and Aristotle,can be common to all. See Bloom, Introduction to Shakespeare’s Politics, pp. 1-12.