In Paradise Lost, what methods does Satan use to tempt Eve to eat the forbidden fruit, and how does Eve's eating of the fruit change both herself and the world?

Satan uses techniques of classical rhetoric, or the art of persuasion, to compel Eve to eat the fruit. Accordingly, his appeal to Eve in book nine precisely follows the Ciceronian arrangement. Satan heeds what Cicero prescribed for the parts of an oration, with certain rhetorical techniques due for each one. The exordium, or introduction, is the opener, the part of the argument that reaches out to seize the attention of the audience. As such, Satan begins his appeal to Eve with flattery to gain her attention:

Fairest resemblance of thy Maker fair, Thee all things living gaze on, all things thine By gift, and thy celestial beauty adore, With ravishment beheld—there best beheld Where universally admired (538–542, book 9)

The next four parts of the oration (narration, division, proof, and refutation) employ logical arguments. For the second part of a classical oration—the narration, where the speaker provides an account of what has happened and the nature of the case—Satan lies to Eve about how he gained the power of speech. Next comes the division, where the speaker outlines what is at stake in the case. Here, Satan forces Eve to acknowledge the existence of the Tree of Knowledge, from which he obtained the fruit, and he addresses her reservations about partaking of the fruit. He thus uses logical arguments in accordance with what Cicero deems fit for this stage of an oration. Following the division comes the main body of the speech, the confirmation, where the speaker offers logical arguments as proof. Thus Satan argues by way of logic here:

if what is evil Be real, why not known, since easier shunned? God, therefore, cannot hurt ye and be just;Not just, not God; not feared then, nor obeyed: Your fear itself of death removes the fear. Why, then, was this forbid? Why but to awe, Why but to keep ye low and ignorant, His worshipers? He knows that in the dayYe eat thereof your eyes, that seem so clear, Yet are but dim, shall perfectly be then Opened and cleared, and ye shall be as Gods, Knowing both good and evil, as they know. (697–710, book 9)

Satan ostensibly delineates an inconsistency in God's commandment. In the conclusion, the speaker ends by employing emotional appeals and summing up previously stated arguments.

These, these and many moreCauses import your need of this fair Fruit.Goddess humane, reach, then, and freely taste! (730–732, book 9)

In eating the fruit, Eve disobeys God's commandment, and she and Adam lose their innocence. From this act, sin was brought into the world and amongst humankind.