Andrew Marvell's "To His Coy Mistress" is one gentleman's attempt to woo his lover into consummating their relationship—an appeal to the concept of carpe diem (meaning "seize the day"). The girl has clearly said no before, so he takes on several different strategies to convince her.
The first rhetorical strategy is logos. The speaker appeals to the woman's logic by basically telling her they’re not going to live forever. If they did, they’d certainly take their time:
An hundred years should go to praise
Thine eyes, and on thy forehead gaze;
Two hundred to adore each breast,
But thirty thousand to the rest . . .
This is not the only strategy the narrator uses that presents time as their primary antagonist. He also appeals to fear by warning her that she may die without ever having made love:
. . . then worms shall try
That long-preserved virginity . . .
The final stanza provides grand, sweeping statements meant to appeal to her emotion (pathos). He wraps up his argument with the solution to their conflict with time. She needs to give into his pleas in order to truly live, to "at once our time devour."
Marvell doesn't tell us if these strategies were effective in convincing the young lady, but the narrator certainly did give it a rhetorically diverse try.
Marvell's poem persuades by means of ethos, logos, and pathos, and uses luxuriously sensual language to suggest by parallelism that a similar sensuality would be part of a physical as well as the verbal encounter.
The basic logic of the poem is syllogistic. It suggests that were humans immortal, she could delay consummation of their relationship with his enthusiastic collaboration, but humans are not immortal, and thus they should not delay.
He projects an appealing ethos as a lover in the long description of how he would, were they immortal, devote extended attention to each part of her body, suggesting that he is a skilled and attentive lover.
He manages pathetic appeal by using beautiful descriptive language to evoke an image of sensual pleasure that will appeal to her own physical desires.