The speaker in Andrew Marvell's "To His Coy Mistress" makes three arguments to convince his lady to cavort with him: he is in love with her, time is fleeting, and her beauty will fade.
The first argument the speaker makes is that he does love the woman that he's propositioning. He explains that he would spend tens of thousands of years praising her beauty if he had that much time. There is nothing about her that makes him want to rush. He finds perfection and loveliness in every aspect of her, from her heart to her surface beauty. This is an attempt to flatter and impress her.
Next, he explains that time is fleeting. They will both get old and she will go to her deathbed without tasting the pleasures of love if she isn't willing to move faster. This is an argument designed to convince her that being with him is a limited-time offer. The end is coming but she still has the opportunity to have what he's offering today.
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