Farewell, thou child of my right hand, and joy (1)
The speaker's language—"child of my right hand"—implies that the son has been created by the speaker's hand, almost as if he were a work of art and not a real person. If he's not a real person, then his death isn't as tragic as it otherwise might be. This type of language anticipates the concluding lines of the poem, where the speaker calls his son his "best piece of poetry" (10).
"[…] Here doth lieBen Jonson his best piece of poetry," (9-10)
The speaker compares his son to a "piece of poetry." If his son is a work of art, then he will never really die. Works of art live on forever, for the most part (the famous Roman poet Horace once said "Ars longa, vita brevis," which is Latin for "art is long, life is short"). Thinking about things as works of art is a way of thinking about their deaths in a different way.
"For whose sake, henceforth, all his vows be suchAs what he loves may never like too much." (11-12)
The speaker alludes to the famous Roman epigrammatist Martial here. By referring to a poet that lived and wrote more than 1500 years before him, the speaker further emphasizes the ways in which works of art live for a really long time. He also positions himself in a long and distinguished tradition of poetry. Really, he is boasting in a way.