Ben Jonson really loved his classics (the literature of ancient Greece and Rome), and many of his poems show it. "On My First Son" is no exception. First, Jonson considered the poem an epigram—or at least he put it in a collection he called the Epigrams. The epigram was a genre of poetry that the Greeks and Romans invented and popularized (for more on epigrams, see "In a Nutshell").
Still, it isn't enough for smarty-pants Jonson to just call his poem an epigram. He also emphasizes his understanding and knowledge of ancient epigrams by very subtly alluding to the famous Roman epigrammatist Martial. The concluding lines of Jonson's poem—"all his vows be such / As what he loves may never like too much" (11-12)—echo Martial's Epigrams, VI.xxix: "Whatever you love, may you wish not to have been overly pleased by it."