Proving his beauty by succession thine! (line 12)
This is the goal. Beauty doesn't have to die, but can be passed along like a shiny car to your son. You get the pleasure of looking at it, and you can also say, "Hey, look! That used to be mine, and now it belongs to my son!" Now remember, this poem is being addressed to someone who seems to care a lot about appearances, so it makes sense to boil down all the pleasures of being a parent to one easy-to-swallow package.