"was simply founded upon external beauty
the false image of corporal generation
for it could not ground this love upon the soul"
What is a more familiar phrase for corporal generation?
The example comes from the following passage in the essay Of Friendship, by Michel de Montaigne (1533-1592), as translated into English by William Hazlitt in about 1812,† revising an earlier English translation by Charles Cotton in 1686:
"For what is the love of friendship? Why does no one love a deformed youth or a comely old man?" [That was a quotation from Cicero.] The very picture that the Academy presents of [pederasty in Ancient Greece] will not, as I conceive, contradict me when I say that the first fury inspired by the son of Venus, in the heart of the lover, upon the sight of blooming youth, to which they allow all the insolent and passionate efforts that an immoderate ardour can produce, was simply founded upon an external beauty, the false image of corporal generation; for upon the soul it could not ground this love, the sight of which, as yet, lay concealed, but was now springing up, and not of maturity to blossom.
In simpler language, the very long sentence means: The erotic love of an older man for a teenage boy in ancient Greece was based only on the youth's external, visible beauty, not on his soul. Montaigne calls it a "false image of corporal generation" because it's based on sexual attraction but it doesn't produce children.
"Corporal" is an adjective for "the body". (The corresponding noun is "corpus".) "Generation" in this context means "coming into existence". "Corporal generation" means the biological process of reproduction and growth: how a new living being comes into existence. Corporal generation (génération corporelle in Montaigne's original French) was examined by Aristotle in ancient times. Modern science has an explanation, but back then it was mysterious: How does an interaction between the parents cause an entirely new living thing to come into existence, with a soul of its own, distinct from those of the parents? The concept has some importance for Christianity, because one of its central beliefs is that Jesus did not come into existence through corporal generation.
Some more-familiar terms for corporal generation are begetting and reproduction. "Begetting" is old-fashioned, but most fluent speakers today know it because "begat" appears many times in the King James Bible. "Corporal generation" is much more old-fashioned: it's really an old technical term from philosophy and religion, not known to most fluent speakers today. I doubt that it was well-known even in the 1500s (or in 1812). The plain word today is simply "reproduction".
†Finding the date of Hazlitt's translation was not easy. Nearly every source I found on the Internet was provably wrong: they gave dates after Hazlitt's death. This source is the most credible that I could find.