In a potent description of apologetics, the Apostle Paul said, "We destroy arguments and every lofty opinion raised against the knowledge of God, and take every thought captive to obey Christ" (II Corinthians 10:5). But how did he do that? Did he appeal to some "common ground" with the unbeliever, in order to use it to prove the existence of God? No, never. Rather, he tells us that unbeliever knows that there is a God (Romans 1:18), but suppresses the knowledge. In his discourse on the Areopagus (Acts 17:16-34), this is the common ground he sets out with the pagan Athenians. He cites examples in their own literature to show that they already had an awareness of the biblical God. That is, he cites pagan poets not to prove God, but to prove the suppressed knowledge of God. To put it philosophically, God is the source of logic, not its conclusion.
"The whole discourse [of Paul on the Areopagus] seems to have been
conducted on the principle that the Gospel is its own witness - that the
facts of redemption authenticate themselves; that we can reason from
its phenomena as effects to their origin in the mind of God, as we
ascend from nature up to nature's cause. Paul has evidently taken it for
granted - for there is no allusion to any external proofs of the divine
mission of Jesus, and no intimation that he himself wrought any
miracles in Athens - that, as the heavens proclaim the glory of God and
the firmament showeth His handiwork, so the death and resurrection of
Jesus, when properly apprehended, are their own proofs that He is the
power of God to salvation to everyone that believeth. The work itself
proves its divinity" (James Henley Thornwell, The Necessity and Nature of Christianity).