Paul used whatever was appropriate. Of course when speaking to Jews he used scripture.
But in Acts 17:12 onwards he was speaking to pagan Athenians. He did not argue from scripture but argued from reason and nature, and even from their own writings (vs 28).
The Apostle Paul always based His soul winning squarely on SCRIPTURE.
Let's watch how this chosen vessel of God does that very thing with these ungodly carnal philosophers and those persons wholly given over to idolatry.
παιδαγωγός
(
Strong's #3807 — Noun Masculine — paidagogos — pahee-dag-o-gos' )
"a guide," or "guardian" or "trainer of boys," lit., "a child-leader" (pais, "a boy, or child," ago, "to lead"), "a tutor," is translated "instructors" in
1 Corinthians 4:15 , AV (RV, "tutors"); here the thought is that of pastors rather than teachers; in
Galatians 3:24,25 , AV, "schoolmaster" (RV, "tutor,"), but here the idea of instruction is absent. "In this and allied words the idea is that of training, discipline, not of impartation of knowledge. The paidagogos was not the instructor of the child; he exercised a general supervision over him and was responsible for his moral and physical well-being. Thus understood, paidagogos is appropriately used with 'kept in ward' and 'shut up,' whereas to understand it as equivalent to 'teacher' introduces an idea entirely foreign to the passage, and throws the Apostle's argument into confusion." * [* From Notes on Galatians, by Hogg and Vine, pp. 163,164] Cp. epitropos, "a steward, guardian, tutor
So as we observe Paul we are to emulate what he does if we have such ability..we see that here;
Phil 3:13-20
13 Brethren, I count not myself to have apprehended: but this one thing I do, forgetting those things which are behind, and reaching forth unto those things which are before,
14 I press toward the mark for the prize of the high calling of God in Christ Jesus.
15 Let us therefore, as many as be perfect, be thus minded: and if in any thing ye be otherwise minded, God shall reveal even this unto you.
16 Nevertheless, whereto we have already attained, let us walk by the same rule, let us mind the same thing.
17 Brethren, be followers together of me, and mark them which walk so as ye have us for an ensample.
18 (For many walk, of whom I have told you often, and now tell you even weeping, that they are the enemies of the cross of Christ:
19 Whose end is destruction, whose God is their belly, and whose glory is in their shame, who mind earthly things.)
20 For our conversation is in heaven; from whence also we look for the Saviour, the Lord Jesus Christ: