St. Thomas on fatherhood

[Geremia]

II-II q. 102 (on the virtue of observance) a. 1 co. is a very good, concise/precise definition of fatherhood, typical for St. Thomas:

Sicut autem carnalis pater particulariter participat rationem principii, quae universaliter invenitur in Deo; ita etiam persona quae quantum ad aliquid providentiam circa nos gerit, particulariter participat proprietatem patris, quia pater est principium et generationis et educationis et disciplinae, et omnium quae ad perfectionem humanae vitae pertinent.

just as a carnal father partakes of the character of principle in a particular way, which character is found in God in a universal way, so too a person who, in some way, exercises providence in one respect, partakes of the character of father in a particular way, since a father is the principle of generation, of education, of learning and of whatever pertains to the perfection of human life

I've always liked the relationship between principio (principle/beginning) and princeps (prince). Are these words related (etymologically) to pater? It seems characteristic of manly thinking to be principled, favoring deduction over induction.

And what about ἀρχή?

[Geremia]

My friend replied:

Particularly fitting to fatherhood and to "manly thinking..." "to be principled." For a father, as a reflection of the eternal Father, is to be a manly head (caput -> princeps), a notion that is in fact intrinsic to the idea of intellectual "principle" (from which something else follows deductively) with which divine revelation itself in sacred Scripture begins (its very first word, to be properly broken up as follows): ... בְּרֵאשִׁית = lit.: In/ב the Head/רֹאשׁ of sixfoldness/שִׁית (--> the hexameronic structure Creation consists of)...

[Geremia]

Eph. 3:15: "all paternity in heaven and earth is named" after God the Father.
There are various degrees of fatherhood.

• "divine fatherhood within the Godhead" (fatherhood in the proper sense)
  _{"True generation by way of identity of nature." The Father and Son are both God.}

Fatherhood ranked by degree of participation in #1:

• "fatherhood of divine adoption" (Rom. 8:15)
  _{"True generation by way of a participation of nature.
  Formal Paternity."
  By grace we participate in God's nature.}
• "human fatherhood"
  _{"True generation by way of a similitude of nature.
  Formal Paternity."}
• "God's fatherhood of natural creatures"
  _{"No generation, but the procession of living beings by way of a similitude of God's essence.
  Non-formal Paternity."}
• "fatherhood of human adoption"
  _{"No generation, no procession of creatures; but the external principle perfecting generation.
  Non-formal paternity."}

^{source: pp. 276 & 283 Thomas E. D. Hennessy, O.P. "The Fatherhood of the Priest." The Thomist: A Speculative Quarterly Review 10, no. 3 (1947): 271–306.}