Is there a scripture affirming the begetting of the Word?

The following is a list of multitudes of Greek words that share the same suffix -γενής, each with possesses the sense of “born”/ “begotten”:

ἀφρογενής = “foam-born”

Αἰγυπτογενής = “born of an Egyptian”

αἰθρηγενής = “born in Aether (clear sky)”

ἁλιγενής = “sea-born” (also, ποντογενής; θαλασσογενής)

ἀλλογενής = “born of another [race]”

ἀρτιγενής = “just now born”

Ἀσιαγενής = “Asiatic born” (also, Ἀσιατογενής)

Ἀτλαγενής = “born of Atlas”

αὐθιγενής = “born here”

βοηγενής = “born of an ox”

βραδυγενής = “late-born” (also, ὀψιγενής)

γηγενής = “earth-born”

Δηλογενής = “born in Delos”

διδυμογενής = “twin-born” (born as a twin) (also, ὁμηγενής)

διγενής = “double-born” (born as both sexes; androgynous)

Διογενής = “born of Dio” (also known as “Zeus”)

Διθυραμβογενής = “born of Dithyramb” (also known as “Dionysius”)

δρακοντογενής = “born of a dragon”

δυσγενής = “low-born” (also, νοθαγενής)

ἑβδομαγενής = “born on the seventh day”

ἐγγενής = “inborn”; “innate” ἑλειογενής = “marsh-born”

ἐνδογενής = “born in the house” (also, οἰκογενής)

εὐηγενής = “well-born”

ἠπειρογενής = “born or living in the mainland (esp. of Greece)”

θεαγενής = “god-born” (also, θεηγενής; θειογενής; θεογενής)

Ἰδογενής = “born on Mount Ida”

Ἰνδογενής = “born in India”

ἰθαγενής = “legally born”

κακογενής = “evil-born”; “base-born”

κογχογενής = “born from a shell”

Κοιογενής = “born of Koios”

κρατογενής = “head-born”

κρυφογενής = “secretly born” (also, κυθηγενής)

Κυπρογενής = “born in Cyprus”

Λητογενής = “born of Leto”

Λυκηγενής = “born in Lycia”

μελιηγενής = “ash-born”

μεταγενής = “born after”

Νειλογενής = “born in the Nile”

νεογενής = “new-born”

νυμφαγενής = “born of a nymph” (also, νυμφογενής)

ὀφιογενής = “born of a serpent”

ὀμβρηγενής = “born in the rain”

ὀνειρογενής = “born of a dream”

ὀρειγενής = “mountain-born”

παλαιγενής = “born of old”; “born long ago”

πατρογενής = “father born”; “begotten of the father”

Περσογενής = “born in Persia”

πετρηγενής = “rock-born” (also, πετρογενής)

πρεσβυγενής = “first-born”; “eldest-born” (also, πρωτογενής)

προγενής = “born before” (also, προσγενής; προσθαγενής; προτερηγενής)

Πυλοιγενής = “born in Pylos”

πυριγενής = “born in fire” (also, πυρογενής)

Σουσιγενής = “born at Susa”

συγγενής = “born with”; “congenital”

Ταρσογενής = “born at Tarsus”

τετραγενής = “born four times”

τριγενής = “born three times”; “thrice-born”

Τριτογενής = “born of Triton”

ὑδογενής = “born in water”

ὑλιγενής = “born in the forest” (also, ὑλογενής)

ὑπερευγενής = “exceedingly well-born”

φοινικογενής = “born in Phoenicia”

Notice the suffix of all the words. It is -γενής, just like in the word μονογενής.

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As for a verse that confirms the eternal begetting, aside from those containing μονογενής, consider John 8:42, in which it is written,

εἶπεν οὖν αὐτοῖς ὁ Ἰησοῦς Εἰ ὁ θεὸς πατὴρ ὑμῶν ἦν ἠγαπᾶτε ἂν ἐμέ ἐγὼ γὰρ ἐκ τοῦ θεοῦ ἐξῆλθον καὶ ἥκω οὐδὲ γὰρ ἀπ᾽ ἐμαυτοῦ ἐλήλυθα ἀλλ᾽ ἐκεῖνός με ἀπέστειλεν

Therefore, Yeshua a said to them, "If God were your father, you would love me, for I came out of God and have arrived. For neither have I come of myself, but the same sent me."

In De Trinitate ("On the Trinity"), Hilary of Poitiers strives to refute numerous heresies, one of which denied the force of the aforementioned scripture. In response to these heretics, he wrote,

Postremo quod dixit: Ex Patre exivi, et veni (John 8:42), utrum ambiguitatem reliquerit, quin intelligeretur non aliunde quam ex Patre esse quod Deus est? Ex Patre enim exiens, neque aliam nativitatis habuit naturam, neque nullam: sed eum sibi testatur auctorem, ex quo se profitetur exisse. De his autem demonstrandis atque intelligendis posterior mihi sermo est.

(Pending my English translation) See link below for Schaff's translation.

Source: De Trinitate ("On the Trinity"), Book VI, §16. | English | Latin |

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This pdf contains a list of all the NT verses in which we find a conjugation of the verb ἐξέρχομαι followed by the preposition ἐκ/ ἐξ. What this list demonstrates is that Yeshu'a must have actually come out of God --- not in a figurative way, nor by simply being sent (which is expressed elsewhere by another Greek phrase: ἐγὼ παρὰ τοῦ θεοῦ ἐξῆλθον, cp. John 16:27), but actually, by a spiritual generation.

The peculiar thing about this Greek phrase is that it is also used in the LXX to indicate offspring being begotten from a father (cp. Gen. 15:4: ἐξελεύσεται ἐκ; Gen. 17:6: ἐκ...ἐξελεύσονται; Gen. 35:11: ἐκ...ἐξελεύσονται; Gen. 46:26: ἐξελθόντες ἐκ) and coming forth from a mother's womb (Job 1:21: ἐξῆλθον ἐκ), both acts of generation.

Commenting about the Greek phrase ἐκ τοῦ θεοῦ ἐξῆλθον in John 8:42, John Gill notes,

the former of these phrases is observed by many learned men to be used by the Septuagint, of a proper natural birth, as in (Gen. 15:4, 35:11); and here designs the eternal generation of Christ, as the Son of God, being the only begotten of the Father, and the Son of the Father in truth and love; and the other is to be understood of his mission from him, as Mediator:

In his commentary on John 8:42, Henry Alford notes,

ἥκω conveys the result of ἐξῆλθον, as Meyer; who also remarks that mere sending will not exhaust ἐξῆλθον, which must be taken metaphysically, of the proceeding forth of the Eternal Son from the essence of the Father.