The Son is second to the Father in rank [τάξει] because he is from him. He is second to the Father in dignity [άξιώματι] because the Father is the principle and cause by virtue of which he is the Son’s Father and because we approach and access the God and Father through the Son. Even so, the Son is not second in nature [φύσει δὲ ούκέτι δεύτερος], since there is one divinity [ή θεότης . . . μία] in both of them. Likewise, it is clear that, even if the Holy Spirit is below the Son in both rank and dignity—something with which we too are in total agreement [όλως συγχωρήσωμεν]—it is still not likely that he is of a foreign nature.
A Summary of Basil’s Against Eunomius, Book 3, Skylar D. McManus
https://skylarmcmanus.com/2019/08/19/a- ... ius-book-3
Ὡς γὰρ ὁ Υἱὸς τάξει μὲν,
δεύτερος τοῦ Πατρὸς, ὅτι ἀπ’ ἐκείνου· καὶ ἀξιώματι,
ὅτι ἀρχὴ καὶ αἰτία, τῷ εἶναι αὐτοῦ πατέρα,
καὶ ὅτι δι’ αὐτοῦ ἡ πρόσοδος καὶ προσαγωγὴ
πρὸς τὸν Θεὸν καὶ Πατέρα· φύσει δὲ οὐκέτι (10)
δεύτερος, διότι ἡ θεότης ἐν ἑκατέρῳ μία· οὕτω δη
λονότι καὶ τὸ Πνεῦμα τὸ ἅγιον, εἰ καὶ ὑποβέβηκε τὸν
Υἱὸν τῇ τε τάξει καὶ τῷ ἀξιώματι (ἵνα καὶ ὅλως
συγχωρήσωμεν, οὐκέτ’ ἂν εἰκότως, ὡς ἀλλοτρίας
ὑπάρχον φύσεως, ἀκολουθεῖν, ἐκεῖθεν δῆλον.
This is perfectly orthodox. (Sounded sketchy but I haven't thought about it for 45 years.)Lampe Lemma: τάξις, ‑εως, ἡ
1. body of troops, in gen., band, company, 2. post or place in the line of battle, 3. order, 4. orderliness, regularity of the stars, 5. order, discipline in Church, 6. monastic rule, 7. order, ordinance, 8. rank, position, 9. role, office, 10. principle, 11. class, group, order, 12. plur., records, acts, 13. form, order, 14. phrases: κατὰ τάξιν, in order, πρὸς τάξιν, in due order, μετὰ τάξεως, in an orderly way, εἰς τ. ἄγω, bring into order, ἐν τ., in due order, in the position in the character of, of things, in the way of, by way of, in the form of, under the form of
Lampe Lemma: ἀξίωμα, ‑ματος, τό
1. honour, high reputation, 2. worth, value, 3. dignity, high status, worthiness, 4. rank, position, 5. honourable person, dignitary, 6. proper quality
 Against Eunomius (Fathers of the Church Patristic Series) Hardcover – March 28, 2011
by Basil of Caesarea (Author), Mark DelCogliano (Translator), Andrew Radde-Gallwitz (Translator)
Postsript: Time Travel (off topic)
Looking for citations of this passage from Basil, Adversus Eunomium 3.1, I stumbled across a 2011 article by H. Wayne House. Reading it was like time travel back to winter quarter 1975 hearing lectures and reading exactly the same sources cited in the article. I have reason to suspect H. W. House might have had access to a copy of W. Robert Cook's Systematic Theology in Outline Form.
http://hwhouse.com/images/House,_Eterna ... Recent.pdf