As the opening title of this thread states, this is another letter from the pen of St. Basil. (IMO, this letter needs to be read in conjunction with his 125th epistle, provided in the previous thread.)
Given the length of this letter, I am only going to provide the first few paragraphs, and an important section that identifies the monarchy of God the Father (though I highly recommend to everyone that they take the time to read the entire epistle - see link provided below.) I think all will immediately identify the close relationship (doctrinally speaking) that this letter has with his 125th epistle.
TO GREGORY HIS BROTHER, ON THE DIFFERENCE BETWEEN SUBSTANCE AND PERSON
Seeing that many, in treating of the mysterious doctrine of the Trinity, because they fail to discern any difference between the general conception of substance and that of the persons, come to like notions and think that it matters not whether they use the term "substance" or "person" (and for this reason some of those who accept such things without investigation are pleased to attribute one person to God just as they do one substance ; and vice versa, those who profess three persons feel obliged to assert as a consequence of this truth the same number of divine substances ) : for this reason, in order that you too may not fall into the same error, I have composed this brief discussion of the subject by way of a memorandum for you. Now, the meaning of these words, to explain it in brief, is as follows.
Those nouns which are predicated of subjects plural and numerically diverse have a more general meaning, as for example '' man." For when you say "man," you thereby signify the general class, and do not specify any man who is particularly known by that name. For "man" is no less applicable to
Peter than to Andrew, John, or James. This common element of the thing predicated, seeing that it refers to all alike who are included under the same term, demands a further note of distinction if we are to understand, not merely man in general, but " Peter" or "John" in particular.
Other nouns have a very specific denotation, whereby it is not the common property of the class that is indicated by the term employed, but rather a limitation to a particular thing, this delimitation implying no participation in the genus so far as the individuality of the object is concerned ; for example, "Paul" or "Timothy." For such expressions no longer have reference to the properties common to the nature of the objects, but, by setting apart certain delimited objects from the comprehensive term, specify what they are by means of these names. Now when a name is sought for two or more similar objects, as, for example, "Paul," "Silvanus," and ''Timothy," which will indicate the substance of these men, you will not apply one term to the substance of Paul, but a different one to that of Silvanus, and still another to that of Timothy ; but whatever terms indicate the substance of Paul will apply to the two others as well ; and those who are described with reference to their substance by the same terms are consubstantial with one another. And when you have learnt the common element and turn your investigation to the individual characteristics whereby the one is differentiated from the other, then the description which conveys knowledge of each will not agree in all respects with that which describes the other, even if in certain respects it is found to include the element common to all.
This, then, is our statement of the matter; that which is specifically referred to is indicated by the expression "hypostasis " (person). For if you say "man" by the indefiniteness of the term used you have produced in our minds a sort of vague concept, so that, although the nature of the thing is indicated by the noun, yet the thing which subsists in that nature and is specifically indicated by the noun is not made evident to us. But if you say "Paul," you have indicated by the noun the nature subsisting in the particular object. (English translation by Roy Joseph Deferrari, Loeb Classical Libaray, St. Basil - The Letters, 1926, vol. 1, pp. 197-201 - online pdf copy.)
And a bit later, Basil makes a clear reference to the monarchy of God the Father:
As for the Son, who through Himself and with Himself makes known the Spirit which proceeds from the Father, and who shines forth as the onlybegotten from the unbegotten light, He in the matter of the individual tokens which distinguish Him has nothing in common with the Father or with the Holy Spirit, but alone is recognized by the note just named. And God, who is over all, alone has an exceptional note of His person, in that He is Father and proceeds from no other principle ; and by this note again He is also recognized individually Himself. Therefore we assert that in the community of substance there is no accord or community as regards the distinguishing notes assigned by faith to the Trinity, whereby the individuality of the persons of the Godhead, as they have been handed down in our faith, is made, known to us, for each is apprehended separately by means of its own particular distinguishing notes. It is by means of the marks just mentioned that the distinction of the Persons is ascertained ; but regarding attributes denoted by the terms infinite, incomprehensible, uncreated, uncircumscribed by space, and all others of like nature, there is no variation in the life-giving nature—I mean in the case of the Father, or of the Son, or of the Holy Spirit—but a certain continuous and uninterrupted community appears in them. (Ibid., pp. 207, 208 - bold emphasis mine.)
There is so much more in this exceptional letter, including an interpretation of Heb. 1:3 (pp. 219 ff.); and so, I would like to end here by urging all, once again, to take the time to read the entire epistle.
Grace and peace,