III. The three Persons in the Trinity are perfectly equal in all things
But although, dearly-beloved, the actual form of the thing done was exceeding wonderful, and undoubtedly in that exultant chorus of all human languages the Majesty of the Holy Spirit was present, yet no one must think that His Divine substance appeared in what was seen with bodily eyes. For His Nature, which is invisible and shared in common with the Father and the Son, showed the character of His gift and work by the outward sign that pleased Him, but kept His essential property within His own Godhead: because human sight can no more perceive the Holy Ghost than it can the Father or the Son.
For in the Divine Trinity nothing is unlike or unequal, and all that can be thought concerning Its substance admits of no diversity either in power or glory or eternity. And while in the property of each Person the Father is one, the Son is another, and the Holy Ghost is another, yet the Godhead is not distinct and different; for while the Son is the Only begotten of the Father, the Holy Spirit is the Spirit of the Father and the Son, not in the way that every creature is the creature of the Father and the Son, but as living and having power with Both, and eternally subsisting of That Which is the Father and the Son. And hence when the Lord before the day of His Passion promised the coming of the Holy Spirit to His disciples, He said, “I have yet many things to say to you, but you cannot bear them now.
But when He, the Spirit of Truth shall have come, He shall guide you into all the Truth. For He shall not speak from Himself, but whatsoever He shall have heard, He shall speak and shall announce things to come unto you. All things that the Father has are Mine: therefore said I that He shall take of Mine, and shall announce it to you.” Accordingly, there are not some things that are the Father's, and other the Son's, and other the Holy Spirit's: but all things whatsoever the Father has, the Son also has, and the Holy Spirit also has: nor was there ever a time when this communion did not exist, because with Them to have all things is to always exist.
In them let no times, no grades, no differences be imagined, and, if no one can explain that which is true concerning God, let no one dare to assert what is not true. For it is more excusable not to make a full statement concerning His ineffable Nature than to frame an actually wrong definition. And so whatever loyal hearts can conceive of the Father's eternal and unchangeable Glory, let them at the same time understand it of the Son and of the Holy Ghost without any separation or difference. For we confess this blessed Trinity to be One God for this reason, because in these three Persons there is no diversity either of substance, or of power, or of will, or of operation.
Source: Sermons (New Advent)