I am not trying to add to what CovenantInblood or Pilgrim have already said. Just thought I would post a couple sections from a couple of great books.

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An Exposition of the Westminster Confession of Faith
by Robert Shaw
Section III.–In the unity of the Godhead there be three Persons of one substance, power, and eternity: God the Father, God the Son, and God the Holy Ghost. The Father is of none, neither begotten nor proceeding; the Son is eternal begotten of the Father; the Holy Ghost eternally proceeding from the Father and the Son.
II. The Sacred Three are distinguished from each other by their personal properties. It is the personal property of the Father to beget the Son.–Ps. ii. 7. It is the personal property of the Son to be eternally begotten of the Father.–John. i. 14. It is the personal property of the Holy Ghost to proceed eternally from the Father and the Son.–John xv. 26; Gal. iv. 6. These are called personal properties, to distinguish them from the essential perfections of Deity. Essential perfections are common to the Father, the Son, and the Holy Spirit, but a personal property is something peculiar to each, something which may be affirmed of one, but cannot be affirmed of the other two. Paternity is peculiar to the first person, filiation to the second, and procession to the third. We pretend not to explain these personal properties; here, if in anything, it is safest to abide by the language of Scripture.

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Body of Divinity by Thomas Watson

The Trinity

II. Let me speak of the Trinity in Unity.
[I] The first person in the Trinity is God the Father. He is called the first person, in respect of order, not dignity: for God the Father has no essential perfection which the other persons have not; he is not more wise, more holy, more powerful than the other persons are. There is a priority, not a superiority.
[2] The second person in the Trinity is Jesus Christ, who is begotten of the Father before all time. 'I was set up from everlasting, from the beginning, or ever the earth was. When there were no depths I was brought forth; when there were no fountains abounding with water. Before the mountains were settled, before the hills, was I brought forth.’ Prov 8: 23 - 25. This Scripture declares the eternal generation of the Son of God. This second person in the Trinity, who is Jehovah, is become our Jesus. The Scripture calls him the branch of David, Jer 23: 5, and I may call him the flower of our nature. 'By him all that believe are justified.’ Acts 13: 39.


Have a good Lord's day,
William


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