What are the personal properties of the three persons in the Godhead?

It is proper to the Father to beget the Son,[1] and to the Son to be begotten of the Father,[2] and to the Holy Ghost to proceed from the Father and the Son from all eternity.[3]

1. Heb. 1:5-6, 8

   For to which of the angels did God ever say,
   
   “You are my Son,
   today I have begotten you”?
   
   Or again,
   
   “I will be to him a father,
   and he shall be to me a son”?
   
   And again, when he brings the firstborn into the world, he says,
   
   “Let all God's angels worship him.”
   
   But of the Son he says,
   
   “Your throne, O God, is forever and ever, the scepter of uprightness is the scepter of your kingdom.

   
   
   
2. John 1:14, 18

   And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth.
   
   No one has ever seen God; the only God, who is at the Father's side, he has made him known.

   
   
   
3. John 15:26

   But when the Helper comes, whom I will send to you from the Father, the Spirit of truth, who proceeds from the Father, he will bear witness about me.

   Gal. 4:6

   And because you are sons, God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!”

Westminster Larger Catechism, Question 10. Scripture quoted from the ESV.