“You are Peter, and upon this rock I will build my church”? Matthew 16:18
Cyprian of Carthage (about 250 AD) explains how this unity of the Church is held together :
If anyone considers and examines these things, there is no need of a lengthy discussion and arguments. Proof for faith is easy in a brief statement of the truth.
The Lord speaks to Peter:
‘I say to you,’ He says, ‘you are Peter, and upon this rock I will build my church, and the gates of hell shall not prevail against it. And I will give you the keys of the kingdom of heaven; and whatever you shall bind on earth shall be bound also in heaven, and whatever you shall loose on earth shall be loosed also in heaven.’ (Matthew 16:18-19)
Upon him, being one, He builds His Church, and although after His resurrection He bestows equal power upon all the Apostles, and says: ‘As the Father has sent me, I also send you. Receive the Holy Spirit: if you forgive the sins of anyone, they will be forgiven him; if you retain the sins of anyone, they will be retained,’ (John 20:21-23) yet that He might display unity, He established by His authority the origin of the same unity as beginning from one.
Surely the rest of the Apostles also were that which Peter was, endowed with an equal partnership of office and of power, but the beginning proceeds from unity, that the Church of Christ may be shown to be one.
This one Church, also, the Holy Spirit in the Canticle of Canticles designates in the person of the Lord and says: ‘One is my dove, my perfect one is but one, she is the only one of her mother, the chosen one of her that bore her.’ (Canticles 6:8)
Does he who does not hold this unity think that he holds the faith? Does he who strives against the Church and resists her think that he is in the Church, when too the blessed Apostle Paul teaches this same thing and sets forth the sacrament of unity saying: ‘One body and one Spirit, one hope of your calling, one Lord, one faith, one baptism, one God’? (Cf. Eph: 4:4-6)
This unity we ought to hold firmly and defend, especially we bishops who watch over the Church, that we may prove that also the episcopate itself is one and undivided. Let no one deceive the brotherhood by lying; let no one corrupt the faith by a perfidious prevarication of the truth.
The episcopate is one, the parts of which are held together by the individual bishops. The Church is one which with increasing fecundity extend far and wide into the multitude, just as the rays of the sun are many but the light is one, and the branches of the tree are many but the strength is one founded in its tenacious root, and, when many streams flow from one source, although a multiplicity of waters seems to have been diffused from the abundance of the overflowing supply nevertheless unity is preserved in their origin. Take away a ray of light from the body of the sun, its unity does not take on any division of its light; break a branch from a tree, the branch thus broken will not be able to bud; cut off a stream from its source, the stream thus cut off dries up.
Thus too the Church bathed in the light of the Lord projects its rays over the whole world, yet there is one light which is diffused everywhere, and the unity of the body is not separated. She extends her branches over the whole earth in fruitful abundance; she extends her richly flowing streams far and wide; yet her head is one, and her source is one, and she is the one mother copious in the results of her fruitfulness. By her womb we are born; by her milk we are nourished; by her spirit we are animated. [Chapters 4 and 5 of The Unity of the Church by Cyprian of Carthage. Text here Downloadable as a free PDF.]
H/T Orthocath for this and the link to The Unity of the Church