5 Furthermore, the Son of God decreed that the Church should be His mystical body, with which He should be united as the Head, after the manner of the human body which He assumed, to which the natural head is physiologically united. As He took to Himself a mortal body, which He gave to suffering and death in order to pay the price of man's redemption, so also He has one mystical body in which and through which He renders men partakers of holiness and of eternal salvation. God "hath made Him (Christ) head over all the Church, which is His body" ( Eph . i., 22-23). Scattered and separated members cannot possibly cohere with the head so as to make one body. But St. Paul says: "All members of the body, whereas they are many, yet are one body, so also is Christ" (I Cor . xii., 12). Wherefore this mystical body, he declares, is "compacted and fitly jointed together. The head, Christ: from whom the whole body, being compacted and fitly jointed together, by what every joint supplieth according to the operation in the measure of every part" ( Eph . iv., 15-16). And so dispersed members, separated one from the other, cannot be united with one and the same head. "There is one God, and one Christ; and His Church is one and the faith is one; and one the people, joined together in the solid unity of the body in the bond of concord. This unity cannot be broken, nor the one body divided by the separation of its constituent parts" (S. Cyprianus, De Cath. Eccl. Unitate , n. 23). And to set forth more clearly the unity of the Church, he makes use of the illustration of a living body, the members of which cannot possibly live unless united to the head and drawing from it their vital force. Separated from the head they must of necessity die. "The Church," he says, "cannot be divided into parts by the separation and cutting asunder of its members. What is cut away from the mother cannot live or breathe apart" ( Ibid .). What similarity is there between a dead and a living body? "For no man ever hated his own flesh, but nourisheth and cherisheth it, as also Christ doth the Church: because we are members of His body, of His flesh, and of His bones" ( Eph . v., 29-30). Another head like to Christ must be invented - that is, another Christ - if besides the one Church, which is His body, men wish to set up another. "See what you must beware of - see what you must avoid - see what you must dread. It happens that, as in the human body, some member may be cut off - a hand, a finger, a foot. Does the soul follow the amputated member? As long as it was in the body, it lived; separated, it forfeits its life. So the Christian is a Catholic as long as he lives in the body: cut off from it he becomes a heretic - the life of the spirit follows not the amputated member" (S. Augustinus, Sermo cclxvii., n. 4). The Church of Christ, therefore, is one and the same for ever; those who leave it depart from the will and command of Christ, the Lord - leaving the path of salvation they enter on that of perdition. "Whosoever is separated from the Church is united to an adulteress. He has cut himself off from the promises of the Church, and he who leaves the Church of Christ cannot arrive at the rewards of Christ....He who observes not this unity observes not the law of God, holds not the faith of the Father and the Son, clings not to life and salvation" (S. Cyprianus, De Cath. Eccl. Unitate, n. 6).
Source: Satis Cognitum (Vatican.va)