I would like to continue stressing that the popes in their teaching did not write differently than these Fathers of the Church (see Part I and II).  They were deeply conscious that they had received a treasure and had to transmit it perfectly to the next generations. as it is defined in the First Vatican Council, dogmatic Constitution Pastor Aeternus :

“The Roman Pontiffs, moreover, according as the condition of the times and affairs advised, sometimes by calling ecumenical Councils or by examining the opinion of the Church spread throughout the world; sometimes by particular synods, sometimes by employing other helps which divine Providence supplied, have defined that those matters must be held which with God's help they have recognized as in agreement with Sacred Scripture and apostolic tradition. For, the Holy Spirit was not promised to the successors of Peter that by His revelation they might disclose new doctrine, but that by His  help they might guard sacredly the revelation transmitted through the apostles and the deposit of faith, and might faithfully set it forth.” (Denzinger Sch. 3069-3070). Here are two examples.

Tradition in the liturgy:

In a decretal letter of 416 A.D., Pope St Innocent I wrote: "If the priests of the Lord wanted to preserve the ecclesiastical institutions, as they are regulated by the tradition of the Holy Apostles, there would be no discordance in the offices and the consecrations. But when everyone thinks he can observe, not what comes from Tradition but what seems good to him, it follows that we witness a diversity in the manner of celebrating, according to the diversity of places and of Churches.  This inconvenience causes scandal for the people, who not knowing that the antique traditions have been altered by a human presumption, think that either the Churches don't agree among themselves, or that the Apostles have established contradictory things." (Dom Guéranger)

Tradition in Church law:

For example, on the order of the goals of marriage in canon 1013: “The primary end of marriage is the procreation and education of children; the secondary end is mutual support and a remedy for concupiscence”. The sources of this text are found in numerous documents of the Church over the centuries given in the footnotes of the Code of 1917 (NB. look at the years):

Eugenius IV, in the Council of Florence, Const. “Exultate Deo”, Nov. 22, 1439, n. 16; Benedict XIV, Const. “Dei miseratione” Nov. 3, 1741, n. 1; Leo XIII, Encycl. Letter “Arcanum”, Feb. 10, 1880; Holy Office, instr. (to the bishop of St Albert), Dec. 9, 1874, n. 5; Cong. of Prop. Fide, instr. (to the Greek-Rumen Bishop) 1858.

Popes always quotes their predecessors of past centuries.  That is the sign that they want to be faithful to Tradition.  So do we!