The Ten Barbarian Nations of the Divided Roman Empire

The historian Machiavel, without the slightest reference to this prophecy [that of Daniel 7], gives the following list of the nations which occupied the territory of the Western Empire at the time of the fall of Romulus Augustulus, the last emperor of Rome.

The Lombards, the Franks, the Burgundians, the Ostrogoths, the Visigoths, the Vandals, the Heruli, the Sueves, the Huns, and the Saxons; ten in all. 

Guinness, Henry Grattan, The Divine Programme of the World's History, London: Harley House, 1892, p. 318.

"the set times and the laws" of Daniel 7:25

Fifth, this power attempted to do something with God's law. The prediction was that he will "try to change the set times and the laws" (vs. 25). There are two words for time in this verse. One is iddan, used to describe the duration of the little horn's persecution of the saints; it would last three and a half times ("a time, [two] times and half a time"). The word iddan means a span of time. The other word for time used in this verse is zeman (plural, zimmin). "He will . . . try to change the set times and the laws." This Aramaic word has more of a function of a point in time, but it is in the plural form indicating repeated points of time. These are connected with God's law (the word for "law" is singular in the original language). The feature of God's law that best fits this description is the fourth commandment where the recurring seventh day is featured as a point of time, or as regularly occurring points of time.

Shea, William H., Daniel, 2 vols., Boise, Idaho: Pacific Press Publishing Association, 1996, vol. 2, p. 139.

The Rise of the Roman Catholic Church Coincident with the Fall of the Roman Empire

It is, therefore, by a particular decree of Divine Providence that, at the fall of the Roman Empire and  its  partition  into  separate  kingdoms,  the  Roman  Pontiff, whom  Christ  made  the head  and  center  of  his entire  Church, acquired civil power.

Pius IX, Apos. Let. Cum Catholica Ecclesia, March 26, 1860

(Papal Teachings: The Church, Selected and arranged by the Benedictine Monks of Solesmes, trans. Mother E. O’Gorman, Boston, MA.: Daughters of St. Paul, c1962, par. #225, p. 160)

Poiché per operare liberamente, come era necessario, doveva fruire di quei supporti che rispondevano alle condizioni e alle esigenze dei tempi, per una speciale disposizione della divina Provvidenza avvenne che, quando l’Impero Romano si dissolse e fu diviso in vari regni, il Romano Pontefice, costituito da Cristo capo e centro di tutta la Chiesa, ottenne un Principato civile.  

Pius IX, Apos. Let. Cum Catholica Ecclesia, March 26, 1860, 2 (<http://www.intratext.com/IXT/ITA0493/__P2.HTM>)