Scotia Which Is Also Called Ireland, Is An Island

Nicholas Serarius, a Jesuit, in his historical notes on the Acts of Saint Kilian, while commenting on the words of the ancient text, wherein it is said ; "Scotia which is also called Ireland, is an island " in the ocean; thus observeth in the margin ;—  Truly it is to be observed, that although the northern part of Britain is now properly called Scotland, yet by that name was Ireland formerly known; this sheweth the venerable Bede when be sayeth that the Picts came from Scythia into Ireland, and there found the nation of the Scots.—Then goeth he through entire pages, confirming this with the divers authorities which we above have cited ; and at length he contendeth thus:—Ireland claimed to herself the name of Scotia; and as out of that Ireland a portion of  the Scots went forth and settled in those parts of Britain which the Picts then possessed ; afterwards they expelled the Picts themselves, and occupying all the northern territory, gave unto  it the name of their original country—Whence it appeareth, that there was one only people of the Scots, but two places which bore the name of Scotland;—one, ancient and proper, in Ireland, another, modern and adopted, in North-Britain;—and from which-ever the preachers of the, Divine word came, they were all termed Scots.—Thus far Serarius.—

Link (here) to The Life and Acts of Saint Patrick; The archbishop, primate and apostle of Ireland by Jocelin, monk of Fumes