Well, almost. The clue is (Norman) French, whence we get a suprising lot of our vocabulary, including, ironically, ‘Britain’. In French, the island you’re talking about is ‘Grande Bretagne’, and the nearby peninsula is ‘Bretagne’. There never was a ‘Lesser Britain’; for that matter, there has never been a ‘Greater Britain’ either. Just Brita[ i ]n[ny] and Great Britain.
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**Uh . . . uh . . . sort of. The first British colony outside the British Isles was Jamestown, Virginia, 1607. That’s ‘James’ as in ‘James I King of England and James VI King of Scotland’, and 1607 is four years after England and Scotland were united. So in that context, the Empire has been British from the start. On the other hand, depending on whom you talk to, Ireland was ‘colonised’ by Henry II in 1171. On the other other hand, at that time, Henry’s demesnes also included a pretty fair chunk of France, and it should more properly be called the ‘Norman Empire’.
Ireland was really a colony of England, and never really had its own ‘ruler’ from 1171 on. Wales was annexed in 1284, but maintained its identity. Scotland, on the other hand, was fiercely independent clear up to 1603. From 1603 to 1801, the kingdom was usually called ‘Great Britain’, which was pretty accurate. Only at this late date was Ireland really a partner in the newly-christened ‘United Kingdom’, and even then it was very definitely a junior partner, but the kingdom was no longer called ‘Great Britain’.
Notoriously not, as the famous Times headline from many years ago illustrates so Britishly.
FOG ENGULFS CHANNEL; CONTINENT ISOLATED
And be careful with the ‘English/British’ distinction; most Scots, Welsh and Manx would not consider themselves any more European than your typical Englishperson. The rule of thumb, as laid down by Flanders and Swann, is:
‘If they’ve done something good, it’s “Another Triumph For Great Britain”; but if something goes wrong, it’s “England Loses Again”.’
Iceland sits astraddle the American and European tectonic plates; and although the majority of the population lives on the western part of the island, and on the American plate, Iceland is traditionally considered ‘European’ (some even call it ‘Scandinavian’). Greenland is the world’s largest island in the world’s largest archipelago (the Arctic Archipelago, the rest of which lies in Canada), and although it is (a self-governing) part of Denmark, it is squarely in North America (as is Saint-Pierre et Miquelon, even though it is a part of France).
Here’s the problem. Before the Germanic and Italic tribes pushed their way in, most of Europe was Celtic, and even past Europe into Turkey. ‘Galat-’, as in Galatians, the people in eastern Turkey that Paul wrote to, comes from the same root as ‘Celt’. So ‘Celtic Isles’ could just as easily apply to Cyprus and Corsica as to the ‘Irish Archipelago’. ‘Gaelic Isles’ is somewhat less accurate than calling them the ‘English Isles’. Of the five Celtic languages spoken recently in the archipelago, three (Scots Gaelic, Irish Gaelic, and Manx) are Goidelic (a subfamily of your Celtic language tree), and two (Welsh and Cornish) are Brythonic (a different subfamily of Celtic). The Welsh would have a big problem living in the Gaelic Isles. Welsh is about as closely related to Scots Gaelic as French is to German. And there are more Welsh speakers than the other four combined.
But you want to know what the #1 Celtic language is in the world today? It’s called ‘Breton’, and it’s spoken by over a million people in northern France. So what’s wrong with ‘British Isles’? The word ‘British’ is a proud Celtic word that succinctly describes the geography of the area.