John Lightfoot on Matthew 4:8

[Showed him all the kingdoms of the world, &c.] That is, Rome with her empire and state. For, 1. That empire is called all the world, (which word Luke useth in this story), both in sacred and profane writers. 2. At this time all cities were of little account in comparison of Rome, nor did any part of the earth bear any vogue without that empire. 3. Rome was 'the seat of Satan,' Revelation 13:2; and he granted to the beast of that city both it and the dominion. 4. This therefore seems to be that whereby he attempts to ensnare our Saviour in this object, namely, that he promiseth to give him the pomp and power of Caesar, and to deliver into his hand the highest empire of the world, that is, the Roman. This, antichrist afterward obtained.