The Mighty He-Goat - The Greek Empire.
‘And as I was considering, behold a he-goat came from the west over the face of the whole earth and did not touch the ground. And the goat had a notable horn between its eyes.'
As we are specifically told later (Daniel 8:21) this he-goat represents Greece, to the west of the Persian empire. Greece had been well known for centuries as a source of trade, and it had provided contingents of very effective mercenaries for foreign armies, including the Egyptian and Persian armies. ‘Over the face of the whole earth' means the Mediterranean ‘earth', but now stretching into Europe as well. ‘Did not touch the ground.' They skimmed over the ground, demonstrating the speed of their conquests. The notable horn was no doubt Alexander the Great.