How were Africa Euroasia Australia and America economically connected during the time 1500-1800?
Through European colonialism: Modern colonialism started with the Age of Discovery. Portugal and Spain discovered new lands across the oceans and built trading posts.
In the 17th century the Dutch, English and French build their overseas empire. Denmark and Sweden had some overseas colonies as well.
The Turks and Russians didn't had overseas territory but they did had expending empires, covering multiple continents.