At the time of America's Declaration of Independence, America had approximately 2.5 million peoples, not of all of whom were revolutionaries or sympathetic even to the revolutionary cause. England, on the other hand, had around 6.5 million peoples, was far wealthier, and during our revolutionary war was able to hire conscripted Hessians to help them in the prosecution of war against the Americans. Additionally, Great Britain, was the preeminent naval empire in the world of that age, experienced, and with the monies to replace and to upgrade their naval fleet which had been severely weakened during the "Seven Years' War", whereas America's navy was virtually non-existent, and consequently America primarily relied upon its land forces to hold back and to eventually defeat Great Britain, with the help of the French naval fleet which bombarded and pinned Cornwallis' troops at Yorktown.
While the loss to Great Britain of America was a blow to their budding empire, Britain, knew that they could make up for the loss of America, by concentrating on their trade instead with India, which was a country of nearly 200 million peoples, a land rich in textiles and spices, which became a valuable aid to the British empire, and easily more than made up for their defeat in America, as India, and its valuable trading wealth, was the reason behind Columbus' travel that discovered America in the first place.
In the late 18th century, the major powers in Europe were France and England, with France having a population estimated at 25 million peoples. Yet, if we fast forward to Europe and its population at the present day, neither France nor England have populations which are even at 100 million peoples, with Germany as a united nation, having the largest population of any European country, and that population is about 82 million, whereas America alone is over 300 million, and India is over 1 billion peoples. While Europe still has influence and significance throughout the world, their collective power has significantly waned over the last sixty years, and has been eclipsed by United States, as well as essentially too by China, Japan, and Russia, with Brazil and India, noted as rising powers.
While there is something to be said about the size of the land that your country occupies, there is far more to be said of the size of your country's population, and while natural resources and their wise exploitation also play their part in countries' status, wealth, and power; the bottom line is that countries that have little or no natural resources can still be economically powerful, with notable examples of Japan as well as South Korea, demonstrating that intellectual wealth properly applied will translate into prosperity.
All of the aforementioned means that the decline of European powers can mainly be attributed to their overall decline in numbers relative to the other countries of the world. This is also one of the reasons why the European Union was formed, so as to help to bolster the economic effect and the influence of Europeans on a global basis. The fact of the matter is, though, had France, England, Germany, Italy, and Spain increased their populations and subsequently their overall density of their lands, they would, properly governed and with wise use of their attributes, would have today much more material and economic impact upon the world, rather than instead having suffered a precipitous decline in their dominance. You cannot hope to be a worldwide power, or to have worldwide influence, without the numbers and the knowhow to back it all up, people, are often in the end, your most important asset and ultimately your legacy for the future, without such, your light will surely dim.