@Constantinople: Thank you. So I will go on.
"A new, peaceful age?"
18th century:
1700: Peter I of Russia attacks Germany. Poland and Prussia become battlefields again. The hastily mobilized German army soon throws the Russians behind their borders, but has to find out that Russia doesn't want peace and that it's not easy to conquer such a huge country. For years, the various consuls and dictators organize invadings of the Baltic, the Balcans and Western Ukraine, but Peter continues to send new armies against them. The war makes Germans, Scandinavians and Western Slavs working closer together again. But it also proves that the country has become too particularist and too lazy.
The Spanish Habsburgs die out, their Austrian relatives inherit the throne.
~1700: The Spaniards make contact with the Aztecs from Texas. News about an unbelivably rich country spread to Madrid, Spain attacks the Aztecs and destroys their empire (1702-08). Lots of gold flow to Spain and make the nation feel as great as never since the Reconquista. Until 1800, the Spaniards conquer all of Central America with the Maya cities, California and the north of South Atlantis.
1701-14: After French seafarers discovered Hudson Bay, France started its new colony Quebec there. Trying to gain a foothold in North Atlantis, they clash with Britain. Italy wants to hurt France, supports Britain with gold and arms, so war breaks out. Britain soon conquers Quebec and united it with its own colony Markland, forming Canada, but Louis XIV isn't willing to make peace. He even tries landing in Britain, but William of Orange always beats him back. Only when France is almost broke and even the officers grumble about the war being futile, peace is made (although Louis XIV could've made peace 10 years earlier).
1709: Germany tries to decide the war by invading Russia. They plunder Kiev, cross the Dnepr, but find out that an army as far away from the home country is very vulnerable. Peter the Great meets their army at Poltava and defeats it. Now the hard struggling near the border begins again. Both states waste their resources, but nobody wants peace.
1720: After the Russians lost Finland in the North, Czar Peter is willing to make peace. Meanwhile both sides are happy that the war is over. Germany keeps Finland, but is so deep in debt that it has to sell its half of Cuba to Italy and its colony Großfriedrichsland (OTL Carolina and Georgia) to rich Spain.
1700-50: Britain, Italy and Germany extend their colonies in Atlantis until reaching the Rockies. Italy stops expanding west, while Germany and Britain (and Spain) are willing to go even further.
1733-35: After Spanish galleons have been robbed several times by British pirates, both states make war. It's not sure that the Spanish fleet is strong enough for an attack against Britain, but the Spaniards are smart enough to stay in the Caribbean. In the peace they get the British islands in the Caribbean, although Britain offers them to give them their last colony of Canada instead. But with the sugar grown there, the Caribbean is worthier of course.
1740: Friedrich von Hohenzollern, son of a severe officer who had to leave Großfriedrichsland after the Spaniards bought it, and great-grandson of the Great Governor, becomes German consul. The smart young man is popular among the people, because he manages to clean up the corrupt bureaucracy. He also fosters arts and science and makes other reforms, like eliminating torture. He works that much that people say the two German consuls were really Friedrich and Wilhelm von Hohenzollern. But he also reorganizes the army, because he read the history of the Teutonic Order, and dreams about conquering the Baltic lands. When he's sure that the people are behind him, he offers Russia to sell at least the southern Baltic. When Russia brusquely declines, Friedrich starts the war. The Protestant Balts welcome him as a liberator. Although some Germans want to expand the war, Friedrich stays wise and considered, keeps the war in the Baltic and finally gets it in the peace of 1742. He also introduces the potato to Germany, gives the Reich more rights (at the expense of the Länder), and even declares that homosexuality isn't a crime but "just" a disease. Most of the inner customs are abolished, leaving only two big areas, Germany and Atlantis (later, Argentinien will follow).
1741-48: France and Spain make the Great Atlantean War, which gives La Florida back to Spain. In this war, the Italian macchiavellists supported both sides again, to hurt them both. The war damages many Spanish colonies in Atlantis and hampers its expansion.
1744: Russia tries to reconquer the Baltic, but is beaten back by Friedrich. In the following year, they return to status quo of the peace of 1742.
1756: Russia allies with France against Germany. Friedrich wants to keep them from striking first by a preventive war, but the third Baltic War becomes much harder. Russia and France already make plans for after the war: Russia wants Poland, Hungary, Prussia and the Baltic, France wants Lorraine and Wallonia.
1762: After the death of Czarina Elisabeth new Czar Peter II makes peace with Friedrich whom he admires. The Six-Year War is over. To everyone's surprise Friedrich doesn't even demand a thing in the peace - because he says, stability is the most important thing for Europe, but this is impossible if all the nations swear revenge and every war creates a new one. All the witnesses are in unison that only a popular man like him can have such an opinion, which would be considered cowardice or slackness at everyone else. Even new Czarina Catherine II admits: "He is a republican, but on par with every monarch!" She doesn't want another war with Germany either, because the four wars in this century didn't help Russia in any way and held it off from expanding into Asia, where they only acquired worthless areas so far - Mongolia (nothing but Steppe), Afghanistan (mountains), and Arabia (empty desert, and the water is polluted with oil). At least, the long competitor Choresm is now defeated. After the destruction of the Holy Cities of Mecca and Medina the Islam splinters into many sects.
1765: James Watt invents the steam machine in Britain.
1770: James Cook starts his first journey, founds British colonies along the coast of Braseal and Argentine. Later he'll start more journeys from there, refutes the existence of a big Southern continent, discovers Australia and claims it for Britain.
1772: Germany and Russia agree for the division of Hungary. The west (incl. Slovakia) goes to Germany, the East (Transsylvania, Banat) to Russia. Now the last smaller independent country in Europe has disappeared.
1776: The Canadians under Washington, Franklin and Jefferson rebel against backward and corrupt British rule, which suppresses non-Catholics, and gain independence with German help. But that's not the only reason why the new country stays German-friendly...
Adam Smith discovers modern economy and announces it in his book "An inquiry into the nature and causes of the wealth of nations". The British government changes their economic politics following his advice, bringing Britain great wealth in the following decades. But industrialization will have other consequences too...
1781: Friedrich Schiller publishes his first book, "The new knights", about some revolters in the Peasant Wars. He becomes the greatest German author, famous for history dramas like "Wallenstein", "Martin Luther", "The History of the Revolt of the Netherlands". He's also famous for being friends with Goethe, who writes after his great success "Werther" less popular and often ununderstandable works, f.e. about an obscure medieval doctor, which few people actually understand. Schiller is revered by the Germans, OTOH; they like to see their famous history depicted in his dramas.
1783: In Great Britain, Pitt Jr. becomes Prime Minister, starts his reforms. Industrialization is fostered. As a replacement for lost Canada, Australia and New Zealand are settled. Under his leadership, Britain concentrates to gain influence in the world by expanding its industry - with success. He doesn't want to make war, following a "splendid isolation" policy instead.
1789: French Revolution. People introduce a constitution, nationalizes church property and declares the human rights. The pope leaves the country, goes to Toledo, Spain.
1790: Russia conquers and destroys Mecca and Medina.
1791: Count Mirabeau, one of the smartest people of the revolution, dies. Without him, the more radicals in the estates become stronger.
1792: The Girondists succeed with their demand for a war. France declares war on Spain, invades Catalonia.
1793: The radical Jacobins take power, guillotin the king (and later their political enemies) and make France a republic. In the French colonies in Atlantis the monarchist loyalists declare that they don't accept the Jacobin government and see themselves as the legal French government.
1794: The moderated republicans win against the Jacobins in France, Robespierre dies under the guillotine. Spain is defeated and divided into several satellite republics. Italy fears an all-powerful France, declares war. French invade Northern Italy and defeat the Italians. The macchiavellist government has a crisis.
1795: General Napolione Buonaparte from Corsica becomes new commander of the Italian army, kicks out the French from Italy again. Talking with French POWs he learns a lot about their reasonings, has the idea that Italy should be changed too. However, he doesn't think about a republic, but something else every Italian still knows: The Empire of Augustus.
1796: Napolione invades South France, allies with anti-Central government groups, which eases his advancing.
1797: France and Italy make peace. South France becomes the independent republic of Occitania, which also includes Catalonia.
1798: Italian government unwary about Napolione's uprise. Since they can't simply kill such a popular man, they decide to send him abroad, let him conquer Egypt, the last independent Muslim state around the Mediterranean. In France, the directory has to declare bankruptcy, the country falls into chaos.
1799: Unrests in France spread to Occitania, Italian satellite government toppled. Chaos threatens to spread to Italy. Napolione who already defeated Egypt returns to Italy, topples the old government, makes himself Augusto (emperor), declares new Roman empire. The Catholic church is reorganized as "Imperial-Catholic church", with himself on top. It's not the state religion anymore, but all other religions have to submit under the Augusto.
The pope in Britain declares Napolione a heretic, makes the British government declare war upon him. (The Conservative party is very pro-Catholic.)
In Germany, people are unwary about Napolione: A new emperor fighting a republic? But Napolione can calm them down: He promises that 1) the old German-Italian friendship will continue, 2) it was him who gave the Protestants in Italy and Occitania full rights and 3) New Rome has interests in the Mediterranean and South Atlantis, but not in Central Europe. This is a hint for his next targets: The Inca Empire and Russia. But he didn't tell about his biggest dream: Since the Egyptian expedition he's obsessed with finding a way to India.
Germany and New Rome make an "everlasting non-aggression pact" and a secret alliance against Britain and Russia.
In the same year, Napolione kicks out the French from Italy, reconquers Occitania and is accepted in Italia Nuova.
1800: Canada and the German and Spanish colonies have reached the Pacific. Canadians meet to their surprise Russian scouts who claimed Alyeska. Now it's proven what scientists already told: The Earth is round.
Napolione defeats France, adds it to the New Roman Empire, declares Paris the second Roman capital. Meanwhile the French are happy about the restored order. Italian troops in Atlantis conquer loyalist Louisiana and the Spanish colonies at the Atlantic coast. Morocco and Algeria are also added to the New Roman Empire. (France and Spain are in chaos and can't prevent that.)
Edit: A map of 1775, before the Canadian and the French revolution.