Thanks to all. As said in the first post, I'll continue this TL until the year 2000 or today's tech level is reached, whichever comes first.
Yes, the Nahuatl language in Mexico will survive, or is at least stronger than OTL. No, they don't sacrifice people anymore - they were catholized (by France) since the Great Occidental War in the 16th century.
Kumania is the southern Ukraine between Dnepr and southern Bug. Dvoryans... I didn't find a better word yet, I had believed for unknown reasons that this meant "warrior", and they are the Cossacks of TTL. So that's a Dvoryan republic - a Cossack state. BTW, Nobles republics aren't that uncommon - Poland-Lithuania was very much like that, and ITTL Aragon and Norway became nobles' republics (or elective monarchies, if you prefer that term) as well.
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And now...
Some retcon about religion in Europe:
At the council of Ghent (1551-56) the Occidental church was reunited with the rest of the Catholic church (doctrines were somewhat changed), so different religious opinions were restricted to the "outlaw states" of Bohemia and Münster, which were conquered anyway in 1587 and 1679 respectively. The princes had gained quite some power - church lands were confiscated in all countries, and in many ones (France, E-C-P, Hungary, several German states) the princes now even had the power to decide about positions in the church, as long as they didn't touch the Papal doctrine. However, when Francois IV misused the pope in Avignon too openly as his tool and E-C-P fell apart, many European states took complete control over the church, effectively splintering it into many national churches (as in Sweden, England, Spain and the Netherlands, where the power over church didn't even go to the king, but the parliament). During this time, many countries introduced special national holidays for the first time (St George's Day in England, f.e.). When France lost the anti-French War, they couldn't bring the national churches back into the fold either. In 1698, it was finally agreed that a new council would be held on neutral ground - in Cork in Ireland, the only Catholic European country that had stayed out of the anti-French War. (In 1700, the council still didn't finish its work.)
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History of science in the 17th century:
General state of the art:
Western Europe: The first modern canal is built between Spree and Oder rivers in Brandenburg-Silesia. Islamic knowledge (mostly physics, esp. optics) spreads through all countries. Better clocks, first adding and multiplicating machines built. Alchimists in Italy discover first new element, phosphor.
Russian lands: Much of Chinese knowledge introduced and later even improved (statistics, galvanization). Materials categorized into conductors and non-conductors.
Islamic World: The introduction of the printing press leads to faster progress and more widespread knowledge. An encyclopedia is printed and slowly distributed. In Persia, bacteria are studied under the microscope for the first time. Aberration of light discovered. Astronomians also discover Halley's comet and a new planet, Uranus.
India: Kerala school stays undisturbed by Islamic conquests, makes even more mathematical discoveries at the level of OTL 1900.
China: They learn about the Europeans, but aren't really interested in what they have to offer. Science stagnates.
1604: Ophiuchus Supernova observed.
Read [post=963447]about the medicinal achievements of the University of Zanzibar[/post]!
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Summary of the 17th century:
Atlantis: French Louisiana mostly divided between Germans, Italians and English. Mexica subjugated by Spaniards. Braseal and Argentine colonized by England. RUssians take Alyeska and the West Coast down to San Francisco Bay.
Europe: Triple monarchy of England-Castille-Portugal falls apart. Englands suffers a Civil War that brings Stafford dynasty to power. During this power vacuum, France greatly expands its influence over most of Europe under absolutist Francois IV. In the great anti-French War their empire breaks together, and Scotland and Portugal lose independence. Hungary practices religious tolerance.
Russian lands: Siberia becomes the independent republic of Novorossiya, as good relations with China. Kipchak lands north of the Black Sea conquered by Russians, formed into the new "Dvoryan republics". Science and humanities blossom in Novorossiya.
Muslim world: Seljuks still lose against Europeans, but achieve some victories in the second half of the century. Persia conquers Oman, Delhi.
East Asia: Independent nations between China and Russians conquered by the latter. Hong China loses power and influence, at the expense of the "rim people" (Japanese, Koreans, SE Asians). Western Europeans enter the scene.
Rest of the world: Songhay empire in Africa becomes stronger. French visit and ally with Ethiopia. Many Portuguese go to the "ship settlements" in the sea of Guinea. Swedes reconquer Australafrica.
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Edit: Map of the world - before and after the Anti-French War. (Note I didn't bother to draw all the borders in Europe. For that, we have the detailed map.)
Colors:
Red - Britain
Pink - France
Yellow - Spain
Brown - Denmark-Braunschweig
Black - Sweden
Blue - Italy
Orange - Inca (not Dutch
)
Purple - Novorossiya
Greens - Islamic states (Seljuks, Persia, Choresm, Melaka)
Note in W Africa: The upper country is Songhay, below it is the Portuguese-influenced Greater Guinea.
India isn't a French colony, but independent Vijayanagar and some smaller states.