Regarding the middle ages, with a slight bias towards the German term "Mittelalter": this name, or a variation of it, was first used towards the end of what we some historians traditionally define as the middle ages (ending in 1492). The Italian humanist Petrarca (1304 - 1374) used the words "medium tempus" when he talked about the desire to revive the noble, classical age of the Greeks and Romans, seeing himself in the dark time in between the classical age and the revival of it – hence the words "medium tempus".

The Swiss historian and politician Aegidius Tschudi (1505 - 1572) is noted for probably the first use of the word "Mittel Alter" (which is essentially the same as today’s German word "Mittelalter" – "middle age"), not only as a historiographic term, but also in everyday language.

The German historian Christoph Cellarius (1634 - 1707), in his Historia Univeralis (1702), finally established the traditional division of history into the trias of Classical Age – Middle Age(s) – Modern Age.

One more thing – as you might have gathered, the term "middle ages" had a mainly negative connotation at the time, due to the comparison with the noble, classical age that had ended with the end of the Western Roman Empire. It was not until the age of romanticism around 1800 that the term was used in a positive sense. Especially in Germany, medieval myths and stories gained popularity and were also instrumentalised by German nationalists in their campaign for unification.