Early Modern Science - Europe
Tycho Brahe (He looks funny because his nose got
cut off in a duel and he wore a false one made of brass.)
By 1600 AD the fashion for building new observatories that had swept from China west through Samarkand to Istanbul finally reached Prague, just west of the Ottoman Empire in the Holy Roman Empire. The emperors paid for these observatories in order to get accurate horoscopes from astrologers.
In 1602, the astronomer Tycho Brahe, working a little south of Copernicus (and just outside the Ottoman Empire) in his new observatory at Prague, reversed the progress made by Copernicus, and returned to the idea that the sun went around the earth.
In the late 1500s AD, the telescope was invented, and in 1610, in Padua, Italy, Galileo used one to look for parallax in the stars - but his telescope wasn't strong enough for that. What Galileo did see was the moons of Jupiter, moving around Jupiter. If the moons of Jupiter went around Jupiter, then it began to seem more likely that Earth's moon went around the Earth, and that the Earth and Jupiter were the same: both planets that went around the sun. Aristarchus had been right.
In 1628, William Harvey in England did many dissections - cutting dead people open - and was able to show exactly how the heart and the lungs worked together to circulate air through people's bodies. This was not a new idea - Ibn Nafis had already laid it out in the 1200s - but Harvey described it much more completely.
In 1629, Giovanni Branca published a description of a steam engine, possibly building on the work of Taqi al-Din in the 1550s.
In 1637, Rene Descartes published a more complete version of Oresme's medieval work showing the relationship between Greek geometry and Islamic algebra - that these were two different ways of representing the same natural world. Fermat took this a step further, showing that the connection between geometry and algebra worked not just for two-dimensional equations but also for three dimensions.
In 1650, John Greaves translated two works of the Ottoman mathematician Ali Qushji into Latin, but I don't know if this served any purpose mathematically or was just for historical purposes.