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Eyeglasses were invented in AD 1290. Telescopes were invented by AD 1608. Thats basically three centuries before someone put these pieces together. Fundamentally, there's nothing stopping someone from inventing the telescope at any point after AD 1290 (we can be even more assertive and suggest that earlier lenses would have done the job just fine, but baby steps). So, let us suppose that the telescope is developed in the early 14th century - at least by AD 1340, just to give us a cutoff date. In case there's any confusion, I'm suggesting a refracting telescope.

The first impact, I imagine, would be maritime, just like in our world. I'm inclined to think that it would be invented in Italy, in this time period, so that could give the Italian maritime Republics a further leg up in naval matters, both commercial and military. I'm quite curious what the overall effect would be on exploration - in our history, the telescope came about well after the discovery of the New World. Here, the telescope would predate all the great European voyages of Exploration.

Of course, there's also the impact it would have on astronomy. Again, here we see the telescope predating the great astronomers such as Copernicus, Brahe, and Kepler, rather than entering the stage during Kepler's and Galileo's time. Assuming that the telescope is used to astronomical ends relatively quickly, we have an interesting situation here. The scholastic movement is in the middle of the process of digesting Thomism and its amendments to the Aristotelian framework into the philosophical and theological worldview of Christian Europe, and we're two centuries before the Reformation, and the religious strife that would color the astronomy of our 17th century.

Oh, and we’re likely to get microscopes around the same time, as well. We’ll assume within 25 years of the telescope.
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