This question is quite specific, because I’m trying to write a historical fiction novel where in one scene the character sails to Havana and whilst onshore, witnesses a naval battle between 3 ships. The scene I’m writing is inspired by this historical event:
May 5-6th 1711. This night the 44-gun Thetis of Jean François de Choiseul, compte de Beaupré and former governor of Saint Domingue (Haiti) is intercepted three miles outside Havana by the 60 gun HMS Windsor of Captain George Paddon and the 48-gun Weymouth of Richard Lestock. They batter their French opponents into submission, killing or wounding 65 of 180 crewmembers. Captives are set ashore at the Cuban capital, including the wounded Choiseul, who expires shortly thereafter. Source
So three miles outside of Havana would be this distance
My character uses a spyglass to take a look at the ships, close enough to see them in enough detail that he would be able to determine what kind of ships they are. But, I don’t know if a spyglass would be useless to look at 3 ships that are 3 three miles from shore because I'm not sure if a spyglass from that time would be too weak to see a large ship at that distance, and to me it seems pretty far for a spyglass, let alone the naked eye, and I don’t know how powerful even the biggest spyglass from the period would be for a person to see in great detail, 3 fairly large frigates.
You could easily observe a ship three miles away using a spyglass provided it was a calm and sunny day (smoke from battle and cannon fire would obviously obscure your vision too). You could also easily make a ship out from that distance with your naked eye (though not with any great detail), even against the shoreline which would make a ship harder to spot.
As a general rule, a sail can be spotted on the open ocean at as much as seven leagues distance or just over twenty miles using a spyglass (again assuming good weather and a vigilant lookout). The closer it got the more of it you would be able to see and telescopes were actually much more powerful than most modern binoculars. That's why they're so much longer. If you can see something three miles away with binoculars, you could definitely see it using an early 18th century nautical telescope.
Sources:
The Sea Rover's Practice: Pirate tactics and techniques, 1630-1730 by Benerson Little
Personal experience living next to a bay that's several miles across
