Titan was discovered on 25 March 1655 by Christiaan Huygens, an astronomer from the Netherlands. Earlier, in 1610, Galileo Galilei had discovered four of Jupiter's moons. This inspired Huygens: he also wanted to discover new moons. Because Huygens had also improved the telescopes of the time, making them a lot better, he thought he might be able to discover a new moon.
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