|MadSci Network: Astronomy|
Up until the 17th century, even the new Copernican astronomers like Kepler and Galileo--although they realized the Sun, not the Earth, was the center of the Solar System--thought the stars were something different from the Sun or the planets. It wasn't until later in the century that philosophers like Rene Descartes realized that, if seen from a great distance, the Solar System would be invisible and the Sun would be just a point of light--just like a star. The next logical step was concluding the Sun was a star, too.
When spectroscopy was invented in the 19th century, it was possible to determine the chemical composition of the Sun, as well as other stars, demonstrating conclusively that the Sun was part of a particular family of stars known as "yellow dwarfs".
Here's a link to Rene Descartes' illustration from his 1644 book Principia philosophiae showing how he percieved the stars and other solar systems as forming.
You'll find the whole site a good intoduction to the history of solar physics.
Try the links in the MadSci Library for more information on Astronomy.