According to the received view, the first spyglass was assembled without any theory of how the instrument magnifies. Galileo, who was the first to use the device as a scientific instrument, improved the power of magnification up to 30 times. How did he accomplish this feat? Galileo does not tell us what he did. We hold that such improvement of magnification is too intricate a problem to be solved by trial and error, accidentally stumbling upon a complex procedure. We construct (...) a plausibility argument and submit that Galileo had a theory of the telescope. He could develop it by analogical reasoning based on the phenomenon of reflection in mirrors—as it was put to use in surveying instruments—and applied to refraction in sets of lenses. Galileo could appeal to this analogy and assume Della Porta’s theory of refraction. He could thus turn the spyglass into a revolutionary scientific instrument—the telescope. (shrink)