1) In the Renaissance, most philosophers including René Descartes and Johannes Kepler believed that the speed of light was infinite.
2) Christiaan Huygens and Robert Hooke proposed the wave theory of light, which implied that light must travel at a finite speed through a medium.
3) Galileo Galilei was skeptical of the infinite speed theory and tried an experiment to measure the speed of light using lanterns on hilltops 1 mile apart, but the speed was too fast to measure with the crude instruments of the time.