"Galileo, like Beeckman also suspected that the speed of light wasn't infinite and made passing references to an experiment involving lanterns in some of his wo

"Galileo, like Beeckman also suspected that the speed of light wasn't infinite and made passing references to an experiment involving lanterns in some of his work." That's some good thinking in that time... any idea what could have made them suspect this back then? There were hardly even newtonean physics, and you can't see with the naked eye that it's a finite speed, so I'd love to know how they reasoned aobut it.