Can someone explain to me how men in the 17th century figured out that light has a finite speed?

Say a jovian moon ped behind Jupiter at a certain time T1. Having observed the moon, they could calculate when the moon light would re-appear on the other side of the planet T2. T2-T1 was never what it it should have been - the most marked discrepancy occurred when the earth was opposite Jupiter on the other side of the sun. Someone finally realized that the major time discrepancy occurred when the light had to cross the distance of earth's orbit to get to us and that this crossing did not occur at infinite velocity