(Ibid. 3) "You shall not light a fire in all of your dwellings": From (Exodus 34:21) "From plowing and harvesting shall you rest," we derive: Rest from plowing at the time of harvesting, i.e., that one rests from the eve of shemitah to shemitah (i.e., he may not eat on shemitah what he has harvested on the eve of shemitah). I might think that just as he rests from the eve of shemitah to shemitah, so he rests from the eve of Sabbath to Sabbath.
Someone Might Extend This Logic to the Sabbath
Mekhilta Tractate Shabbata 2:8