*dā(i)-, *di-

The core idea of this root was:

dividing

It has evolved in various quite different directions, but the theme of dividing is present in most of the offspring.
Here’s a little (incomplete) overview :

• time (“dividing time”)
• tide (“time of water”)
• tidy (originally: “in a timely manner”)
• deal (“divide, distribute”)
• demon (“dealer of destiny” used to be neutral in Greek and Latin)
• democracy (demos originally referred to a “district” of a region or settlement)
• demagogue (“district leader”)
• epidemic (“on a district”)
• pandemic (“across districts”)