Two Modems on One Cable - Good Idea???

[Kosovo Survivor]

Hi folks,
Before I subscribed to the only (competition free) cable internet provider
in Ottawa, Canada, I had another cable modem just sitting under the desk.
Rogers Cable provided me their own cable modem and a nic.

I had this idea last night, since, everyone in my apt. building shares the
same cable for TV and internet, could I share the cable provided to me
between two cable modems? I do have a spare nic for the other cable modem.

My plan is connect the CABLE-TV cable to two CABLE-MODEMS using a
2-WAY-SPLITTER, then each of the CABLE-MODEMS to the NIC cards hosted on
one linux box.

But, I don't know if this is possible.
Would the second modem SHARE the bandwidth of the first or would it have
another (extra) bandwidth, doubling the bandwidth?

I don't have any experience with cable modems, so don't mind me expressing
an idea like this.

Kosovo Survivor