internet connection on 2 computers

Euclides(=computer1) uses linux(Redhat 5.2). On this computer 2 NE2000 NICs are installed. Eth0 is used for my cable connection and is set by DHCP. Eth1 (192.168.0.100) is the is my connection to Archimedes(=computer2).

Euclides can go on the internet and can ping Archimedes (192.168.0.2).
Archimedes can ping 192.168.0.100.

Now my question: Archimedes can not get on the internet. Why?

more info:
--
ifconfig:
lo        Link encap:Local Loopback  
          inet addr:127.0.0.1  Bcast:127.255.255.255  Mask:255.0.0.0
          UP BROADCAST LOOPBACK RUNNING  MTU:3584  Metric:1
          RX packets:25 errors:0 dropped:0 overruns:0 frame:0
          TX packets:25 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0

eth0      Link encap:Ethernet  HWaddr 00:80:C8:FC:B8:F5  
          inet addr:10.67.228.13  Bcast:10.67.231.255  Mask:255.255.252.0
          UP BROADCAST NOTRAILERS RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:4055 errors:0 dropped:0 overruns:0 frame:0
          TX packets:1797 errors:0 dropped:0 overruns:0 carrier:0
          collisions:2
          Interrupt:11 Base address:0xff40

eth1      Link encap:Ethernet  HWaddr 00:C0:26:80:69:3B  
          inet addr:192.168.0.100  Bcast:192.168.0.255  Mask:255.255.255.0
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:28 errors:0 dropped:0 overruns:0 frame:0
          TX packets:13 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0
          Interrupt:10 Base address:0xff20

route -n:
Kernel IP routing table
Destination     Gateway         Genmask         Flags Metric Ref    Use Iface
192.168.0.0     0.0.0.0         255.255.255.0   U     0      0        1 eth1
10.67.228.0     0.0.0.0         255.255.252.0   U     0      0        1 eth0
127.0.0.0       0.0.0.0         255.0.0.0       U     0      0        0 lo


Archimedes:
IP   192.168.0.2
SUB 255.255.255.0
Gateway: 192.168.0.100