You can do that, but it means that you need to configure the PC with internet connection as a router. How you do that depends entirely upon the operating system you are using (Windows, Linux, Apple-OSX).
rubberman
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its sounds like you are trying to share the internet connection through one computer. As rubberman is suggesting, why not have an Internet Router connected between the LAN and your provider. This way, each PC goes through the router to access the Internet. In your scenario, every other host on the network would have to get their access through this one PC.
JorgeM
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