The short answer is yes.
If you want to be able to use both pcs independently you should get a router.
The cheper option is to network the 2 pcs,only problem with this is pc with internet connection has to be on to use 2nd pc.
Fujitsu Lifebook P727 laptop review
Best of the Grad Shows 2017: University of the West of England (UWE)
Best value Mac: Which is the best £1249 Mac to buy
Les meilleures GoPro 2017