In your laptop's network settings, configure your Ethernet card with a static ip in the same range subnet as your miner.
Example: If your miner is at 192.168.1.99. Set your computer to something else 192.168.1.34
Now you will have access to your miner with your internet browser.
Yes this is correct. I was used MAC OSX with S3 last year. May be you have a difficulty to find networking settings in OSX. Open System Preferences and look for Network icon. On the left side choose Ethernet and there is a settings on the right side of panel. Just change the value in the Configure IPv4 from DHCP to manual address and put IP mentioned above.
I recommend to switch your S3 for using DHCP and then switch back you Mac to DHCP too. Next time will work without any changes to network configuration.