It sounds like your mini is the PowerPC version (G4). You can check what processor is in the computer using Apple Menu -> About This Mac.
Information on the latest versions that different OSs from that period can use can be found at [url]http://apple.stackexchange.com/questions/43664/what-is-the-latest-version-of-safari-that-runs-on-powerpc-ppc[/url]
Actual downloads for older versions of Safari are available at [url]http://www.oldapps.com/mac/safari.php[/url]
The biggest difference between time and space is that you can't reuse time.