upgrade iMac G4 to 10.5 via firewire

Hi, this is my first time posting, and have been looking around for a solution, but have not yet found one specific to my situation..

I have an old iMac G4, 1.25Ghz, 160GB, 1GB of internal RAM (the 2nd slot is not detecting the other 1GB of RAM), and runs on Mac OS 10.4.11.

I want to install 10.5 on the old iMac, and I believe it meets the requirements.
I have an Mac OS 10.5 Leopard upgrade disc, but it is on a dual layer DVD, which the iMac cannot read.

I have a newer macbook (white/intel) with 10.7.5. I hooked it up to my iMac G4 via firewire and using the macbook as an external drive to run the disk. I guess you call it target disk mode?
The iMac detected the DVD disc, displayed it on the desktop, and I double clicked on the icon 'Install Mac OSX'. The OSX Installer window comes up with a button saying 'restart'. I clicked on it, and let it run. The iMac restarted, but when it reboot, it stayed on the blank white/gray apple screen with the grey apple symbol in the middle. No timer, no other activity/progress.. nothing.. It stayed like that, and the disk in my macbook eventually stopped running, and it didn't do anything for a long while. So I did a hard shut down and rebooted it, thought I'd try it again, and the same thing happened.

Am I missing something? Why isn't it doing anything/upgrading? Why does the iMac screen stay blank w/the grey apple logo?
Is there an easier, more correct way to do this? Please let me know.. Thanks so much!!

Thanks. I just tried that. I clicked on the upgrade disc on the desktop, clicked on the 'Install Mac OSX' icon, and it asked for me to restart the macbook. When it reboot, the startup screen had a keep out symbol, then it disappeared, then a folder with a question mark, then it disappeared, then a progress timer with the grey apple symbol. It then proceeded to startup the macbook regularly, with the install OSX disk on the desktop (back to square one). Any ideas? Thanks again. I really appreciate it.