Tom is correct. Short of ridiculously expensive adapters, it is impossible.
To recap in short form:
Older computers only have analog video out. On the Mac, this is Apple's proprietary DB-15 plug. Apple's Cinema Displays all use digital video. The very first 22" model, and all of the Aluminum models use DVI, most of the 'Clear lucite' models use Apple's custom ADC plug. In order to turn the analog video out into digital video, you need an expensive adapter.
Long form:
Modern video cards generally have a DVI plug that contains both analog and digital signals. For a digital monitor, you plug the DVI connection directly in. For an analog (VGA) monitor, you use an adapter that connects the analog pins in the DVI plug to the appropriate pins in the VGA plug. The reverse is not possible, because VGA and Apple DB-15 video ports to not contain a digital signal, so there is no digital signal to 'pass through'. All cheap "DVI to VGA" adapters are the first kind. To pass through the analog signal from a video card's DVI plug to an analog VGA monitor.