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VGA, DVI, and HDMI connections all require a timing signal generated external to the video signal. A monitor needs this timing signal to function properly.
The ATI 5870 only has two timing signal generators, even though is has four outputs: 2xDVI, 1xHDMI, and 1xDP (DisplayPort). Thus, in order to use three monitors with this GPU, one needs to utilize the DP connection.
There are actually two types of DP connections: DP and DP+. DP+ connections are capable of passing through signals for other connection types (such as DVI and VGA). DP-only connections cannot do this. If one were to connect an inexpensive passive DP-to-DVI adapter to a DP+ port and a DVI monitor, it would work properly. But if one tries the same thing with a DP-only port, it will not work. This is a why an "active" adapter is needed; it actively transcodes a DP signal into DVI (or some other connection standard). These adapters must be powered; most (all?) use a simple USB connection.