After a quick look my guess is that this circuit takes the log of the two inputs and then does a simple sumation. I forget the exact formula but when you take the log of something you can change multiplies into addition and then inverse log.
If you want mode insite into the circuit look up log amplifiers on google.
Hi Electronist,
Most of us at this superb site just use a Multiplier or Log IC instead of your pile of parts and let the IC manufacturer worry about how they work. I vaguely remember seeing your circuit in about 1975.