Hmmm, 'The Baby' might not really be the FIRST analog computer after all. There is an OOPArts (Out Of Place Artifact) called the ‘Antikythera mechanism’ which might get that prize. I first read about this OOPA in a book: The Ancient Puzzle of Man by Donald Chittick. The cover shown on the left is of the book I read, but I think there is a later and updated edition now out, so if you decide to get it and you realllllly should, look for the updated edition.
Anyway, as noted in Chittick's book, it was “an analog computing device or ‘computer’ (that) was recovered from a ship which had sunk in the Aegean Sea in the first century B.C. ...”
To read more about this Antikythera mechanism, CLICK HERE
And to read even more and to see additonal pictures, CLICK HERE.