This is a fascinating article from a 2004 issue of Engineering & Science that investigates the “Tunnel of Samos”, constructed on the eponymous Greek island 2500+ years ago.
One of the greatest engineering achievements of ancient times is a water tunnel, 1,036 meters (4,000 feet) long, excavated through a mountain on the Greek island of Samos in the sixth century B.C. It was dug through solid limestone by two separate teams advancing in a straight line from both ends, using only picks, hammers, and chisels. This was a prodigious feat of manual labor. The intellectual feat of determining the direction of tunneling was equally impressive. How did they do this? No one knows for sure, because no written records exist. When the tunnel was dug, the Greeks had no magnetic compass, no surveying instruments, no topographic maps, nor even much written mathematics at their disposal. Euclid’s Elements, the first major compendium of ancient mathematics, was written some 200 years later.
Since the engineers of the time dug the tunnel from both directions simultaneously, meeting in the middle, it required advanced knowledge of surveying and mathematics techniques to get the geometry just right. An inaccurate elevation, direction, or location by even a couple of degrees or inches would mean widely missing the mark to join the two tunnels. The author investigates a few possible methods for how the ancient Greeks could’ve completed the feat. A few techniques and simple tools would’ve been required, but a research team was able to recreate a potential method. Amazing that with such primitive technology they could’ve completed such a monumental project.