The two British historians mentioned are June Goodfield and Stephen Toulmin. They visited the tunnel at least twice, in 1958 and 1961. You can read their report [here](https://www.journals.uchicago.edu/doi/abs/10.1086/349924?journalCode=isis).  As long as the diagonals are of equal length you ensure right angles at the corners. It is worth noting that after the collapse of the Roman Empire, tunnel-building virtually ceased for 1,000 years, resuming in the 16th century in Moscow, where Tsar Ivan Grozny (the Terrible) built an immense labyrinth of tunnels apparently used as catacombs. More recent measurements have calculated the longitudinal distance of the tunnel to be 1,043 meters. ### Dioptra The word *dioptra* means simply ‘something to look through’. No actual physical example of a dioptra from ancient greece has yet been found. The name is first applied to the simplest of devices for sighting by Euclid in the early third century BC.  *Three stages in the evolution of the dioptra, from a simple horizontal sight, to a multi-angle measuring tool* The tunnel of Samos was definitely a long tunnel by the standards of the time but it was not the longest tunnel of its time. For instance, the drainage tunnel of Lake Nemi in Italy was over 1600 meters and was built around 500 B.C.  *Drainage tunnel of Lake Nemi* Why would you need pillars to construct the right angles? Can' you just keep track of the elevation? One obvious concern would be water supply during a siege. If water was being supplied by an exposed aqueduct the enemy would be able to halt water supply. #### Diagram of water channel  #### Picture of water channel (now covered with safety protection)  More recent studies point to the fact that this change of course was likely due to some geological problem. In fact, a recent survey indicated some risk of rockslides in the north part of the tunnel even today. ### Herodotus on Samos > “I have dwelt the longer on the affairs of the Samians, because three of the greatest works in all Greece were made by them. One is a tunnel, under a hill one hundred and fifty fathoms high, carried entirely through the base of the hill; with a mouth at either end. The length of the cutting is seven furlongs- the height and width are each eight feet. Along the whole course there is a second cutting, twenty cubits deep and three feet broad, whereby water is brought, through pipes, from an abundant source, into the city. The architect of this tunnel was Eupalinos, son of Naustrophus, a Megarian. Such is the first of their great works; the second is a mole in the sea, which goes all round the harbour, near twenty fathoms deep, and in length above two furlongs. The third is a temple; the largest of all the temples known to us, whereof Rhoecus, son of Phileus, a Samian, was first architect. Because of these works I have dwelt the longer on the affairs of Samos.” *Herodotus, Histories, III translation by George Rawlinson* ### Groma The *Groma* was a fairly simple instrument, possibly of Greek origin, which became almost the trademark of the typical Roman land surveyor. Its function was limited to sighting and setting out straight lines and right angles. The principle is straightforward enough. A horizontal cross, its arms at right angles, was carried on a vertical support, and from the end of each of the four arms hung a cord or plumb line tensioned by a bob. The surveyor sighted across one pair of these cords to project a straight line, and across another pair to set out a right angle.  *Depiction of a surveyor using a Groma* ### Two ended construction vs Shafted tunnels In antiquity, the majority of tunnels used to transport water were "shafted tunnels". In a shafted tunnel a series of well-like shafts was constructed from the surface and their feet were linked together by relatively short tunnels underground. This technique was used extensively in Persia for irrigation purposes (where these tunnels are called *qanats*). In Samos, the underground conduits bringing water from the source to the main tunnel and from its lower end to the town are shafted tunnels. The advantage of shafts is that each of them increases the number of working faces by two. Despite the extra material to be removed shafts speed up the work, and the connecting tunnels, because they are relatively short, are at less risk of missing each other. Shafts also provide for easy removal of spoil, for improved ventilation, and for access for maintenance once the tunnel is operational.  #### Thales of Miletus Even tho Euclid’s elements was only written some 200 years later, some of the inhabitants of Samos likely contacted with Thales of Miletus (ancient Miletus was about ~50 miles off Samos).  Thales of Miletus was a pre-Socratic Greek philosopher recognized by many as one of the first individuals in western civilization to engage in *scientific philosophy*. Thales travelled extensively in Egypt and was familiar with the knowledge of Babylonia. He was known for his innovative use of Geometry. He understood similar triangles and right triangles and used this knowledge for practical purposes. He was able to calculate the height of the pyramids by measuring the shadow at the hour of the day at which it is equal in length to the body projecting it.