With regard to the above, it may be interesting to consider the “Delian Problem,” a legend (Theon of Smyrna) about a disastrous pestilence on the Isle of Delos. The oracle of the god Apollo declared that the god wanted a cubic marble altar built for him, twice the size of the previous one. The inhabitants built a new cube by doubling the dimensions of the previous altar, but the pestilence continued. This was because, obviously, the new cube was eight times the size (or volume) of the old one, and not twice the size.

The problem was solved by Eratosthenes with the invention of the mesolabium. The word “mesolabium” comes from the ancient Greek words μεσoς (middle) and λαμβανω (to take). The mesolabium makes it possible to graphically compute two mean proportional line segments x and y between two given line segments a and b...

You do not currently have access to this content.