The rule of marteloio is a medieval technique of navigational computation that uses compass direction, distance and a simple trigonometric table known as the toleta de marteloio. The rule told mariners how to plot the traverse between two different navigation courses by means of resolving triangles with the help of the Toleta and basic arithmetic. Those uncomfortable with manipulating numbers could resort to the visual tondo e quadro (circle-and-square) and achieve their answer with dividers. The rule of marteloio was commonly used by Mediterranean navigators during the 14th and 15th centuries, before the development of astronomical navigation. Etymology The etymology comes from the Venetian language. In his 1436 atlas, Venetian captain and cartographer Andrea Bianco introduced a table of numbers which he called the toleta de marteloio ("table of marteloio"), and the method of using it as the raxon de marteloio ("reason of marteloio"). The meaning of marteloio itself is uncertain. The most widely accepted hypothesis, first forwarded by A.E. Nordenskiöld, is that marteloio relates to "hammer" ("martelo" in Venetian), referring to the small hammer that was used to hit the on-board ship's bell to mark the passage of time. It has been suggested that the -oio suffix implies that marteloio meant not quite the hammer itself nor the hammerer, but rather "the hammering", intending to indicate "the hammering, the din, the racket" from the change of the watch every four hours. As there were many hands on deck during a change of the watch, it would be an opportune moment for the ship's pilot to order a change in bearing (if necessary). Alternative hypotheses (not nearly as accepted) are that "marteloio" is a corruption of mari logio (meaning "rule of the sea"), or from mare tela (meaning "sea network"), or that it derives from the Greek homartologium (όμαρτόλογίον, meaning "companion piece"), or from the Greek imeralogium (ήμερόλογίον, meaning "daily calculation") or that it might be from the northern French matelot, which in turn comes from Breton martolod (meaning "sailors"). Purpose The "rule of marteloio" was used in European navigation in the Middle Ages, most notably in the Mediterranean Sea between the 14th and 16th centuries, although it may have older roots. It was an integral part of navigation by "compass and chart", before the advent of geographical coordinates and the development of celestial navigation in Europe. Medieval navigation relied on two parameters, direction and distance. On board ship, direction