The problems involved in determining ones position on the surface of the Earth were well known to the Greeks in antiquity, the first people to produce mathematical cartography. Determining latitude, that is one position north or south relative to the poles or the equator, is a comparatively simple mathematical-astronomical procedure that is basically also the same procedure as that for determining local time. Local time is determined to be noon or mid-day when the sun is at its highest point in the sky. Determining longitude, that is ones position east or west of a given fixed point on the equator (Ptolemaeus the father of mathematical cartography used the meridian through the Canary Islands as his fixed point), is not so simple. The Greeks already knew that if one could determine the local time simultaneously for two different points then one could also determine their longitudinal separation. As the equator is a circle divided into 360° (a standard introduced by the Greeks) and the Earth rotates once in 24 hours then four minutes difference in time is equivalent to one degree difference in longitude (360° longitude is equivalent to 24 X 6o minutes time). The problem is that one can’t be in two places at once!
During the Renaissance three different methods where proposed that enabled sailors, cartographers and surveyors to get around this problem and to be able to accurately determine their longitude, in what follows I will sketch those three methods and their proposers.