Measuring a country with triangles
Measuring long distances on the ground with chains and rods piles up errors quickly, and hills, rivers and forests make it slower still. Triangulation avoids most of the trouble. A surveyor measures one baseline with great care on level ground, then fixes a distant point by measuring the angles to it from both ends of the line. Each new point forms a triangle with two known ones, and the process continues in a chain. Angles can be measured accurately over long distances far more easily than lengths can.
Early work
The Dutch mathematician Willebrord Snellius used the method in the 1610s on a chain of triangles between Alkmaar and Bergen op Zoom. He published the results in 1617 in a book called Eratosthenes Batavus, a reference to the ancient Greek who first estimated the size of the earth. His aim was to calculate the earth's circumference.
National surveys
In France the Cassini family led the first survey of an entire country, work that ran for much of the eighteenth century and involved four generations of the family. The resulting map, the Carte de Cassini, was built on a triangulation of the whole kingdom.
Britain followed in the 1780s. General William Roy measured a baseline across Hounslow Heath in 1784, and from it a triangulation was carried across the Channel to link the Royal Observatory at Greenwich with the Paris Observatory. The Board of Ordnance took the work over, and the Ordnance Survey was founded in 1791.
Triangulation remained the basis of national mapping until satellite positioning replaced it in the late twentieth century. Many of the concrete trig pillars built for the retriangulation of Britain from 1936 onward are still standing on hilltops.