In 1737, Father du Chatelard, an associate member of the Académie des beaux-arts de Lyon, wrote that geometry "is undoubtedly the most useful and, at the same time, the most enjoyable of all branches of mathematics". He defined it as "the art of measuring every kind of extent". Indeed, the Age of Enlightenment offered a wide variety of distances to survey. The measurement of horizontal, inclined or vertical lines was known as longimetry. It might involve measuring a distance across a field, the height of a tree or building, etc. Determining the depth of a well could be useful, as it made it possible to assess the remaining water level. Before crossing a river or building a bridge, one might also need to determine its width. Drawing up a local map first required the distances between towns, villages and other points essential to depicting the area. In warfare, determining the distance between the besiegers' camp and the enemy fortifications, and estimating the height of the towers of a besieged town, made it possible to adjust the sights of the guns and avoid needlessly wasting projectiles. Finding the distance between a harbour and a fleet of ships looming on the horizon also helped organize the city's defence.
Accessible and inaccessible distances --------------------------------------
There were many kinds of lines to measure, serving many different purposes. The methods used also varied according to their nature. Some distances were accessible: one could reach them and measure them directly.
However, the width of a pond or forest, or the height of a besieged tower, could not be measured directly. The far edge of a forest could not be seen from the ground and, depending on the density of the vegetation and the terrain, a surveyor might be unable to use his instruments. Moreover, taking measurements while moving across a body of water was hardly convenient, while neither the foot nor the top of a tower was accessible during a siege. Let's begin with the methods and tools used to measure an accessible distance.
With simple tools ----------------------