1764-1818 Those studying at the officer school were exclusively drawn from the aristocracy, so he was not allowed admission to the institution itself. His manual skill was highly regarded, but his mathematical skills were not made use of. Nevertheless, he worked on the development of his ideas in his spare time. At this time he came to contact with
Charles Bossut, the professor of mathematics at the École Royale du Génie. "I was a thousand times tempted," he said long afterwards, "to tear up my drawings in disgust at the esteem in which they were held, as if I had been good for nothing better." A fort should protect the defenders. That is, from any point on the terrain outside, there cannot be direct
line of sight into defending positions inside. This safe space is called the
defilade, and could be pictured as follows: Place a lamp at each location where the attacker may fire, then the shadow space cast by the walls is the
defilade. The
défilement is a kind of
defilade, where the attackers may be raised above the ground. This would protect the defenders against artillery placed on raised platforms built during a siege.
Defilade and
défilement would avoid
enfilade. A particularly dangerous kind of artillery fire is
enfilade fire. The top edge of a fort wall is a polygonal line. On each segment, defenders can move. If an attacker can place an artillery on a point along that straight segment, then the attacker can shoot directly along the line, and hit all the defenders on that line segment. Computing the
défilement is a complex problem, since to counter the development of artillery, European forts was becoming increasingly complicated in their geometry, as represented by the
star fort. The famous military engineer
Vauban proposed a slow and manual process to measure the
défilement. Soldiers would be sent to strategically critical positions outside the fort. At each position, they would measure the shape of the polygonal line created by the upper edge of the
curtain wall. This creates a sequence of triangles that together create a polygonal dome in space. The space under the polygonal dome would then be the
défilement of the walls, within which the defenders are safe from direct lines of sight. Other than the observational method, there was also an established method for doing this, which involved lengthy calculations that would take a week, but Monge devised a way of solving the problems by using drawings. At first his solution was not accepted, since it had only taken two days, but upon examination the value of the work was recognised, and Monge's exceptional abilities were recognised. The essence of Monge's method was to graphically construct visibility cones. For example, consider a hemisphere
H, with a raised point
p above
H, representing a point on the fortification wall. The visibility cone at
p is a cone that is tangent to
H and apexed at
p. Continuing his researches, Monge began the subject descriptive geometry, which was kept as a French military secret for years. After Bossut left the École Royale du Génie, Monge took his place in January 1769, and in 1770 he was also appointed instructor in experimental physics. His remains were first interred in a
mausoleum in
Le Père Lachaise Cemetery in Paris and later transferred to the
Panthéon in Paris. A [//upload.wikimedia.org/wikipedia/commons/3/35/GaspardMongeStatueBeaune.jpg statue] portraying him was erected in Beaune in 1849. Monge's name is one of the
72 names inscribed on the base of the Eiffel Tower. Since 4 November 1992 the
Marine Nationale operate the
MRIS Monge, named after him. == Work==