The History of Mathematics: A Brief Course

366 12. MODERN GEOMETRIES

FIGURE 10. Newton's degree-preserving projection.

FIGURE 11. Brianchon's theorem for a circle.

of opposite sides of a hexagon inscribed in a conic meet in three collinear points.

The case of a circle is illustrated in Fig. 11.

2.7. Monge and his school. After a century of relative neglect, projective ge-
ometry revived at the Ecole Polytechnique under the students of Gaspard Monge
(1746-1818), who was a master of the application of calculus to geometry. Klein
(1926, pp. 77-78) described his school as distinguished by "the liveliest spatial in-
tuition combined in the most natural way possible with analytic operations." Klein
went on to say that he taught his students to make physical models, "not to make
up for the deficiencies of their intuition but to develop an already clear and lively
intuition." As a military engineer, Monge had used his knowledge of geometry to
design fortifications. His work in this area was highly esteemed by his superiors