  Today projective geometry does not play a big role in mathematics, but in the late nineteenth century it came to be synonymous with modern geometry. Projective methods had been employed by Desargues (b. 1591, d. 1661) and Pascal (b. 1623, d. 1662), but were later eclipsed by Descartes's method of coordinates. They prospered, however, after Jean-Victor Poncelet (b. 1788, d. 1867) showed that the projective properties of figures furnished grounds of proof that were at least as powerful as, and certainly more intuitive and ostensibly compelling than the Cartesian procedure of setting up and solving equations between numbers representing points. 