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 by projection of the figures. The projection is not effected here by parallel rays of prescribed direction, as with Monge, but by central projection. Thus perspective projection, used before him by Desargues, Pascal, Newton, and Lambert, was elevated by him into a fruitful geometric method. In the same way he elaborated some ideas of De Lahire, Servois, and Gergonne into a regular method—the method of "reciprocal polars." To him we owe the Law of Duality as a consequence of reciprocal polars. As an independent principle it is due to Gergonne. Poncelet wrote much on applied mechanics. In 1838 the Faculty of Sciences was enlarged by his election to the chair of mechanics.

While in France the school of Monge was creating modern geometry, efforts were made in England to revive Greek geometry by Robert Simson (1687–1768) and Matthew Stewart (1717–1785). Stewart was a pupil of Simson and Maclaurin, and succeeded the latter in the chair at Edinburgh. During the eighteenth century he and Maclaurin were the only prominent mathematicians in Great Britain. His genius was ill-directed by the fashion then prevalent in England to ignore higher analysis. In his Four Tracts, Physical and Mathematical, 1761, he applied geometry to the solution of difficult astronomical problems, which on the Continent were approached analytically with greater success. He published, in 1746, General Theorems, and in 1763, his Propositiones geometricœ more veterum demonstratœ. The former work contains sixty-nine theorems, of which only five are accompanied by demonstrations. It gives many interesting new results on the circle and the straight line. Stewart extended some theorems on transversals due to Giovanni Ceva (1648–1737), an Italian, who published in 1678 at Mediolani a work containing the theorem now known by his name.