*178.* Another method of generating a conic is due to Maclaurin.(16) The construction, which we also leave for the student to justify, is as follows: _If a triangle __C’PQ__ move in such a way that its sides, __PQ__, __QC’__, and __C’P__, turn __ around three fixed points, __R__, __A__, __B__, respectively, while two of its vertices, __P__, __Q__, slide along two fixed lines, __CB’__ and __CA’__, respectively, then the remaining vertex will describe a conic._ *179. Descriptive geometry and the second revival.* The second revival of pure geometry was again to take place at a time of great intellectual activity. The period at the close of the eighteenth and the beginning of the nineteenth century is adorned with a glorious list of mighty names, among which are Gauss, Lagrange, Legendre, Laplace, Monge, Carnot, Poncelet, Cauchy, Fourier, Steiner, Von Staudt, Möbius, Abel, and many others. The renaissance may be said to date from the invention by Monge(17) of the theory of _descriptive geometry_. Descriptive geometry is concerned with the representation of figures in space of three dimensions by means of space of two dimensions. The method commonly used consists in projecting the space figure on two planes (a vertical and a horizontal plane being most convenient), the projections being made most simply for metrical purposes from infinity in directions perpendicular to the two planes of projection. These two planes are then made to coincide by revolving the horizontal into the vertical about their common line. Such is the method of descriptive geometry which in the hands of Monge acquired wonderful generality and elegance. Problems concerning fortifications were worked so quickly by this method that the commandant at the military school at Mézières, where Monge was a draftsman and pupil, viewed the results with distrust. Monge afterward became professor of mathematics at Mézières and gathered around him a group of students destined to have a share in the advancement of pure geometry. Among these were Hachette, Brianchon, Dupin, Chasles, Poncelet, and many others.