College. Von Staudt's geometry of position. was for a long time disregarded, mainly, no doubt, because his book is extremely condensed. An impulse to the study of this subject was given by Culmann, who rests his graphical statics upon the work of von Staudt. An interpreter of von Staudt was at last found in Theodor Reye of Strassburg, who wrote a Geometrie der Lage in 1868.
Synthetic geometry has been studied with much success by Luigi Cremona, professor in the University of Rome. In his Introduzione ad una teoria geometrica delle curve piane he developed by a uniform method many new results and proved synthetically all important results reached before that time by analysis. His writings have been translated into German by M. Curtze, professor at the gymnasium in Thorn. The theory of the transformation of curves and of the correspondence of points on curves was extended by him to three dimensions. Ruled surfaces, surfaces of the second order, space-curves of the third order, and the general theory of surfaces have received much attention at his hands.
Karl Culmann, professor at the Polytechnicum in Zürich, published an epoch-making work on Die graphische Statik, Zürich, 1864, which has rendered graphical statics a great rival of analytical statics. Before Culmann, B. E. Cousinery had turned his attention to the graphical calculus, but he made use of perspective, and not of modern geometry.[62] Culmann is the first to undertake to present the graphical calculus as a symmetrical whole, holding the same relation to the new geometry that analytical mechanics does to higher analysis. He makes use of the polar theory of reciprocal figures as expressing the relation between the force and the funicular polygons. He deduces this relation without leaving the plane of the two figures. But if the polygons be regarded as projections of lines in space, these lines may be treated as recipro-
