X \.\\1 GEOMETRICAL STATICS. 



of special by that of universal causation (Philosophies naturalig principia 

 mathematica. London, 1687). 



Varignon in his "Projet (Tune noundlt mecanique," in the same year (1687), 

 and independently of Newton, applied for the first time the general princi- 

 ple of the composition of motions. From this he passes, in the Noutn 

 mecanique ou statique, dont le projet fut donne en 1087 (published after 

 his death, Paris, 1725), by means of the axiom that " les effets sont toujours 

 proportionnels d leura causes ou forces productriccs " to the composition of 

 forces also. 



The Statique of Varignon is purely geometrical. He postulates nothing 

 beyond books 1-6 and 11 of Euclid, and even explains the significance of 

 + and signs. In this work, the first founded upon the parallelogram of 

 motion and of forces, we find also the force and equilibrium polygons 

 (Funiculaire, Section II.), to the application and development of which 

 almost the whole of Graphical Statics is to be attributed. Varignon recog- 

 nized the value of the equilibrium polygon, and gave it as the seventh of 

 the simple machines. 



After the great Interim of Geometry, Monge wrote a Traite eUmentairs 

 de Statique (Paris, 1786). The work claims to contain for the first time 

 everything in statics which can be synthetically deduced. In a later edi- 

 tion we learn that synthetical statics must be taken up as preliminary to 

 analytical, just as elementary geometry before analytical geometry. Thus 

 the work of Monge contains the necessary preparation f or Poissorfs "Traite 

 de mecanique " (Paris, 1811). 



The greatest influence upon the development of geometrical statics was 

 exercised by Poinsot. By the introduction of force pairs, he solved in the 

 most elegant manner the fundamental problem of any number of forces 

 acting upon a body (Elements de Statique, Paris, 1804, and Memoire tur 

 la composition des moments et des aires dans la mecanique}. 



Chasles completed the solution by the proof that the contents of the 

 tetrahedron, which is determined by the resultant forces, is constant, how- 

 ever the forces may be composed. 



In the hands of Mobius, geometry and geometiical statics were most com- 

 pletely developed. 



Of the greatest importance, for later applications, was the introduction 

 of the rule of signs. 



The germ of this had existed already in the preceding century.* Mobius 

 recognized its significance, extended it to the expression of the contents of 

 triangles, polygons, and three-sided pyramids, and applied it systemati- 

 cally (Barycentrischer Calcul. Leipzig, 1827). 



A new impulse, extended field of action, and numerous additions were 

 given to geometrical statics by the Graphical Statics of Culmann. 



* Mobius alludes to this, and we find, for example, in Kastner ( OecmetriscTu 

 Abhandlungen, I. Saml., 1790, p. 464), the equation A B + B A = o. 



