01 A PABTIGLE. 11 



1 1 we construct a polygon A of which 



the sides are respectively equal and paral I straight 



line* :**t vert. 



l>t liii.- .t/'uill r. ; u.. nt m magnitad* aod 



the resultant of all the force*. 



maj c that the necessary nd sufficient coo- 



cmiilil.rium of a niiiiil- c* acting uo 



a particle IB, that the point D should coincide wit 



figure Al\/:... /> .should be a mm** 

 polygon. ccs in the fagure are not necessarily all in 



no plan.-. 



The result here obtained mar be enunciated thus: If UM 



ritk*o/<i*v ;u./yv-.'i M*vi in ..r,t, r uv mp* !"''/ . r }> * I : ; 



to tit m<i</mtfa <ffon* acting ol a 



fadirectwiu of the force*, 0** thforct* inV/ /< in ' 



This proposition is called the Polygon of Ik 



Ti Hist carefully notice the conditions 



i tliis proposition is asserted to hold; the forces are sup- 



posed all to act at one txmi/, and are to be represented by the 



of a {x>lygon toim tn order. As an example of the 



ii, suppose a quadrilateral ABCD\ then if forces 



ii may be represented bj- Mi B0 l ' . act at a 



forces will be in equilibrium : forces will not 



..jiiiliWitiiM it r. presented by AH, DC, DC, DA, or by 



J 9 



The direction and magnitude of the resultant may also be 

 mined analytically, as in the following Articles. 



Any number qfjorcet ad on a parttclt tin oax 

 required to find Oe mag***** amd dirtetim of tlmr ** 



forces, and o . the angles 



4 make with a fixed straight lino drawn throogh 



proposed point .light line for the axis 



and one perpendicular v. Then, by 



ay be resolve oos . and / ; , tin a, actsug 



along the axes of x and y respoctiv c other forces may 



