ATlNtJ IN A 1 ! U 



m*nnfr t knowing that the result is true for ; 

 that it is true for a 



II ' are joined together by 



smooth hinges at 4, so as to form a plane 



polygon. Forces set al its of the sides of the 



polygon in the plane of the polygon; the forces act at 



4 to the sides, and are rcs|>ectivclr proportional to the 

 sides in magnitude; shew that, if the forces all act inwards 

 or all vrards, where there is equilibrium, a circle can 



be descr o polygon. 



.1 />' 'in: I represent the polygon. Consider one of thr 

 : ;.; :;;. i ..:-..,: 

 on by a force at the middle 

 point // at right angles to AD. 

 and by actions from the hinges 



a! .1 .11. 1 //. Ti.- ! :::. : ! ' .- 



>portional to AB, and may 

 ]< om ' ' / ' ' i 

 c forces must meet at a 

 t, suppose A"; then by re- 

 solving parallel to AD, we find 

 that the actions at A and B 

 must be equal; we will denote 

 ilcsolvc the forces st right angle* to ABi thus 

 lt.AD**2R&\ii A 



rod DC is eaual and opposite to 

 c we obtain in the same manner 



.in .!' /; 



sin CBL m so " srazB* 



:.< shews that KDL touches at B the circle described 

 round ADC. 



AK touches at A the circle described 





m*ABK AB 



