PARALLELOGRAM OF FOtCO. 9 



between AKtuu\ AD\ but by mppOM&m the rouliant is AK 

 not between AKtad AB. This U abtostL 



<ame manner we may shew that erery direerioo 



* Alt leads to an absurdity, and therefore the n*ultant 



ilons AD, whether the force* be commensurable or 



incommensurable. 



II. To b ! ^cflMmfafaof tfce resultant. 



'. AClx the directions of the giren 



resultant; take A K opposite to 



AD, and of such a length as to represent the 



magnitude of the resultant Then tin- i rcrs 



icnted by A tlanoe each 



.IE and All as adjacent sides 



gram J ten the 



diagonal . direction of the resultant 



alAMu 



ce AC is in the same stro 



is a parallelogram; and 

 '-F/?-J/>'. I!-;. t 

 'it is represiMiti-d in ;/</'//<>/ as ^ 



liagonafof the parallelogram. 



Tims the proposition called the l\troUdoyram of Forom u 

 established. 



18. II P and Q represent two component 



; at an angle a on a particle, the resultant II is given 

 e equation 



TTfon three force* acting on a pojrMf are I'M *^m"- 

 >n they are re*pecttre?y tn 0* fame proportion as fir 

 of the angle* included by tne directions of tie otter 



For if we refer to the third figure of Art 17 we hare 



"r JttyiAD 



\BD 

 :: sin t VI A': sin DAE: sin DAC. 



