The Laws of Statical Equilibrium. 387 
Fxsine ABC=G sine ABC. 
=‘sine DBC sine DBA 
AP=ABxXcos. PAB; and CR=CBxcos. 
RCB ; hence cos. K=Fx PAB+Gx cos.RCB. 
Now aszZPAB+4RCB=2 ABC, it follows 
that if the directions of F and G converge to 
a point infinitely distant from A, C, the 
angle ABC will become evanescent, and 
the cosine of PAB become=cos. RCB=Ra- 
dius=Unity; hence in this case K=F+G; 
from which we easily infer that whatsoever 
supports a body acted upon by gravity, sus- 
tains the whole weight of it. This is also 
assumed as an axiom by some writers on ma- 
thematics. (vide Emerson.) 
Art. 12. Let AB, CB be the directions of 
two forces F, G, fig. 1; and let DB denotethe 
direction of their equivalent K ; through any 
point L in the line BD, draw any right line 
ST meeting AB, CB in S, T; also draw LV 
any how meeting CB in V; then LBXsine 
LBS=LS<xsine LSB; and LBxsine LBT 
=LT sine LTB=LV sine LVB; hence as 
sine LBT: sine LBS:: LT Xsine LTB: LS 
xsine LSB; but as sine LBT: sine LBS :: 
G: F, Art. 11; therefore as LSXsine LSB: 
LTXsine LTB ::G@: F; for the same reason 
as LSxsine LSB : LVxsine LVB::G: F. 
Art. 18. Suppose ST to be an inflexible 
Moreover 
