The Laws of Statical Equilibrium. 385 
DB; but F and G are the only forces which 
affect the state of B; consequently parts of 
these forces are destroyed in maintaining this 
equilibriam, and the remaining parts consti- 
tute a quantity K; hence the sum of the 
components is greater than their equivalent. — 
Art. 8. All that has been concluded res- 
pecting F', Gand K, relates to abstract forces 
having no particular ratios or differences ; 
consequently if three right lines be taken pro- 
portionate to these magnitudes, atriangle may 
be formed of them; because any two are 
greater than the third: conversely the three 
sides of any triangle may represent three 
forces in magnitude ; any two of which are 
the components of the remaining one. 
Art. 9. Let AB, CB, fig. 2, including the 
angle ABC, denote two forces, F and G, in 
magnitude and direction; also, suppose BM 
to be the direction of their equivalent: join 
AC meeting BM in M; through B draw PR 
perpendicular to BM; and make AP, CR 
perpendicular to PR. Then as Fis to the 
force in PB, so is AB to PB; and as Gis to 
the force in RB sois CB to RB; but as Fis 
to G, so is AB to CB by hyp.; therefore as 
the force in PB is to force RB, so is PB to 
RB., Now these forces are equal and con- 
trary by Art. 7, hence PB = RB; but BM 
VOL, III. ccc 
