402 DEMONSTRATION of the 
the force M: Confequently the force W will have the fame ten- 
dency to turn the lever round F as the force w; and this will 
hold true, whether the arms AF, FB, are ftraight or curvili- 
neal, provided that they are both of the fame form. 
Prop. III.—Jf a force acts in different directions at the same potnt 
in the arm of a lever, its tendeney to turn the lever round its centre 
of motion, will be proportional to the perpendiculars let fall from 
that centre on the lines of direction in which the force is applied. 
Ler AB, (fig. 4.) be the lever, and let the two equal forces 
BM, Bm, act upon it at the point B, in the direction of the lines 
BM, Bm. Draw BN, Bz, refpectively equal to BM, Bm, and 
forming the fame angles with the line PB » perpendicular to AB. 
To BM, Bm, BN, Bz, produced, draw the perpendiculars AY, Ay, 
AX, Ax. Now, the fide AX = AY, and Ax = Ay, on account 
of the equality of the triangles ABX, ABY; and if M/Z, Ma, 
be drawn perpendicular to Ba, the triangles ABY, BM/, will 
be fimilar, and alfo the triangles ABy, Bm: Hence we ob- 
tain 
AB: AY = BM: Bd, and 
AB: Ay= BM: Ba 
Therefore, ex equ, AY: Ay= BJ: Ba. 
Complete the parallelograms BM oN, Bmwn, and B/, Ba will 
be refpectively one-half of the diagonals Bo, Bw, 
Now let two equal forces BM, BN, act in thefe diredtions 
upon the lever at B, their joint force will be reprefented by 
the diagonal Bo, and confequently one of the forces BM will 
be 
