Fundamental Property of thee LEVER. 399 
In Prop. II., which is totally independent of the firft, the de- 
monftration is general, and extends to any proportion between 
the arms. 
‘In Prop. III. the property is eftablifhed, when the forces act 
in an oblique direction, and when the lever is either rectilineal, 
angular, or curvilineal. In the demonftrations which have ge- 
nerally been given of this laft propofition, the oblique force has 
been refolved into two, one of which is directed to the fulcrum, 
while the other is perpendicular to that direction. It is then 
affumed, that the force directed to the fulcrum has no tendency to di- 
sturb the equilibrium, even though it acts at the extremity of a bent 
arm; and hence it is eafy to demonftrate, that the remaining 
force is proportional to the perpendicular drawn from the ful- 
crum to the line of direction in which the original force was 
applied. As the principle thus affumed, however, is totally in- 
admiffible as an intuitive truth, we have attempted to demon- 
ftrate the propofition without its affiftance, 
Prop. 1.—Jf one arm of a straight lever is any multiple of the other, 
a force acting at the extremity of the one will be in equilibria with 
a force acting at the extremity of the other, when these forces are 
reciprocally proportioned to the length of the arms to which they 
are applied, 
Let AB (PiaTE XI. fig. 1.) be a lever fupported on the two 
fulcra F,f, fo that Af=fF =FB. Then, if two equal weights 
C, D, of 1 pound each, be fufpended from the extremities A, B, 
they will be in equilibrio, fince they act at the end of equal arms 
Af, BF ; and each of the fulcra f, F, will fupport an equal part of 
the whole weight, or r pound. Let the fulcrum f be now remo- 
ved, and let a weight E, of 1 pound, aé upwards at the point 
Jf; the equilibrium will ftill continue ; but the weight E, of 1 
pound, acting upwards at f, is equivalent to a weight G of 1 
pound, acting downwards at B. Remove, therefore, the weight 
E, 
