28^, 



ON THE FUNDAMENTAL PROPERTY OF THE LEVER. 





AxJcwa. 



Pra^j&iifiatis 



mental property of tlie lever, which shall be at the same 

 time simple and legitimate, we shall assume only one prin- 

 ciple, which has been universally admitttjd as axiomatic, 

 namely, that equal and opposite forces, deling at the extre- 

 mities of the equal arms of a lever, and at equal angles to 

 these arijis, will be in equilibrio. With the aid of this axiom, 

 the fundamental projit-rty of the lever may be tslablished by 

 the three following propositions. 



Ill Piop. I, the property is deduced in a very simple 

 manner, when the arms of the lever are commensurable. 



In Prop. II, whic!) is totally independent of the first, the 

 demonstration is general, and extends to any proportion 

 between the arms. 



In Prop. Ill, the property is established, when the forces 

 act in an oblique direction, and when the lever is either rec- 

 tilineal, angular, or curvilineal. In the demonstrations 

 'vhich have generally been given of this last proposition, the 

 oblique force has been resolved into two, one ef which i6 di- 

 rected to the fulcrum, while the other is perpendicular to 

 that direction. It is then assumed, that the force directed to 

 the fulcrum has no tendency to disturb the equilibrium, even 

 "though it acts at the extremity of a bent arm ; and hence it is 

 easy to demonstrate, that the remaining force is propor- 

 tional to the perpendicular drawn from the fulcrum to the 

 . line of direction in which the original force was applied. As 

 fiere dfepensed t^£- principle thus assumed, however, is totally inadmissible 

 •viih. ag unintuitive truth, we have attempted to demonstrate the 



proposition without its assistance. 





PT»3p. I, 



Demooiitrated, 



Prop. I. If one arm of a straight lever is any muhiple of the 

 other, a force acting at the extremity of the one will be 

 in eqnilibrio tcith a force acting at the extremity of the 

 other, tvhen these forces are reciprocally proportional to the 

 length of the arms to which they are applied. 



Let AB (PlateVlIIjfig. 1,) be a lever supported on the two 

 fulcra F, /, so that A/— /FzzFB. Then, if two equal 

 weights C, D, of 1 pound each, be suspended from the ex- 

 tremities A, B, they will be in equilibrio, since they act at 

 the end of equal arms A/, BF ; and each of the fulcra jT, F, 

 ^ill support an equal part of the whole weight, or 1 pound. 



Let 



