ON THE FUNDAMENTAL PROPERTY OF TUE I.EVER. '^81'* 



to obtain a simple and satisfactory demonstration of the fun- petty olfthe 

 damentai property of the lever, the solution of this problem ^'-^'^^'^ 'w^^^ 



. , . ', , ,,.,,, . , , , sati-Mcliorilv 



gjven t>y Arcniniedes should still be considered as the raost demoni trated. 

 legitimate and elementary. Galileo, Huygens, De la Hire, ^tjg„^,,^ j^ 

 Sir Isaac Newton, Maclaurin, Landen, and Hamilton, have 

 directed their attention to this important part of mechanics; 

 but their demonstratio'ns are in general either tedious or ab- 

 struse, or founded on assumptions too arbitrary to be recog- 

 nised as a proper bai? for mathematical reasoning. Even 

 the demonstration given by Archimedes is not free from ob- ArcHimedes, 

 jections, and is apj.licable only to the lever considered as 

 a physical body. Galileo, though hi3 demonstration is su- GaUi«o 

 perior in point of simplicity to that of Archimedes, resorts 

 to the inelegant contrivance of suspending a solid prism 

 frmn a mathematical lever, and of dividing the prism into 

 two unequal parts, v/hich act as the povver and the weight. 

 The demonstration given by Huygens assumes as an axiom, Huyjcns, 

 that a given weight, removed from the fulcrum, has a great-". 

 er tendency to turn the lever round its centre of motion; ' 

 and is, besides, applicable only to a commensurable pro- 

 portion of the arms. The foundation of Sir Isaac Newton's Sir I, Newton, 

 demonstration is still more inadmissible. He assumes, that, 

 if a given power act in any direction upon a lever, and if 

 lines be drawn from the fulcrum to the line of direction, the 

 mechanical effort qf the power will be the same when it is 

 applied to the extremity of any of these lines; but it is ob- 

 vious, that this axiom is as difficult to be proved, as the pro- 

 perty of the lever itself. Mr, De la Hire has given a de-OelaHire 

 monstration which is remarkable for its want of elegance. 

 He employs the reductio ad absurdum, and thus deduces the 

 proposition from the case where the arms are commensura- 

 ble. The demonstration giyen by Maclaurin has been high- Maclauirln, 

 ly praised ; but if it does not involve a petitio prmcipii, it 

 has at least the radical defect of extending only to a com- 

 mensurable proportion of the arms. The solutions of Lan- I.anden, and 

 den and Hamilton are peculiarly long and complicated, and ^"^"'*>"' 

 resemble more the demonstration of some of the abstrusest 

 points of mechanics, than of one of its simplest and most 

 elementary truths. 



In attempting to give a new demonstration of the funda- A newdemon- 



inental 



