[ io 7 ] 
the nature of each machine feparately in the order I 
have fet them down. 
The lever is faid to be a right line, inflexible and void 
of weight. Its fundamental property is this; when any 
two forces adbagainft each other on the arms of a level, 
they will continue in asquilibrio, if their quantities are 
inverfely as the diftances between the points to which 
they are applied and the point round which the level 
turns, which point is called the fulcrum or prop. 
Several methods havebeen ufed,by different authors, 
to prove, that this property muft neceflarily belong to 
the lever. We find, in the works of Archimedes, a 
proof brought for this purpofe, which has fince been 
made ufe of by feveral writers of mechanics ; who, I 
find, have fomewhats altered the form of his aigu- 
ment, the fubftance of which is generally exprelfed 
as follows. — “ When a cylinder of any uniform 
£{ matter is fupported at its middle point, it will con- 
« tinue at reft; for all the parts on one fide muft ba- 
££ lance thofe on the other, being exadly equal to 
££ them both in weight and fituation, fo that the 
£C whole weight of this cylinder may be looked up- 
£{ on as adding on the middle point on which it is f u P" 
£t ported.” From hence it is inferred, that the weight 
of fuch a cylinder will add upon whatever fuppoits it, 
in the fame manner as it would do if it was all con- 
tracted into the middle point of its axis. If theie oie 
we fuppofe the cylinder to be diftinguifhed into two 
unequal cylinders or fegments, the diftances between 
the middle points of thofe fegments and the middle ot 
the whole cylinder will be inverfely as the lengt s o 
the fegments; that is, inverfely as their weights , but, 
as it was faid above, the weight of each cylinder 
ads in the fame manner as it would do if contrat e 
