54 .Statics. 



LG - 

 - 



We remark in passing, that if the height KL of the trapezoicl 

 were infinitely small, and the difference of the two sides AB, CD, 

 were infinitely small, these sides must, be considered as equal, so 



that the distance LG would reduce itself to ^ KL ** AB or 



x, JiJj 



\ KL ; that is, the centre of gravity in this case is equally distant 

 from the two opposite bases. 



Fig. 35. 95. To find the, centre of gravity of the surface of any polygon, 

 we divide it into triangles, and having found the centre of gravi- 



93 - ty of each triangle in the manner above shown, we determine the 

 common centre of gravity of all the triangles, by considering 

 them as so many masses proportional to their surfaces, and con- 

 centrated each at its particular centre of gravity, agreeably to 



86. the method already adopted. 



It will hence be seen how we should proceed in determining 

 the centre of gravity of the surface of any solid figure terminated 

 by plane surfaces. 



96. In fine, it is not always necessary to have recourse to 

 moments in finding the centre of gravity. If it were proposed 

 for example, to determine the centre of gravity of the perimeter 

 Tig 36. f a regular pentagon ABODE, I should draw from the vertex of 

 one of its angles A, to the middle of its opposite side, a straight 

 line AH; likewise from the vertex of another angle E, to the 

 middle of its opposite side, a straight line El, and the intersection 

 G of these lines will be the centre of gravity. 



Indeed the common centre of gravity of the two sides AB, AE, 

 is evidently the middle c, of the line b a, which passes through 

 their middle points. The common centre of gravity of the two 

 sides J5C, DE, is for the same reason the middle of the line IK 

 which passes through their middle points; and the side CD has 

 its centre of gravity in JFJ. Now it is manifest that the line AH 

 passes through the middle points c, e, and H; it accordingly 

 passes through the common centre of gravity of the five sides. 

 It may be shown, in like manner, that IE also passes through the 



